A Quicker Way to Mathematically Measure the Surface Flows of Jacuzzi Water

Science is an interesting thing, and it's fun to study light waves, sound waves, ocean waves, and even to ponder what's going on with the Jacuzzi jets while you are in your hot tub. For instance, although the math is complicated, or it gets complicated right away when you start adding four or five, or six Jacuzzi jets into a non-symmetrical shaped Jacuzzi we can still figure it all out.
That is to say we can predict the wave energy, interactions, and the motion of the ocean so to speak.

Okay so let's talk about this for second shall we? At Los Alamos many years ago, they were working inside of one of the canyons near the lab and they set forth virtual grid boxes in the canyon and measured the airflow from one point to another.
Once they had figured out all the math, it was very easy to make predictions of what the airflow as they progressed along the canyon and what it would be against which canyon wall, and knowing the air pressure at the beginning of the canyon, and the airflow they could predict the amount of wind passing through each point at the end of the canyon within that 3-D virtual grid.

Interestingly enough, the computational mathematics for determining the current flows within your Jacuzzi work in a very similar fashion.
Still, there are other flows which are also interacting with the water flows.
For instance, there might be cloud like steam coming from the surface of the water in the Jacuzzi, and then there is the surface tension interacting with the surface flows.

Have you ever noted where waves on the top on the surface of the Jacuzzi water interact with one another, how they form small vortex funnels, or tiny rogue waves which jump up every once in a while intermittently? It seems that the current flows on top of the surface of the water are much different than what is happening below the water, this is because it is interacting with a different medium, namely air. Nevertheless, there is another set of (similar) formulas you can use, the same formulas which are used by oceanographers when studying the swash zone at the beach.

This is the area where water is pushed up very quickly along the sand, and then it falls back again, only to be pushed up with more water being delivered by the next wave. It's that same area that you can walk on the beach and only get your feet wet, but never have to worry about getting hit with a big wave, as long as you move out of the way real quick if you see one coming.
If you'd like to learn more about the swash zone and the mathematical modeling involved this will help you better understand what is happening on the surface of your Jacuzzi with all that interaction going on.
Please consider all this and think on it from a mathematical perspective of course.
Swash Zone Modeling; Relevant Research Paper on This Topic: 1.

) Petti, M and S.
Longo, Turbulence experiments in the swash zone, Coastal Eng.

43, 1-24, 2001.