Water Surface with Bernouli's Equation

In summary, the conversation is about a question regarding using a simplified version of the Bernouli-Equation to calculate the evolution of surface heights of oceans. The equation in question is (∂4h(x,t)/∂t4)=g2*∆2*h(x,t) and it is being questioned if it is suitable for calculating the surface height of any position on a two-dimensional watersurface or if it needs to be changed. The speaker is new to this type of physics and is seeking help.
  • #1
Phong
5
0
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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  • #2
##\nabla^2## features partial derivative with respect to y.
 

1. What is Bernoulli's Equation?

Bernoulli's Equation is a fundamental equation in fluid dynamics that describes the relationship between fluid velocity, pressure, and elevation. It states that as the velocity of a fluid increases, the pressure decreases, and vice versa.

2. How is Bernoulli's Equation used in relation to water surfaces?

Bernoulli's Equation can be used to calculate the pressure difference between the top and bottom of a water surface, which is known as the hydrostatic pressure. This is important in understanding the behavior of water surfaces, such as waves and ripples.

3. Can Bernoulli's Equation be applied to all water surfaces?

Bernoulli's Equation can be applied to water surfaces that are at rest or in motion, as long as the flow of water is steady and the fluid density remains constant. It is also important to consider the effects of viscosity on the water surface.

4. What is the significance of Bernoulli's Equation in practical applications?

Bernoulli's Equation has many practical applications, including in the design of airfoils for airplanes, calculating water flow in pipes, and understanding the behavior of fluids in hydraulic systems. It is also used in meteorology to predict weather patterns and in the study of ocean currents.

5. Is Bernoulli's Equation always accurate in predicting water surface behavior?

No, Bernoulli's Equation is a simplified model and does not take into account factors such as surface tension, turbulence, and external forces. In certain situations, such as when the water surface is disturbed or when there are obstacles present, Bernoulli's Equation may not accurately predict the behavior of the water surface.

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