Water Surface with Bernouli's Equation

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SUMMARY

The discussion centers on using a linearized version of Bernoulli's Equation to calculate the evolution of ocean surface heights. The specific equation referenced is (∂4h(x,t)/∂t4)=g2*∆2*h(x,t), derived from Jerry Tessendorf's work in "Simulating Ocean Water" (SIGGRAPH 2004). The user questions the applicability of this one-dimensional equation for two-dimensional water surfaces, indicating a need for clarification on its suitability and potential modifications. The conversation highlights the importance of understanding the dimensionality of equations in fluid dynamics.

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  • Understanding of Bernoulli's Equation in fluid dynamics
  • Familiarity with partial differential equations
  • Basic knowledge of oceanography and surface wave dynamics
  • Experience with mathematical modeling in physics
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  • Research the application of Bernoulli's Equation in two-dimensional fluid dynamics
  • Study the derivation and implications of the wave equation in fluid mechanics
  • Explore numerical methods for simulating ocean surface dynamics
  • Investigate modifications to Bernoulli's Equation for multi-dimensional surfaces
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Physics students, oceanographers, and computational fluid dynamics researchers interested in modeling ocean surface behaviors and wave dynamics.

Phong
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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
 
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