Wind against Tide AGAIN....Sorry

[SHUG]

I have been re-visiting some of the earlier posts on this subject and would like to know a bit more about the specific change in the wave-shape.
One notion is that the wind blows into the face of the wave causing that part to slow down and steepen so that the surface of the wave facing the wind becomes more vertical.
However, as the wind strength increases, the wave will break on the leeward side of the wave making that the steeper side.
Has anybody got some graphics which show how the wave-shape changes as the wind velocity inreases, with and without tide.
I apologise for raising this subject again but the specific answer did not seem to be in the earlier posts.

 

[Ric]

Wave mechanics are best described by hyberbolic sinusoids (sinh, cosh, tanh etc). The waves formed at the interface between two non-compressible fluids with relative movement to each other can be readily modelled by these functions.

Somebody will come along with some waffly pub answer if you prefer to not really understand what is happening.

 

[sighmoon]

I was proud of my [waffly pub] answer the last time it came up, but I'd lost my audience by that point. OK, it's mostly not really my answer, it was really a combination of other people's answers, particularly from Halcyon's link to a science website, but I feel I have a handle on it. Tell me what you think:

The speed of a wave in water is proportional to the square root of the wavelength. This is how fast the wave is traveling, and this is of course less than the wind speed that produced it. As an example a wavelength of 2 meters would be travelling at 3.44 knots, whatever the wind speed.

Should the wave be slowed down, the wavelength needs to decrease proportionate to the square of the decrease in speed (i.e. if the speed halves, the wavelength is 1/4 what it was). However, the wave has the kinetic energy of the original longer wave, and has the momentum of the amount of water in the long wave, and so the waves become steeper, higher, and unstable (i.e begin to break)

The key thing here is that a small variation in speed, means a big variation in wavelength. For the wave of 2.0m length, travelling at 3.4 knots, a reduction in speed (i.e. opposing tide) of about 1 knot, would halve the wavelength from 2.0m to 1.0m, and so double the height of the wave (because of the momentum of water in the wave).

Now the case of a river, where the water is moving at a constant 5 knots for the entire fetch. I think it doesn't exist in reality, and if it did, there would be no observable wind over tide effect. In reality, the water will be traveling at slightly different speeds all over the width and length, and those slightly different speeds are enough to have a big effect.

 

[sighmoon]

Wave mechanics are best described by hyberbolic sinusoids (sinh, cosh, tanh etc). The waves formed at the interface between two non-compressible fluids with relative movement to each other can be readily modelled by these functions.

Go on then, show us your hyberbolic sinusoidal wave model.

 

[macd]

Go on then, show us your hyberbolic sinusoidal wave model.

He admits it's all hyperbole. Obviously no idea what he's talking about.

While we've got a line to an expert, can he explain why people often talk about confused seas but never baffled ones?

 

[sighmoon]

Can he explain why people often talk about confused seas but never baffled ones?

Isn't the sea in a marina baffled?

 

[boomerangben]

Wave mechanics are best described by hyberbolic sinusoids (sinh, cosh, tanh etc). The waves formed at the interface between two non-compressible fluids with relative movement to each other can be readily modelled by these functions.

Somebody will come along with some waffly pub answer if you prefer to not really understand what is happening.

Last time I looked, air is compressible, in fact I spent most of my day staying out of the water by compressing literally tons and tons of air.

However, linear Airy wave theory used in maritime engineering is based on hyperbolic sinusoids.

Simply put, the rate that energy that propagates down wind with wind waves is reduced by the tide, meaning that there is more energy per unit length of sea. That energy is transfered by the water surface becoming steeper and higher.

As for the shapes of the waves, I guess it will depend on the wind strength, the fetch, the speed of the tidal current, the depth and the seabed profile. In other words it's complicated and probably not terribly well modelled.

 

[Ric]

Last time I looked, air is compressible, in fact I spent most of my day staying out of the water by compressing literally tons and tons of air

It is not considered a compressible fluid in the range of Reynolds numbers that are being discussed here.

If you want to read more about hyperbolic functions, a start is here.

http://en.wikipedia.org/wiki/Hyperbolic_function

They are also used, amongst many other uses, to model wave erosion on the seabed, breaking waves on a shoreline, or even in satellite tracking of submarines by virtue of their surface wake. They can actually model wind over tide wave effects very simply by comparison - indeed probably the first example that is used to teach undergraduates.

 

[boomerangben]

Ric,

I bow to your superior knowledge. My wave theory lectures were a long time ago!!

 

[electrosys]

Now the case of a river, where the water is moving at a constant 5 knots for the entire fetch. I think it doesn't exist in reality, and if it did, there would be no observable wind over tide effect. In reality, the water will be traveling at slightly different speeds all over the width and length, and those slightly different speeds are enough to have a big effect.

I've re-read the above several times, and I still don't know whether or not you're claiming it has an effect or not on rivers ....

Late last year I took a small dinghy down the River Welland - it was a lovely, gentle day - just a wisp of a breeze, and the ebb tide (springs) coasted me along and out into The Wash just perfectly.
On the return trip however, the wind got up and blew straight down the Welland - 'straight' being the operative word, as it's more like a canal than a river. There was a good 5 knots of flood tide, and a good 15 knots (or even more ?) of wind in exactly the opposite direction. The result - much to my amazement, was not just a fist-full of white horses, but several rollers actually developed in the centre of the channel which caused me little dinghy to become airborne. Came as quite a shock, I can tell you.

So - wind over tide in a river - can indeed cause disturbed water, especially if the river is relatively shallow.

 

[sighmoon]

electrosys,

I'm hypothesizing that if your model of a river is one of water moving at a constant velocity over the entire width and fetch, then there would be no steepening of waves. However, that model bares little resemblance to a real river (like the Welland), where the velocity varies all over the river, and this change in velocity is what causes the waves to steepen and break.