Graphics Reference
In-Depth Information
-13-
Ocean Modeling
Simulating the ocean is an ongoing challenge in computer animation. This
chapter will demonstrate a series of simplifications that allow relatively
calm ocean surfaces to be eciently simulated; eciently handling rough
oceans, or large-scale interactions between the ocean and solid objects im-
mersed or floating in it, is currently an open research problem. The chief
resource in graphics is the work by Tessendorf [Tessendorf 04].
The main diculty in the ocean setting is scale. Essential to the look
of waves are both large-scale swells and small ripples, and as we'll see
in a moment, to get the relative speeds of these different sizes of waves
correct, a simulation needs to take into account the true depth of the
water. (In particular, the shallow water model of the previous chapter is
completely wrong.) A na ıve brute-force approach of just running a 3D fluid
simulator like the ones we've looked at so far would result in an excessively
and impractically large grid. Therefore we'll take a look at changing the
equations themselves.
13.1
Potential Flow
Recall the vorticity equation (9.1) from Chapter 9, and since we're dealing
with large-scale water, drop the small viscosity term:
∂ω
∂t
+
u ·∇ω
=
−ω ·∇u.
It's not hard to see that if vorticity starts at exactly zero in a region,
it has to stay zero unless modified by boundary conditions. Since the
ocean at rest (with zero velocity) has zero vorticity, it's not too much of a
stretch to guess that vorticity should stay nearly zero once calm waves have
developed, as long as boundaries don't become too important—i.e., away
from the shoreline or large objects, and assuming the free surface waves
don't get too violent. That is, we will model the ocean as
irrotational
,
meaning the vorticity is zero:
∇×
u
=
ω
=0.
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