Shallow Water Equations and Initial Conditions

In summary, the conversation discusses the use of simulations in studying the shallow water equations and how they involve initial displacement in the water to observe the propagation of waves through a medium of constant or variable depth. The speaker then poses a question about reversing this scenario and having a flat surface with a perturbation in depth, which leads to a reference to Russell's experiment and the need to look into solitons and the Kortweg-de Vries equation, specifically in the book "Solitons an Introduction" by Drazin and Johnson from Cambridge University Press.
  • #1
TheFerruccio
220
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I have seen lots of simulations using the shallow water equations, and every one I've seen involves having some sort of initial displacement in the water, resulting in a propagation of waves through a medium of either constant or variable depth, as a function of position.

However, can you reverse this? As in, can you just have the initial conditions for the surface of the water be completely flat, then have a perturbation in the depth of the water, showing how the waves propagate in that manner?
 
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  • #2
What you are seeking is Russell's experiment (1834).

You need to look up solitons and the Kortweg-de Vries equation

Solitons an Introduction

Drazin and Johnson

Cambridge University Press
 

FAQ: Shallow Water Equations and Initial Conditions

1. What are the Shallow Water Equations?

The Shallow Water Equations are a set of partial differential equations used to model the behavior of shallow water flows. They are derived from the Navier-Stokes equations and take into account the effects of gravity, Coriolis force, and bottom friction.

2. What do the Shallow Water Equations describe?

The Shallow Water Equations describe the evolution of the water surface elevation and horizontal velocity in a two-dimensional shallow water system. They are often used to model oceanic and atmospheric flows.

3. What are the initial conditions for the Shallow Water Equations?

The initial conditions for the Shallow Water Equations typically include the initial water surface elevation and horizontal velocity at each point in the system. These initial conditions are essential in determining the behavior of the system over time.

4. How are the Shallow Water Equations solved?

The Shallow Water Equations are typically solved using numerical methods, such as finite difference or finite element methods. These methods discretize the equations and solve them iteratively, taking into account the initial conditions and boundary conditions.

5. What are some applications of the Shallow Water Equations?

The Shallow Water Equations have a wide range of applications, including weather forecasting, oceanic and atmospheric modeling, flood prediction, and tsunami simulation. They are also used in engineering for the design of coastal structures and offshore structures.

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