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## Homework Statement

Hello. This is not a homework question (my school will never offer a fluid dynamics course), but I figure this would be the best place to ask it.

I am interested in writing a computer model of high speed winds blowing over the ocean - or any body of water. I am wondering how I might do this. I have only a... how should I put it, "MCAT style" introduction to fluid dynamics, and so it may seem a bit silly of me to be trying something so complex. Nonetheless...

I thought I'd model the wind and the water in 2-dimensions, like looking at a rectangular slice of the water-wind intersection... like looking through a camera half in and half out of water. On this rectangular slice, I'd initially have the upper half have some uniform density rho and the lower half have some uniform density 10 * rho, to model the different densities of wind and ocean water.

What I'm not sure about exactly are two things: 1) how to model the wind and 2) which fluid equations to use. For 1), I thought that I'd just have the velocity field of the upper half of the slice (wind) be uniformly to the right (positive) and the bottom half (water) be uniformly zero. But I wasn't sure if keeping the velocity -constant- throughout the simulation would work or be sensible... might I just initially have the velocity field set up in some way, and then solve the equations based on that? If I keep the velocity field constant, then a lot of the terms in various fluid equations disappear...

For 2), I think I'll use:

## Homework Equations

Euler's equations of inviscid gas dynamics!

## The Attempt at a Solution

I think Euler's equations apply because the wind and the water are Newtonian and I can model them as inviscid. The fluid is definitely compressible because the Mach number would be around 1 or above, etc. But I'm not positive that Euler's equations would be best. A few things about Euler's equations from wikipedia made me wonder, for instance, the energy equation was confusing (is e, the internal energy, a dynamical variable I have to monitor as well as pressure, density, and velocity?).

Also, for the wind-water system I'm trying to simulate, would the ideal gas law be a good equation of state? If so, what would the adiabatic index (gamma) be?

Sorry if this is rambling. Any help, criticisms, ideas etc. would be awesome.