Water Surface with Bernouli's Equation

[Phong]

Hi!

I got a question concerning a solution to calculate the evolution of surface heights of oceans. Since I'm only interested in the surface itself I omit the volume underneath and the air above the surface. I grabbed a linearized and simplified version of the Bernouli-Equation which I looked up in a paper by Jerry Tessendorf who utilized this equation to make further calculations for ocean surfaces ['Simulating Ocean Water', Jerry Tessendorf, SIGGRAPH 2004]. The equation is the following:

(∂4h(x,t)/∂t4)=g2*∆2*h(x,t)

in which x is the position of the surface and t the time. But this equation looks like it could only resolve the height of a one-dimensional "surface" since there's no y position given. So what do you think of it - is this equation suitable for calculating the surface height of any position on the two-dimensional watersurface or do I need to change the equation? I'm still very new to this kind of physics, so maybe one of you guys can help me?

Thanks a lot!


Phong

 

[Chestermiller]

$\nabla^2$ features partial derivative with respect to y.