Numerical Calculations Of Viscous Effects
On Water Waves
Author(s)
G. Baker & J. Wang
Abstract
The motion of periodic ocean waves can be calculated directly by applying spectral
methods in the horizontal direction and the second-order backwards difference
formula for time-stepping. The resulting semi-discrete equations constitute a
boundary-value problem in the vertical coordinate, which is solved by decoupling
growing and decaying solutions. Overall, an iterative method is used to solve the
nonlinear system. With this method, Stokes waves can be followed sufficiently in
time to see the viscous effects of air and water.
Keywords: interfacial motion, slightly viscous flow, incompressible flow, Stokes
waves.
1 Introduction
Although both viscosities in air and water are very small, they play a crucial role
in transferring energy from wind shear to ocean waves. The challenge in studying
this effect numerically is the design of an algorithm which captures the many
spatial scales on the water surface and does not introduce numerical smoothing
that can mask the true effects of viscosity. Current methods, such as Volume-of-
Fluid or level sets, succeed primarily for large scale motions where surface details
are not important. We present a new approach which ensures a highly accurate
representation for the water surface, and avoids unnecessary smoothing from grid
effects.
Clearly, only a finite region of the ocean can be studied and, since any patch of
ocean is probably similar to any other patch, it is perfectly reasonable to assume
the region is doubly periodic in the horizontal plane. It is natural, then, to use a
spectral representation for the surface and flow variables in the horizontal coordinates.
In essence, the flow equations have become a family of equations in time and
Keywords
interfacial motion, slightly viscous flow, incompressible flow, Stokes
waves.
Related Book
Other papers in this volume
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