The Equal Levels Moment

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

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The Equal Levels Moment

Postby packo » Fri, 28 May 2021 12:32 am

***** The Bass Strait/Port Phillip Bay "Equal Levels" Moment *****

The equal levels moment at Port Phillip Heads occurs roughly every 6 hrs when the "outside" ocean water level matches the "inside" water level in the vast "main body" of the Bay. The "main body" region begins roughly 15 km inside the entrance. It is a whopping 1,700 square kilometres or so in area. It is the tidal breathing of the vast "main body" surface area with its fairly well synchronised tides that produces such high current speeds at the entrance.

Between the entrance and the large "main body" area there is a wedge shaped "connection region" which acts to restrict the flow of water to and from Bass Strait. This restriction is due firstly to its narrow width at the southern "Heads end" of the connection, and secondly the extensive shallow areas (known as "The Great Sands") that occur in the northern section of the connection. In other posts I have called this whole region the "choke zone". However in this post I will use the words "connection region" to emphasise its role as a connecting channel between two very large bodies of water:-
Image

Significant consequences of the constricted connection between the ocean and the Bay's vast "main body" region are that:-

a) Water level height differences of a metre or more are typical across this 15km connection at times of maximum flow.

b) Tidal currents through the entrance may reach 6 knots, and from 2 to 4 knots at other places within the connection.

c) The "main body" tidal range is only 30% to 60% of the ocean tidal range. (Lower % values for faster flowing tides.)

d) The High and Low Tide times in the "main body" region are delayed by around 3 hours behind the "outside" tide times.

During this 3 hour tidal delay period the water levels in the two regions move in opposite ways with the ocean falling and the main body rising or vice versa. The delay periods for the last half of the flood stream and ebb stream are shown below in this diagram of typical "outside" and "main body" tide curves. The "equal levels" and predicted "slack water" times are also marked.

Image

These curves were taken from the VPCM website which does not plot either the Lorne or West Channel Pile tide data. The Hovell Pile tide gauge (off Rosebud) has a curve very similar to the West Channel Pile (and Williamstown) tide curves. Either of these is a suitable proxy for the "main body" tide. The Point Lonsdale tide curve is also a rough proxy for the "outside tide" even though its amplitude is somewhat lower.

The tidal current through the entrance is primarily determined by the rate of rise or fall of the tide over the enormous "main body" region, with only a small contribution due to tide height changes within the much smaller connection region. During the 3 hour delay period, areas near the entrance experience the minor "brain-bend" of an incoming tidal stream but a falling tide level, or an outgoing stream but a rising tide level.

While at first this might be confusing to those boating around Port Phillip Heads, remember that the tide height at your location is dictated largely by the ocean level a few kilometres away to the south, whereas the tidal current at your location is dictated largely by the rise or fall rate of the 3 hour delayed tides in the vast area northwards. This is well over your horizon and 40 kilometres or so away. It is really a case of "out of sight - out of mind" that enables the confusion to persist as to why the horizontal and vertical components of tidal motions near the entrance behave at times in what at first glance may appear to be in unexpected ways.

At the "Equal Levels Time" the gravity forces are balanced and so there is no net sideways force attempting to push the water one way or the other through the entrance. Note however this "zero driving force" moment does not imply zero velocity (or slack water) as "ALWL" claims. Rather at that moment the water will just continue to "coast along" as before. This is evident from the continuing trend of the "inside" tide curve beyond the equal levels moment. The flow is neither assisted by any downward slope between the two water bodies, nor impeded by any upward slope. Frictional drag is the only active force during these few equal level minutes.

However a reverse water surface slope will then begin to grow because the two water levels are now moving apart with one rising and the other falling. The current flow does not reverse at this time but continues to flow towards the higher water body due to the residual momentum within the tidal stream, but of course it is now losing speed more rapidly than before.

The timing of the brief equal levels moment is a little variable depending on the details of each tidal cycle. On average it occurs a little over 2 hours after high or low tide at the entrance. However this can vary somewhat because the timing for the Hi -> Lo, or the Lo -> Hi phases of the "outside" tide can be as short as 5 hours, or as long as 7 hours. This can shift the equal levels time around by around 30 minutes either side of the average.

On a "big tide" day the entrance tidal stream is still running at around 2 knots at the equal levels time. This occurs because in the weakening tidal stream the decreasing frictional drag is simply insufficient to remove all the forward water momentum by the time the equal levels moment is reached.

All waters within the Bay will also be in motion at this time but with lesser speeds as the underwater cross-section of the Bay expands about 20 times as you move northward into the central basin of the Bay. However there is sufficient residual momentum stored in this now 25 billion tonnes of slowly moving water to allow the entrance stream to keep flowing in the same direction (and now slightly uphill) for around another 40 minutes on a flooding tide, or around 60 minutes on an ebbing tide.

These long lasting up-slope flows before a tidal stream is halted are in part due to the wedge shape of the "connection region" between the ocean and the main body of the Bay. This tends to focus the water momentum onto a smaller area of coastline around the entrance. In turn this means a much higher reverse level difference over this smaller area is required to generate sufficient force to halt the tidal stream compared to a situation where no focussing effect occurs.


***** Is The "Equal Levels" Moment Really Any Big Deal? *****

In one sense it isn't a big deal because all bays and harbours with a constricted entrance will have their own "equal levels" moment. This is simply because the inside level will continue to rise due to inflow for some time after the outside level begins to fall and so there will be a level "cross-over" point at some time in every flood stream. During the outflowing ebb stream it is the rising ocean level that will "cross-over" the falling mid-Bay level at the "equal levels" moment.

At Port Phillip Heads it is far more of a big deal for these three reasons:-

-- "Big Deal" reason #1:- "Sheer Size"

Due to both the size and shape of Port Phillip Bay the "Equal Levels" moment is of astonishing physical extent. Over those one or two minutes the crests and troughs from wind waves and swell will average out at any particular point. However this average water height is pretty much dead level from a few tens of kilometres outside the Heads to all the way into at least the middle of the Bay.

That is a distance of around 50 km with the average water level no more than a few centimetres different over all that distance! There may be a slight kick-up of a few extra centimetres approaching Williamstown as the incoming tidal stream runs into a "dead end" at the north end of the Bay.

-- "Big Deal" reason #2:- "An improved understanding"

Officialdom has for many many years claimed "slack water" and "equal levels" are simultaneous events. This is not true, but this falsehood has been widely accepted by seemingly just about everyone! Eventually this will be overturned but I am afraid this will take many more years because of a strongly entrenched mentality that "water can only run downhill".

In PPB the very high inflow and outflow rates of up to 80,000 tonnes per SECOND, plus the relatively high speed of these flows at up to 10 kph, allows high levels of forward water momentum to build up. Later on, any residual momentum allows the tidal streams to overrun the equal levels time and so begin to flow UP a growing surface slope.

A better understanding of how water at "The Heads" behaves requires diving, boating, and yachting folk to realise that the "equal levels moment" is a separate event to the "slack water moment" and typically occurs from 40 to 80 minutes earlier.

Under the flawed official "both together" advice, many folk are encouraged to think the outside to inside level difference (ie. the "driving force") steadily drops to zero at slack water and then steadily rises again in the reverse direction. These leads them to think the current slows down more and more slowly approaching slack water. Then after spending some time stationary the water builds up speed more and more quickly in the reverse direction as time goes by.

In other words it encourages the view that the current speed reversal has a rather gentle "U" shaped bottom to it. The reality is somewhat different, with the zero-drive point occurring 40 to 80 minutes before slack water and a substantial (and growing) reverse level difference already in place by slack water time.

At the equal levels point, where the current is still typically somewhere between 1 and 2 knots (ie. 2 kph to 4 kph), the only slowing force at this time is frictional drag. From that point onwards the deceleration force is a combination of the dwindling frictional force as the water slows down, plus a growing reverse slope force as the reverse height difference increases. Under this combination the total deceleration force actually grows somewhat the closer we get to slack water.

This means the rate at which the water slows actually gets bigger approaching slack water. (ie. "the brakes" are applied harder the closer we get to slack water.)

A significant point of the real situation is that rather than a gentler "U" shaped reversal of speed that many believe occurs, we have something much closer to a sharper "V" shaped reversal of speed. This is consistent with a body being reversed by a roughly constant force in the reverse direction. This effect is shown below from several data runs at and near the Heads using a free drifting buoy equipped with GPS tracking.

Image

-- "Big Deal" reason #3:- "An accurate 2nd timing reference"

Using fairly basic equipment, or even by very careful observations by eye, you can measure the exact moment of slack water at the Heads accurately to within a few minutes. However trying to relate slack water time to the time of some other tide event such as observations of high or low tide at any particular place is fraught with difficulties.

One common attempt is to try to relate slack water time to the previous High/Low tide time at Pt Lonsdale. However because this event occurs between 2.5 and 3.5 hours before slack water, it gives plenty of time for changing weather conditions to intervene and affect the timing relationship between these two events.

A better proposition is to try relate the observed slack water time to either the High or Low tide observations at say Williamstown where the timings are much closer together. The problem here is that with these smaller amplitude tides the rate of height change around high or low tide is quite small and it is difficult to time the peak accurately.

The other problem is that although "Rip slack" and Hi/Lo at Williamstown occur fairly close together in time, they are apart in distance by around 50 km. Again this might allow weather fluctuations over this distance to muddy the timing relationship. The final problem is that because the Williamstown High/Low tide occurs a little after slack water, any observed timing variations in the Hi/Lo times can't then be used to adjust an earlier slack water prediction.

In contrast to all these situations timing the "equal levels" moment appears very attractive for improving our understanding of slack water. Water levels at the Heads are changing very rapidly at this time, yet very slowly in Bay's central basin, so it is theoretically easy to measure the cross-over time (ie. equal levels time) to within one or two minutes of accuracy. This event also occurs sufficiently ahead of slack water to potentially allow an "off-theoretical" observed equal levels time to then be used to "weather correct" an upcoming slack water prediction time.

The slight fly in the ointment is that the exact height of each tide gauge's zero mark needs to be accurately known with respect to a common height datum such as the Australian Height Datum (AHD). Unfortunately it seems the port authorities don't really publish this calibration because they rarely have the need to compare the absolute tide heights between the different gauges. (Most tide info for mariners is expressed relative to the chart datum of that particular location. Absolute chart datum heights differ by around a metre between "inside" and "outside" locations.)

To be fair, both the highly relevant gauges at the Hovell and West Channel Piles, also stand well offshore on the northern edge of "The Great Sands". These are not amenable to the most common height surveying technique of referencing to a nearby survey marker of known AHD height. Expensive and complicated Real Time Kinematic GPS techniques are needed to achieve the better than the +/- 1cm height accuracy desired. Deploying this technology on an awkward offshore structure is also not an easy task.

I am using a number of work arounds that seems to be focussing down on the relative heights of the zero points across the Bay's tide gauge network to an accuracy of around +/- 2cm which might have to do. This should enable measurement of the equal levels time to an accuracy of about 2 to 3 minutes.

Interestingly this work seems to be showing that excluding moderate and rough weather, many of the weather induced shifts of slack water times are due to shifts in the timing of the "equal levels" moment with the duration of the uphill run staying reasonably close to the predicted value. If this can be confirmed, then it opens up the prospect of detecting these shifts well before slack water and so allowing slack predictions to be corrected before the event occurs.

cheers,
packo



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