## Waves transport energy, but not mass

Usually we see wave crests propagating, and since the eye can’t stop following them, it is easy to assume that they transport water with them instead of leaving the water put and just transporting energy. But here is an example of a situation where bubbles as tracers for water “parcels” show that, despite large waves passing, the water itself only moves up and down, and a little back and forth, but isn’t really transported away:

Of course there is some Stokes drift, but compared to the wave speed the speed associated with that is tiny…

## Stokes drift

When a higher-order effect suddenly becomes important.

During our excursion to Hamburg Ship Model Basin (HSVA), one of the experiments we ran was on Stokes drift. You can already see in that post’s movie that there is some swimming thing moving down the tank in the direction of wave propagation, but of course we had to quantify.

“Experiment” sounds too sophisticated for what actually happened: We dropped a piece of styrofoam in the waves and took the time it took that styrofoam piece to travel two meters. The piece of styrofoam has the advantage over the other swimming thingy that it hardly sinks into the water, and therefore constitutes an almost passive tracer of the waves’ movements.

Now, we all know that Stokes drift is one of those ugly non-linear higher-order things that we ignore as much as possible. It is basically the effect of orbital movements not being closed circles, but rather spirally things. But we have all heard over and over again that the effect can be neglected, and whenever we see a bird bobbing up and down in the waves but also moving horizontally, we quickly rationalize that it must be swimming autonomously, or that there is a current superimposed on the wave field.

So, what do you think, how long will it take for that little styrofoam piece to travel 2 meter’s distance? Of course that depends on the kind of wave field, but give it a rough guess. What’s your estimate?

36 seconds! To travel 2 meters! That doesn’t sound so insignificant now, does it? I’m still trying to figure out why that happened because it seems way too fast. And according to theory it should even have travelled faster than that. So please excuse me while I put on my thinking cap…

## Langmuir circulation, take 2

Attempt at mechanistic understanding of Langmuir circulation.

After  complaining about how I didn’t have mechanistic understanding of Langmuir circulation recently, and how I was too lazy to do a real literature search on it, my friend Kristin sent me a paper that might shed light on the issue. And it did! So here is what I think I understand (and please feel free to jump in and comment if you have a better explanation).

First, let’s recap what we are talking about. My friend Leela (and it was so nice to have her visit!!!) and I observed this:

Long rows of foam on the surface of the fjord, more or less aligned with the direction of the wind (we couldn’t tell for sure since we were on a moving boat, and since it was a tourist cruise we couldn’t ask them to stand still for a minute to satisfy our oceanographic curiosity). Foam is – and so much makes sense – accumulated in regions of surface convergence.

But let’s see. The explanation that Kristin forwarded me is from the paper “Upper ocean mixing” by J.N. Moum and W.D. Smyth for Academic Press Encyclopedia of Ocean Sciences, 2000According to my understanding of their paper and others, Langmuir circulation is related to Stokes drift.

Stokes drift is the small current in the direction of wave propagation that is caused by orbital wave motions not being completely closed (even though they are as a first order explanation, and that’s what you always learn when you think about rubber ducks not being laterally moved by waves).

As the wave orbital motions decrease with depth, there is a shear in the Stokes drift, with strongest velocities being found at the surface. At the same time, if there are small disturbances in the wind field, there are small inhomogeneities in the resulting surface current, hence shear that generates vertical vorticity.

The combination of horizontal and vertical vorticity causes counterrotating vortices at the ocean surface. The convergences between two adjacent rows concentrate the wind-driven surface current into a jet at the convergence, hence providing a positive feedback.

Voila: Stokes drift!