Tide Questions or Arguments

Packo's prediction for the slack water times at Port Phillip Heads.

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Tide Questions or Arguments

Postby packo » Sat, 24 Mar 2018 2:26 pm

Post any questions or other tide arguments/discussions in this thread.



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newman
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Re: Tide Questions or Arguments (None posted yet!)

Postby newman » Tue, 11 Feb 2020 1:23 pm

Hi Packo. I'm new to this forum and am very pleased to have stumbled across this huge repository of local knowledge about tides in the bay. Really great stuff. With a physics background myself, I see a lot of merit in your points about how the tides actually work vs the accepted conventional widsom. For example, it makes perfect sense that the tide can fall in some locations when there is still an incoming tidal stream, and also that the times of maximum or zero water level difference only directly correlate to maximum or zero *acceleration* of the tidal stream rather than maximum or zero *velocity* of the tidal stream.

However, I find some of your explanations a bit hard to follow. For example, in 'Understanding Tides and Streams in the Bay', you write:

'Note the fainter orange lines that divide the "choke zone" region into three parts. The water level difference across the whole zone when a strong tidal stream is flowing divides itself roughly equally across these three parts with around a 40cm drop across each part. Of course the drop across the thinner Rip section gives the highest water surface gradient and the tidal currents there may reach 6 knots. In the middle section the gradient is milder and the tidal currents range from 4 knots down to about 2 knots. In the Great Sands region the gradient is slightly milder again but the much shallower water restricts the speed of the currents to 1.5 to 1.0 knots across the sands. Tidal streams in the channels may run a little faster at up to 2 knots'

If I'm reading this correctly you're not referring to the gradients in the isobaths on the chart, you're simply saying that an incoming 'bulge' of water will produce a tidal current in direct proportion to the water level difference that this creates, and because the height of this 'bulge'/'anomaly' is spread out evenly over the different channels (reduced), that the current speeds in the different channels are therefore reduced in proportion (with friction in the very shallow water perhaps playing a role) ?

A little later you write:
'In summary the effect of the "choke zone" is to reduce the range of the tide in the "main body" zone to around 40% of the tide range in Bass Strait. In doing this the main body tides are also delayed by around three hours behind the high and low tides just outside in Bass Strait.'

Not that I necessarily doubt that conclusion, but I can't see how that summary follows on from anything that was written earlier, which pertains mostly to horizontal current speeds. Maybe the connection could be more explicit, or maybe it's found in the many paragraphs that follow (which are difficult to wade through!).

There are many more things I could ask you about but I'll start with these!

Cheers.



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Re: Tide Questions or Arguments

Postby packo » Wed, 12 Feb 2020 9:16 pm

Hi newman, welcome to the forum!

Great to finally get some questions! (In the old dive-Oz forum days there were quite a few questioners - but on this forum you are the first in over 2 years!). BTW interested to know if you are a diver or sailor in this region, or just have a curiosity interest in Port Phillip Heads.

newman wrote:
Hi Packo. I'm new to this forum and am very pleased to have stumbled across this huge repository of local knowledge about tides in the bay. Really great stuff. With a physics background myself, I see a lot of merit in your points about how the tides actually work vs the accepted conventional wisdom.

Thanks for that. I'm a rusty old physicist myself and it does seem to help see silliness more easily where it exists. There is in fact no wisdom at all in the "conventional wisdom" about the Bay.

It is hard to say exactly how this came about but maybe it was just imported understanding from smaller bays & harbours where the momentum/inertia effects are much, much smaller. For example in Sydney Harbour the water mass transport through those Heads is about 40 times smaller and with peak velocities about 8 times smaller. The injected momentum in this case is a few hundred times less. The shape and bathymetry of the Bay are also quite different from just about any other Bay or estuary.

newman also wrote:
For example, it makes perfect sense that the tide can fall in some locations when there is still an incoming tidal stream,. . .

Good! That's the key point. Basically the Bay has two distinct regions in which the tides behave quite differently. The vast central/northern region has tides that are roughly uniform in size and timing. The dominant component (up to 5.4 knots) of the total current through the Heads is due to the rising and falling tides in this very large region.

The so called "choke zone" from the northern edge of the Great Sands through to the Rip is only about 1/7th the surface area. Although the tide range is a little bigger there, the fact that the tide timings here are not all in sync, (there is about a progressive 3 hr tidal phase delay across this region), means the Heads current component attributable to the rising and falling tides in this region is much smaller at only about a tenth of the max Heads current (ie. up to ~ 0.6 knots).

This is why the timing of slack water is pretty much the same (within 12 minutes on average) across the "choke zone" and is not delayed by 3hrs like the tides are. Unfortunately a number of dive shops, and dive clubs, and DIVA members still promote the 3hr slack delay myth. I've had to give up trying to fix this as it all got too nasty (on both sides!). Sadly we might have to await a drowning and subsequent coroner's inquiry for a final fix.

newman also wrote:
.. and also that the times of maximum or zero water level difference only directly correlate to maximum or zero *acceleration* of the tidal stream rather than maximum or zero *velocity* of the tidal stream.

Hmm! Things might have accidentally got a little arse-about here, but the key point is that both the velocity and acceleration of the water are important and each requires some portion of the driving force to maintain them. The troubling "conventional [un]wisdom" spouted by so many Port Phillip players is that only frictional resistance forces due to the water's velocity need to be overcome by the driving force. [If you listen carefully you might just hear Isaac Newton turning over in his grave.]

The water level difference between the ocean and the Bay's "main body" provides the "driving force" for the system. In the early stages of the flood stream both levels are rising, but because the ocean is rising fast (~ 40cm/hr), and the Bay hardly at all yet because the inflow is still weak, the driving force is growing strongly in the inward direction.

This does two things: 1) Accelerate (all) the water inside and entering the Bay. 2) Overcome the frictional resistance that arises when water is moved across the bottom and around reefs etc. This "bottom friction" grows rapidly with speed, roughly as the square of the speed.

Early on, because the bottom friction is initially low, task 2) requires only a minor part of the total driving force leaving plenty left over for task 1) ie. accelerating the water. As the speed increases so does the share of the total driving force necessary to overcome bottom friction. Thus the water speed will accelerate less quickly than previously.

At around 50 minutes before high tide at Pt Lonsdale, the initial high ocean rise rate of ~40cm/hr has dropped to around ~14cm/hr. This matches the Bay's main body rise rate at this time and so the level difference and driving force reach a peak at this time. They will then start to decline. However there is enough force to overcome the frictional resistance at that water speed and yet still have some left over for a little bit more acceleration.

At around the Pt Lonsdale high tide time (just by coincidence) the now declining driving force is completely consumed in overcoming the frictional resistance of the now slightly faster water. We have reached the maximum water velocity point with no more acceleration possible. From this point onward the frictional resistance exceeds the declining driving force and so the tidal stream begins its deceleration phase.

During this deceleration phase we have a higher but decreasing ocean level, and a lower but still increasing "main body" level. When do the levels "cross-over" to give a zero and then a growing reverse level difference?

Analysis of the appropriate tide curves shows that typically the brief "equal levels" point occurs a little over 2 hours after high tide at Point Lonsdale, with a range from 1.5 to 2.5 hrs depending on the particular tidal cycle. This is well before the slack water time by around 40 minutes.

So the fairly unique thing about Port Phillip is that the stored momentum within the Bay's waters from a flood stream is so large that frictional resistance forces during the deceleration phase cannot dissipate it all by the time the zero level difference point is reached. There is an additional roughly 40 minutes of inward (now uphill) flow before the combination of the dwindling friction force and the growing "reverse drive force" can finally bring the tidal flow to a halt.

To summarise this waffle in terms of newman's point: Maximum stream velocity (and zero acceleration) is attained about 40-50 minutes after the maximum level difference time, and zero stream velocity (and maximum -ve acceleration) is attained about 40-50 minutes after the zero level difference time.

newman also wrote:
However, I find some of your explanations a bit hard to follow. For example, in 'Understanding Tides and Streams in the Bay', you write:

'Note the fainter orange lines that divide the "choke zone" region into three parts. The water level difference across the whole zone when a strong tidal stream is flowing divides itself roughly equally across these three parts with around a 40cm drop across each part. Of course the drop across the thinner Rip section gives the highest water surface gradient and the tidal currents there may reach 6 knots. In the middle section the gradient is milder and the tidal currents range from 4 knots down to about 2 knots. In the Great Sands region the gradient is slightly milder again but the much shallower water restricts the speed of the currents to 1.5 to 1.0 knots across the sands. Tidal streams in the channels may run a little faster at up to 2 knots'

If I'm reading this correctly you're not referring to the gradients in the isobaths on the chart, . . .

Yes correct. I am talking strictly about slopes or gradients in the surface of the water - nothing to do with the profile or slope of the seabed underneath. I see now the potential for that confusion because it so happens by an unrelated coincidence that seabed slopes just happen to be big where the surface slopes are big and small where the surface slopes are small. (Note that just north of the sands the seabed slope drops quite suddenly but the water surface slope is always tiny in that area. It is all just an unfortunate coincidence that I didn't pick up at the time of writing.

newman also wrote:
. . you're simply saying that an incoming 'bulge' of water will produce a tidal current in direct proportion to the water level difference that this creates. .

Yes(ish), but its not quite that simple. Dropping the the word "direct" would make it pretty close though. While the forces produced near the bulge will produce a tidal current away from the bulge, it won't be in direct proportion to the water level differences. The water will slowly accelerate to its "terminal speed" where the driving force due to the slope in its surface just matches the opposing bottom friction.

Since bottom friction rises rapidly with speed the (terminal speed) current isn't directly proportional to the level difference but rises more slowly. For example the max Heads flow for a weak flood stream is about 2 knots and requires the ocean to be only around 20cm higher than the mid bay region. However to achieve a 4 knot max flood stream requires an ocean level around 70cm higher than mid bay. A 6 knot flood stream requires around a 130cm level difference.

The above also relates only to "steady state" flow and applies only to times when the water velocity at each point is hardly changing with time. As an example where both friction and acceleration forces are simultaneously in play I've looked at my modelling for a flood tide that peaked at 5.6 knots. I've then looked at the water level difference at the 3.0 knot point before the peak (ie. in the accelerating phase), and then at the 3.0 knot point during the decelerating phase after the peak.

In the first (accelerating) case the 3 knot inflow needed an ocean level 79cm higher than mid-bay to drive it. In the second (decelerating) case the 3 knot inflow needed only a 13cm level difference to drive it. Note that a steady state 3 knot inflow requires around a 35cm level difference to maintain it. So the velocity of the current does not depend only on level difference, but is also strongly dependent on whether the current is gaining or losing speed.

All this shows that even well away from slack water the inertia and momentum effects of the water being moved about are very significant and cannot be ignored. This is why the official line is so unhelpful in getting a better (and safer) understanding of what is going on.

newman also wrote:
A little later you write:
'In summary the effect of the "choke zone" is to reduce the range of the tide in the "main body" zone to around 40% of the tide range in Bass Strait. In doing this the main body tides are also delayed by around three hours behind the high and low tides just outside in Bass Strait.'

Not that I necessarily doubt that conclusion, but I can't see how that summary follows on from anything that was written earlier, which pertains mostly to horizontal current speeds.

You are right! I have used the words "In summary" inappropriately here. It was not intended to be "a summary" of the previous points, but rather a summary of lots of observed tidal data. So it is not a conclusion to muse about but a summary of facts. I have now adjusted the original wording to correctly reflect what is being summarised.

The only other points I should add here which do relate a bit to our discussion are that:
1) because tidal cycles vary considerably in range and stream strength
and
2) because friction rises rapidly with stream velocity, the momentum/friction ratio differs considerably across various tides.

It is hard to talk about "typical" tide behaviour because of the large behaviour variations produced by different momentum/friction ratios. That is why there are lots of "around" words in the discussion. For example the summary referred to above says the "main body" tidal range "is around" 40% of the outside tidal range. In more detail, the very weakest tides with significantly lower friction levels achieve an inside range of nearly 60% of the outside range, whereas for strong tides this figure may only be 30%. For average strength tides a "typical" inside to outside ratio is approx 40%.

Effectively the much increased friction associated with fast tides significantly decreases the "filling efficiency" of the Bay although of course the numerical inside range is still larger than for weaker tides. Other stream properties will also vary a lot for differing momentum/friction ratios.

As far as the 3hr tide delay is concerned, most tide gurus would explain this by saying the tide behaviour is "progressive" near the entrance before transitioning into a "standing wave" type behaviour in the main body of the Bay. The characteristic of a progressive type tidal regime is "current in phase with height" (ie. slack around mid-tide), whereas the characteristic of standing wave tidal regimes is "currents 90 degrees out of phase with height" (ie. slack around hi/lo tide). We see both types of behaviour in the one Bay because of the high resistance of the "choke zone" and the much lower resistance of the relatively deeper "central basin".

The upshot of this is that the moment of high or low tide creeps across the "choke zone" at roughly 10 mins per kilometre (6 kph), but then accelerates to over 150 kph for the rest of the distance up the Bay. The speed of the slack water point is on average around 80 kph across the "choke zone". So no, despite some folk claiming otherwise, you can't do a true slack water dive at the Heads, and then use a fast boat to "catch up" to true slack water again at say Rosebud.

All this makes the Bay a bit mysterious and difficult to understand. It is then made more so by "Packo" jumping up and down and saying:- "Hey just about everybody, you've forgotten to include acceleration/deceleration forces which alters things significantly away from the official line and highlights some safety concerns."

I'm hoping the official line might eventually be changed. Sorry if the posts are hard work to get through at times. Just remember that in Mother Nature's realm, a tidal stream can, and does, (and should!), flow uphill for a time near the end of its run provided the right circumstances exist.

Some folk find that kinda hard to accept but these same people don't bat an eyelid when a kid at a skate park rolls up the far side of the half-pipe and makes it all the way to the top. It might appear to be a 100% height rebound it that very low friction environment but they cheat a little by standing tall before beginning the down slope and crouch down low when approaching the top of the up slope. Maybe its only a 95% centre of mass rebound.

Perhaps if the kid were to increase his rolling friction a bit, say by dragging his schoolbag behind the skateboard, he may only do a 30% height rebound. He would then suffer a brief "slack water" moment part way up the slope before then rolling backwards down the slope. Although the situation is physically quite different to water at the Heads rolling back and forth between oscillating and out of phase ocean and bay levels, the physics and outcome are somewhat similar.

cheers,
packo



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Re: Tide Questions or Arguments

Postby newman » Thu, 13 Feb 2020 3:29 pm

Thanks for the in-depth reply, Packo.

BTW interested to know if you are a diver or sailor in this region, or just have a curiosity interest in Port Phillip Heads.


Diver, altough my interest in this topic mostly stems from scientific curiosity. I've been diving fairly infrequently over the last 12 years - around 90 dives in total and probably only 10 of those in the Bay. I'm a scientist though, and while I don't work on tides, lets just say that I work in the general field. So we might risk cluttering up this thread with physics; if I think it's getting out of hand I might just PM you instead.

Things might have accidentally got a little arse-about here, but the key point is that both the velocity and acceleration of the water are important and each requires some portion of the driving force to maintain them


I don't think there's any misunderstanding here, I was simply pointing out that a simple 'force is proportional to acceleration and not necessarily velocity' perspective goes a long way in understanding things. Although of course things get a bit more complicated when considering the role of friction and the extent to which the flow is steady state.

Effectively the much increased friction associated with fast tides significantly decreases the "filling efficiency" of the Bay


Ah, this is the connection I was after for the why the tidal range is reduced compared to the ocean. Frictional dissipation leads to less potential energy, makes sense.

As far as the 3hr tide delay is concerned, most tide gurus would explain this by saying the tide behaviour is "progressive" near the entrance before transitioning into a "standing wave" type behaviour in the main body of the Bay. The characteristic of a progressive type tidal regime is "current in phase with height" (ie. slack around mid-tide), whereas the characteristic of standing wave tidal regimes is "currents 90 degrees out of phase with height" (ie. slack around hi/lo tide). We see both types of behaviour in the one Bay because of the high resistance of the "choke zone" and the much lower resistance of the relatively deeper "central basin".


Thanks, I think this explains a lot (if true!). I'm wondering how the following speeds come about, though:

The upshot of this is that the moment of high or low tide creeps across the "choke zone" at roughly 10 mins per kilometre (6 kph), but then accelerates to over 150 kph for the rest of the distance up the Bay. The speed of the slack water point is on average around 80 kph across the "choke zone"


The shallow water wave phase speed for the main zone of the bay, assuming depth=25m, is ~sqrt(9.8*25) ~16m/s ~ 60 kph. Perhaps the tide here is moving with a speed much closer to what the 'equilibrium tide' would have (i.e. the theoretical and highly idealised 'tidal bulge' that zooms around the earth as the earth rotates). Do you have any insight there? Or perhaps you've figured this out empirically, based on the length scale of the Bay and short tidal delays of ~15 minutes that you mention?

EDIT: I suppose the tide probably exhibits some degree of *non-linear* wave behaviour, especially in the choke-zone, and this would presumably have implications for the propagation speed of the tide.



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Re: Tide Questions or Arguments

Postby packo » Tue, 03 Mar 2020 5:48 pm

***** Apology *****
Hi newman,
Very sorry about the many days delay in replying to your post but I have been a little busy. I hope you do manage to revisit this thread again some time to see the much delayed reply to your 2nd Post.

Mixed among the usual time consuming domestic chores were a number of days in the field doing current measurements. There were further delays when I thought I could present some of results in this reply but I have had trouble generating position and velocity plots of my GPS current tracker in jpeg format suitable for posting here.

Also some of your questions are pushing me to the limits of my understanding and required some extra research. As well my posts can take quite a while to write. Let's just say they are "comprehensive" in nature!

In the end I decided to give up trying including those results here although they were pleasingly supportive of the "Packo tables" over the BoM slack water predictions. I'll try and get my ducks all lined up for the April-June Packo table update due in a few weeks. So I've now reedited my reply down just to get it out without further delay. (there is is one mention of a night time observation but I have left that in.)

***** PMs *****
I would rather avoid a PM (Private Message) discussion because that requires a login and hence a lower checking frequency. PM's are for sending me such things as your "best ever dive site" GPS marks. PMs are not for shielding other readers from a bit of physics! It is a forum where info and ideas are presented on a take-it-or-leave-it basis. Believe me, if a reader isn't particularly interested they'll move on very smartly!

However some may stay and have a good read and think about what is being said. That's why you can't judge the merit of any post by the number of views. They could be very fleeting (or even accidental), or represent something more appreciated. As for the "physics content", well I try only to use physics to help explain something I have actually observed or measured, rather than predicting what I might expect to see based on pure theory.

My aim in posting is to try to pass on something useful while strenuously trying to avoid any unintended harm. There is enough of that already floating abound on the web. So it is a bit like a medical doctors oath: Try to avoid killing the patient at all costs and if they gain any relief, then that is a nice side benefit.

***** Back to newsman's 2nd post *****
Regarding my "arse-about" comment, you wrote:
I don't think there's any misunderstanding here . . .


Ok, I re-read that passage. .
. . . maximum or zero water level difference only directly correlate to maximum or zero *acceleration* of the tidal stream . . .

multiple times to try and clarify the intended context.

Still not quite sure, but I first thought you were referring to PPB tidal streams in which friction dominates over momentum (but where the later can't be completely ignored). On that basis I thought the second "maximum or zero" should be "zero or maximum" (ie. "arse-about"). On the other hand you might have been referring to "non-PPB" tidal behaviour.

To avoid confusion among other readers lets just separate out the two extremes of tidal regimes, although most real bays won't be entirely one or the other.

1) High friction near entrance (narrow, shallow, or both) / High speed but low mass inflow & outflows:
---> Tidal Current at entrance driven predominately by large level differences around high/low tide in ocean.
---> & Slack around the zero level difference time usually a little before ocean mid-tide.

2) Entrance open & deep / low speed but moderate mass inflows & outflows:
---> Tidal current at entrance driven predominately by ocean rise or fall rate so is strongest near mid-tide time in the ocean.
---> & Slack around high/low ocean tide where outside level is not changing.

PPB is closer to 1) in behaviour EXCEPT that its moderate entrance size and ENORMOUSLY wide bay allows high speed and high mass inflows & outflows of up to 300gL/hr. Peak entrance flows are around 80,000 tonnes per SECOND, at peak speeds around 10 kph. These fast and very high mass flows allow significant residual momentum to develop within the Bay. This delays slack water to 40-50 minutes after zero level difference ("momentum effect") and delays max current to 40-50 minutes after max level difference ("inertia effect").

In a sense the "main body" of PPB can be considered separately as a "bay within a bay", having its own wide entrance as "open and deep" being located along the northern boundary of the Great Sands. The "entrance" to this bay within a bay stretches along a 27km line roughly from St Leonards across to Rosebud with depths around 20m. Its "outside tide" is then that occurring across the northern edge of the Great Sands. This is the 3 hr delayed and 40% smaller remains of the ocean tide after the "choke zone" has done its work.

As such, this "bay within a bay" behaves very much like the second type of tidal regime where the tidal currents are strongest around its mid-tide time, and its slack water occurs close to high or low tide in its own waters. Note the slack water time is still in close sync with the waters to the south, but the tide delay has converted the characteristics into the type 2) behaviour.

However note this fantasy "bay within a bay" has an extremely wide and open entrance, about 20 times the cross section of the Rip. Its maximum entrance tidal flow speed is low at around just 0.25 knots. These low speeds, but operating over a very large cross-section, are sufficient to supply or remove water at the rate required by the rising or falling tides over all areas up to Melbourne and around to Geelong.

It is the central Bay's width and depth that mean it exhibits very low frictional resistance to flow. Hence the water surface slope to overcome this friction is tiny in comparison to the slopes across the choke zone. Note however that there are still momentum issues to be dealt with and so to decelerate and reverse these tidal flows the north end of the Bay also develops its own reverse slope. It is small in size (~4cm, or roughly 1/10th of that at the Heads) because the huge sweep of the northern shoreline means even a small reverse level difference can generate the required reverse force to stop and reverse the flow.

This effect results in the tidal range at Williamstown and Geelong being around 8 to 10cm larger than in the centre of the bay despite them both being much further from the ocean. This is generally known as "tidal peaking". While the port authorities are perfectly familiar with "tidal peaking" at the closed ends of bays and harbours, they seem reluctant to accept that this also occurs near our Heads.

You don't have to block a tidal flow with solid land to witness reverse levels and "peaking". Even a physical opening to the ocean can also be an effective block against outflow once the outside level rises high enough, or a block against inflow once the outside level falls low enough.

Ok my "waffle alert" has sounded again so back to newsman's post.

In response to my words:
The upshot of this is that the moment of high or low tide creeps across the "choke zone" at roughly 10 mins per kilometre (6 kph), but then accelerates to over 150 kph for the rest of the distance up the Bay. The speed of the slack water point is on average around 80 kph across the "choke zone".


newman wrote:
I'm wondering how the .. speeds come about, though:


and then wrote:
The shallow water wave phase speed for the main zone of the bay, assuming depth=25m, is ~sqrt(9.8*25) ~16m/s ~ 60 kph. Perhaps the tide here is moving with a speed much closer to what the 'equilibrium tide' would have (i.e. the theoretical and highly idealised 'tidal bulge' that zooms around the earth as the earth rotates). Do you have any insight there? Or perhaps you've figured this out empirically, based on the length scale of the Bay and short tidal delays of ~15 minutes that you mention?


From memory your formula for wave speed is ok, but perhaps the assumption of a 25m average depth is rather too generous. Something a tad under 20m would seem more appropriate, giving about a 50kph speed. The length of the "main body" from Williamstown to Hovell Pile is about 52km. There is evidence that sudden weather changes in the south can induce a "Harbour seiche" which is a north-south sloshing (oscillation) as the disturbance runs up and down the Bay.

Somewhere (damn - I can't find now!) I did have tide plots of such an event where the "crests and troughs" of this disturbance are superimposed on the more slowly changing tide heights. Two or three cycles of these small peaks are clearly visible in both the Williamstown and Hovell pile graphs - and they are exactly 180 degrees out of phase. This indicates the disturbance has travelled up and down the Bay a few times before dying out. The round trip is about 104km and the period of the disturbance is about 2 hrs, indicating a travel speed of around 50kph.

I found in the literature that a frequency domain analyses of long period waves in PPB did indicate support for a natural oscillation with a period of around 124 minutes. I have also seen reports of some old and unusual observations of the water level at Williamstown where on a slowly rising tide the observer saw the level suddenly begin rising much faster for about 30 minutes before dropping again for the next 30 minutes and then later to start rising again. I also recall that some years ago I wangled a 1hr pro bono discussion with a coastal engineer. When he saw my plots containing those oscillations he got rather excited and started doing some "back of the envelope" calculations of wave speeds.

***** However. . . *****
However I believe that the progression of the high or low tide points and the shallow water wave speeds in the Bay are not the same thing!

When you model the Bay as a 50km long 20m deep "trough" with hard ends, then "low water" at each end has a special meaning. It is the time when the water stops moving away from that end and begins to approach it again in the reverse direction. The time from "low water" at one end to "low water" at the other (approx. 1hr) represents a full cycle of the water currents associated with that wave from "zero to zero".

However "low water" at the southern end of the real "main body" of the Bay does not have this special meaning because it is not a "hard end". The "low tide moment" there means only that the rate of southbound water draining away towards the Rip has decreased to a point where it matches the rate of southbound water arriving from Melbourne. This gives a momentary steady water level because there is no more net loss of water at that particular location. Any further decrease in the rate on the Rip side means a net gain at the location and the tide level starts to rise again even though the stream direction remains at south(west)ward.

Tide tables show that low water at either Hovell Pile of the West Channel Pile occurs just a small number of minutes before ebb slack water at the Heads. That is when there is still a small amount of southbound water moving across the Bay's "main body". So the time taken for the "low tide moment" to propagate up the Bay's main body is not really a full cycle of anything. Instead it just represents the time required to fully stop the last part of the southward water movement in the main body. Effectively it is the stream's "deceleration time".

For weak tidal flows this may require only a few minutes leading to very high perceived "propagation speeds" (ie. >150kph). On days of stronger flowing tidal streams the "momentum mop-up" may require a few tens of minutes giving lower "propagation speeds" eg. 40-50 km in 30 minutes, or 80-100kph).

The ebb stream on the night Feb 13th was reasonably strong. The low tide at West Channel Pile was around 00:57am on the 14th, a little before the slack I observed around 1:06am. The low tide did not reach Williamstown until 1:30am - a 33 minute delay. This gives a slow "progression speed" of around 70kph.

Around a week later with weaker tides, the predicted low tide delay between south and north was only 7 minutes. This bumps the effective "progression speed" to over 300kph. While the residual water momentum still in the main body at the time of high or low tide at its southern end is an important factor in the delay time, so is the way the tide actually "sloshes around the Bay". On some rare days with extremely weak tides, the high or low tide moment is almost simultaneous in both the north and south of the Bay's main body.

***** Summary *****
While the progress of tides along various parts of the Australian coast might usefully be studied in terms of wave behaviour and propagation speeds, attempts to continue this up through Port Phillip Bay are not very enlightening. In the south of the Bay the fact that the main set of the tidal streams is along the shorelines, rather than perpendicular to them, means the "high tide" and "low tide" points do not mark any special phase of the tidal stream as they otherwise might do. Instead they just mark the rather meaningless times when the current flowing past a particular point is exactly as strong on the up-current side of that point as it is on the down-current side.

While the resultant change in "tide progression" might be interesting, crawling at 6kph through the choke zone yet zipping along at 70-300kph in the main body, there is generally far too much attention paid to tide heights in the south of the Bay. Unless you are at a boat ramp near low tide, or own a deep keel yacht, a knowledge of high or low tide times doesn't inform you much.

Of much greater importance is a knowledge of the strength and direction of the tidal stream, as well as its reversal time and reversal rate. This information will help keep most water sports folk much safer. Plenty of divers, sailors, and boaters have got themselves into trouble by paying too much attention to tide heights and insufficient attention to tide streams.

***** A Different Viewpoint *****
A more useful view of things is that when the time varying Bass Strait water levels meet the Heads, they are converted into time varying tidal currents that flow into and out of the Bay. It is the way these tidal streams accelerate and decelerate in various parts of the Bay that dictate when and where certain activities are possible. The growth and decay of these currents also produce high and low tide moments at different times for the different locations, but as mentioned earlier those times don't really have a particularly relevant meaning to many water based activities and mostly its all about the streams.

In the transformation of Bass Strait water levels into tidal currents it is important not to make the mistake of thinking there are only two factors involved ie, water level difference and water flow friction. That is the mistake that officialdom makes in its Heads advice. There are in fact four forces involved:-

1). The Driving Force: The height difference between the inside and outside levels creates a horizontal pressure differential across the choke zone. In turn this creates a horizontal force that attempts to drive the water either inwards or outwards. The slope in the water surface at the Heads needed just to overcome water friction is of order 20cm/km at 6 knots, decreasing to around 8cm/km at 2 knots.

2). Flow Resistance Force In a tidal stream the water is moving fastest at the surface with the speed decreasing with depth to theoretically zero in the nooks, crannies, and sand grains of the sea floor. The profile and dimensions of this boundary layer depend somewhat of the roughness of the bottom but in all cases we have layers of different speed water sliding over one another.

The frictional forces from this process are directed back in the opposite direction to the flow direction. At higher speeds the flow will also become turbulent and somewhat chaotic with eddies whirlpools and overfalls. All of these increase the friction levels and increase the flow resistance. This resistance does not increase linearly with the average stream speed but at a faster rate.

3). Acceleration/Deceleration Force A fundamental law of Physics is that changing the speed and/or direction of a body with mass "M" requires that a force "F" be applied. The resultant acceleration (or deceleration) "a" is then given by the formula: a = F/M where acceleration "a" is in metres per second per second, mass "M" in Kg, and force "F" in Newtons. (As a rough indication it requires around 3 Newton of force to lift up a paper cup of coffee.)

Now the current reversal rates seen at the Heads are just a tiny fraction of 1m/sec/sec. The "Packo tables" express these in more easily interpretable units of "knots per 10minutes", with the highest values around 0.64 knots/10mins. This converts to roughly 1.2 kph/10mins, or 1200 m/hr/10mins, or 0.33 m/sec/10mins, or 0.33 m/sec/600sec, or 0.0005 m/sec/sec.

From this acceleration rate it is a fairly simple task to calculate that to achieve this rate of change in the current at slack water, the water surface at the Heads needs a reverse slope to the tune of 5.6 cm of extra height per kilometre of water distance.

At the northern end of the choke zone the current speed, and hence acceleration rates, are about 1/4 of those at the Heads. We can then estimate the average water slope over the whole choke zone is roughly (5.6 + 5.6/4)/2 = 3.5 cm/km. To get the very strong flood streams to reverse at slack water at the rate they do, we need a reverse level difference across the ~12km wide choke zone of roughly 3.5 cm/km x 12km = 42cm. This is borne out by the difference in the tide plots.

Leading up to these very rapidly reversing flood slacks, the ocean level is dropping at around 55cm/hr with the main body level rising at around 4cm/hr. The growth of the level difference is then around 59cm/hour. This explains why inward flow continues for some 40 minutes after the equal levels moment because that is the time needed to achieve the 42cm reverse height difference necessary to provide the calculated deceleration rate at the time the flow stops.

4). Kinetic Energy Forces This is the trickiest of the four terms and not very well understood by me. Moving water has kinetic energy associated with its velocity. If a section of the tidal channel has a change of cross-section, then the velocity of flow will be different to that prior to the expansion or contraction of the channel and so the level of kinetic energy will be changed. This requires either a forward or reverse force to achieve depending on how the channel cross-section changes.

Normally the measure of kinetic energy in flowing water is expressed as its "Velocity Head" or "Dynamic Head". This the extra height above the normal water surface that the water could attain if all its kinetic energy could be converted into potential energy. This can be measured by inserting a Pitot tube into the flow.

This is a tube with a "L" bend in the lower part which is pointed upstream into the flow. The stagnation pressure at the submerged mouth of the tube supports a column of liquid that extends above the free surface. This extra height or velocity head is then a measure of the kinetic energy of the main flow of the stream. This head rises as the square of the flow speed. At 6 knots it is equal to around 45cm, and at 1 knot only 1.2cm.

We experience "velocity head" as an elevated patch of water at the point of a boat's bow when it is making way. In the case of a fixed object and moving water we might observe the small water elevation on the up-current side of a south channel pylon when the tide is running at a couple of knots.

How this term fits into predicting the current through the Heads I am not at all sure about. On the one hand from out in Bass Strait we have a sudden constriction to a 3km gap at the Heads followed by an expansion out to 27km or so wide at the north end of the choke zone. Do these two changes more or less "cancel out" the velocity head term? Or is this woolly thinking because there are no real "walls" of constriction outside the Heads?

Iv'e tried some further reading to try to clarify things but it only seems to complicate things because many hydrodynamics texts suggest velocity head effects can be in either direction depending if the flow is laminar or turbulent. (presumably we get a bit of both at various times in the tidal stream cycle.)

My work arounds are:

a) At the low water speeds I am interested in around slack water, velocity head variations across the choke zone are so small they can be ignored.

b) At higher water speeds I simply lump 2) and 4) together to give a combined friction & velocity head term.

Helpful input from anyone else on this issue would be good!


***** WATER HAMMER *****
In the early parts of my work I struggled, probably like some of you readers, to comprehend how such slowly moving water near the end of a tidal stream could possibly perform such feats as climbing uphill to a height of 40cm or so above its own level. To help others in this regard I wish to discuss the "water hammer effect" as perhaps the closest everyday example of the relevant physics in action. Hopefully the modern day prevalence of plastic domestic plumbing (slightly elastic) has not diminished the experience of "water hammer" too much.

In houses with rigid metal plumbing, "water hammer" was noticeable where the was a long run of piping with a tap at the end. With the tap wide open the water flows strongly along the pipe where there might be say 0.5kg of water in the pipe moving at say a few knots. This has a certain amount of momentum (mass x velocity).

If the tap is closed quickly the water mass tends to keep flowing, but now into the "dead end" of the closed pipe. A large pressure spike then develops sounding rather like someone has hit the pipe with a hammer. It is this spike in pressure acting back along the pipe that actually provides the force needed to suddenly decelerate the water. The quicker the tap closes the higher the pressure spike.

It is also possible to have "negative water hammer" where the long run of pipe comes downstream of the tap. In that case a negative (low) pressure spike occurs just downstream of the closing tap. In severe cases the negative pressure spike (ie. a partial vacuum) might be intense enough so some water turns into a vapour bubble. This can cause noise and cavitation when it collapses shortly after.

While both forms of water hammer are just a nuisance in the domestic setting, in larger piping systems such as hydroelectric power stations, these effects must be taken very seriously and the opening and closing of the control valves is done with much care. Failure to do this can (and has) either exploded millions of dollars worth of the high pressure piping leading down from the storage pond to the turbine room, or vacuum crushing the pipework or other infrastructure on the downstream side between the turbine room and the river discharge point.

***** The Hydraulic Ram Pump *****
My own introduction to the impressive power of controlled "water hammer" was as a young kid playing the the deep fern gullies behind the village of Sassafras in the Dandenong ranges east of Melbourne. We are talking way back in the late 1950s when many rural towns didn't have a mains water supply.

Householders lucky enough to sit alongside the gully had a small creek with a reliable flow, but the bottom of the gully was perhaps 40m below their homes. While farmers along the creek used electric pumps to extract their larger water demands, this wasn't an option for an ordinary home owner because of the expense of getting power down into the gully and also the safety factor given that much of it was public land on which naughty little boys like me might play.

Enter the "Hydraulic Ram Pump"! A genius invention that was robust, had only 2 moving parts, was self powering, flood proof, and mostly "curious little boy proof".

A simple small weir was built across the creek and from it water would be guided through a downward sloping stout metal pipe of about 2m in length and into "the contraption". One of the moving parts was a spring loaded valve at the end of the supply pipe. That valve opened inwards into the pipe, but could be kept open by the force of the spring. Water would thus exit past the valve creating a sort of mini fountain, after which it fell back into the downhill section of the creek.

By careful adjustment of the compression spring, you could make it so that when the "water fountain" flow grew strong enough, the force of water escaping past the valve would overpower the spring and snap the valve closed with a loud "clack". This sound was due to the large water hammer pressure spike that developed as the momentum of the few Kgs of water in the supply pipe suddenly crashed into the end of the now closed off pipe.

The second moving part was a one-way valve that allowed some of the high pressure water to escape into a large and partly air filled (compressed) chamber called "the accumulator". This chamber had an exit in its base consisting of a metal delivery pipe that snaked up the side of the gully to the home owner's holding tank some 40m above. As the pressure surge in the supply pipe died away because the water slowed down, the one-way valve closed and so prevented the high pressure water in the accumulator from leaking back into the supply pipe.

As the pressure surge declined to a very low value the "fountain spring" could reopen its valve, allowing water in the supply pipe to start accelerating down that pipe again and the whole cycle would begin over again. The "clack" cycle would endlessly repeat itself about 20-30 times a minute, each time delivering a small amount of water all the way up to the household's water tank far far above.

So by using a mass of slowly falling water at a pressure of no more than 1 psi, the pump used deliberate water hammer to amplify the pressure of a small part of that water to 60psi or more to boost it a long way uphill. Perhaps only 1-2% of the water passing through the machine was pumped up to that high level with the rest returned to the creek to be used by others.

The "power source" was free and these pumps ran for years without attention. They also demonstrated to me the capabilities of slowly moving water masses to do amazing things by harvesting the momentum in that slow flow.

***** "Open Channel Water Hammer" *****
Both the positive and negative pressure forms of water hammer can also occur in open channels, where instead of having a water filled pipe we have a "free surface" always open to the atmosphere. In this case if a valve closes along the channel the pressure spikes are vastly smaller because the water surface is free to rise upwards on the upstream side of a closing valve, and fall downwards on the downstream side. In other words the small +ve and -ve pressure surges show themselves as small level rises and level falls.

The Physics of "Open Channel Water Hammer" states that if you close a valve situated mid-way along a uniform channel of flowing water, then the level rise upstream of the valve and the level fall downstream of the valve depend only on the water's initial momentum and the rate at which the valve is closed. The momentum term is the mass of water in the channel times its velocity.

The key point here is the mass term for a uniform channel rises directly proportional to its length. Thus even if the velocity in the channel is very low, if you have a long enough channel, then momentum values can be quite high and give significant level rises and level falls on either side of the closing valve. In the Bay the channel is long at over 12km.

***** Momentum In The Triangular Shaped "Choke Zone" *****
In the case of Port Phillip the channel connecting the ocean to the Bay's "main body" is not uniform in width, expanding from 3km wide at the Heads to around 30km wide at the main body. Nor is it uniform in cross-sectional area. It expands about 4-5 times in cross section over its 12-15km length.

For most of the duration of a tidal stream the amount of water crossing the northern end of the choke zone is 90% or more of the amount entering or leaving through the Heads. So to a good approximation the average velocity across any cross-section of the choke zone is inversely proportional to the area of that cross-section. This also means that in each kilometre length of the "channel" the momentum contained in that kilometre is close to that in any other kilometre length.

In turn this means that from a momentum perspective the choke zone is roughly equivalent to a uniform channel 3km wide and say 12-15km long, with a water speed equal to that the Heads. The same idea can be extended further up the Bay because it is not until well over half-way up the Bay does the northward flux of water decrease significantly. So our equivalent 3km wide open channel might extend to 30km in length. That is getting quite significant in that typically at the equal levels point the flow velocity at the Heads is in the range 0.5 - 2 knots.

***** Port Phillip Heads as a Controlled "Valve" *****
While there is no physical barrier that comes down to close the opening at the Heads, that region can be considered as a kind of bi-directional valve, whose "openness" or "closedness" is controlled by the ocean to mid-bay level difference.

Effectively during the last half of an ebb tide, the Heads are slowly being "closed for outflow" by a rising ocean level. The favourable level difference for outflow is rapidly decreasing towards zero. The opposing flow friction force (also decreasing) is in part used to provide the deceleration force needed as the stream speed slows.

At the equal levels point friction is providing all the deceleration force. As the reverse level difference begins to grow the "Heads valve" is now being even more rapidly "closed for outflow". The deceleration force is being provided in part by friction (dwindling with speed) and the growing (inwards) reverse slope driving force (mainly due to rising ocean levels).

The positive "water hammer" height gain approaching the Heads is well and truly in action now with ocean levels maybe around 20-30cm higher than the mid-bay level but this is still insufficient to arrest the outflow. Finally at around typically 60 minutes or more after the equal levels point the outflow stops to give slack water. The "Heads valve" is then fully closed for output but it required an ocean level 30-35cm higher than the mid-bay level to achieve this.

As soon as the flood tide begins this level difference quickly opens the "Heads valve" for inflow. Initially almost all of this inward (and growing) driving force is consumed in accelerating the early part of the flood tide.

Three or so hours later we have the scenario of a falling ocean level beginning to slowly close the "Heads valve" for inflow. Due an asymmetry in the way the tides penetrate into Bass Strait, we find that in the region just outside the Heads the water level typically falls at a slightly faster rate than it rises. The effect of this is that the "Heads valve" closes for inflow more quickly than it closes for outflow.

In turn this means that on average slack water at the end of a flood tide is shorter and has a higher reversal rate than for slack water following an ebb tide. Typically this means the reverse level difference needed to produce slack water only requires around 40 minutes to develop after the equal levels point.

The Bay also has its own filling & draining asymmetry with these statistics for all tides in 2020:-

Code: Select all

* average FLOOD stream duration (using Packo slacks):-         6hrs 04mins
* average EBB stream duration (using Packo slacks):-           6hrs 21mins

* average delay of Williamstown HIGH tide after Pt Lonsdale:-  2hrs 58mins
* average delay of Williamstown LOW tide after Pt Lonsdale:-   3hrs 38mins

* average delay of "Packo slack" after Pt Lonsdale high tide:- 2hrs 44mins
* average delay of Cardno/BoM slack" after Pt Lonsdale high:-  2hrs 48mins

* average delay of "Packo slack" after Pt Lonsdale low tide:-  3hrs 22mins
* average delay of Cardno/BoM slack" after Pt Lonsdale low:-   3hrs 33mins

* average Packo Flood slack reversal rate (slack after flood): -0.41 knots per 10 mins
* average Packo Ebb slack reversal rate (slack after ebb):     +0.32 knots per 10 mins

* average "Packo Flood Slack" time before Williamstown hi tide:-    13mins
* average "Cardno/BoM Flood Slack" time before Williamstown high:-  09mins

* average "Packo Ebb Slack" time before Williamstown low tide:-     16mins
* average "Cardno/BoM Ebb Slack" time before Williamstown low:-     04mins

* Number of Packo Flood Slacks at/after Williamstown high tide:-     nil
* Number of Cardno/BoM Flood Slacks at/after Williamstown high:-     63   

* Number of Packo Ebb Slacks at/after Williamstown low tide:-        nil
* Number of Cardno/BoM Ebb Slacks at/after Williamstown low:-        126   


I am not sure of the reason(s) for these flood/ebb tide asymmetries but it may be one or more of:-
a) Asymmetry in Bass Strait rise & fall rates.
b) Higher frictional losses over The Great Sands near end of ebb stream because its low tide there.
c) Ebb stream "Jet" extends for some miles outside Heads, with extra outward momentum.
d) The mysterious "Velocity Head" term in the current equation and changes in choke zone cross section.
e) God only knows!

cheers,
packo




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