7.8 Solutions to the Equations of Motion
Equations (7.12) and (7.19) are four equations, the three components of the momentum equation plus the continuity equation, with four unknowns: u, v, w, p. In principle, we ought to be able to solve the equations with appropriate boundary conditions.
Note, however, that these are non-linear partial differential equations. Conservation of momentum, when applied to a fluid, converted a simple, first-order, ordinary, differential equation for velocity (Newton's Second Law), which is usually easy to solve, into a non-linear partial differential equation, which is almost impossible to solve.
Analytical solutions can be obtained for much simplified forms of the equations of motion. Such solutions are used to study processes in the ocean, including waves. Solutions for oceanic flows with realistic coasts and bathymetric features must be obtained from numerical solutions. In the next few chapters we seek solutions to simplified forms of the equations. In Chapter 15 we will consider numerical solutions.
|Department of Oceanography, Texas A&M University
Robert H. Stewart, email@example.com
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Updated on January 19, 2005