Since the celerity in unsaturated subsurface flow is analogous to the wave celerity in surface flow , the kinematic ratio of unsaturated flow can be 1.5-14.7 times larger than that of surface flow, which implies that the velocity distribution in unsaturated subsurface flow is highly nonlinear.
Veling, "Relation between tidal damping and wave celerity in estuaries," Journal of Geophysical Research: Oceans, vol.
McCowan  theoretically defined the breaker depth index as [H.sub.b]/[h.sub.b] = 0.78 for a solitary wave travelling over a horizontal bottom using the assumption that instability is reached when the particle velocity at the crest equals the wave celerity
and that the crest angle is then 120[degrees].
c(x, y) is the wave celerity, [c.sub.g](x, y) is the group velocity, [omega] is the angular frequency, and
Wave celerity (c) and group velocity ([c.sub.g]) over the computational grid points are given as follows:
For non-deforming waves, in the coordinate system moving with the same speed as the wave celerity, c, the wave profile is standing still and the velocity field becomes steady.
where [nabla] = ([partial derivative]/[partial derivative]x, [partial derivative/[partial derivative]y) is the two-dimensional horizontal gradient operator, c the wave celerity and [c.sub.g] the group velocity (i.e., energy transfer velocity).
where the wave celerity
C = |C|cos [theta]i + |C|sin [theta]i.
where u (x, t) is the wave function and c(x) is an arbitrary continuous or discontinuous function having the meaning of the local wave celerity. The scope and conditions applied to the function c(x), and appropriate boundary conditions for Eqs.
Obtained travelling wave solutions can be applied in oceanography to study the wave transformation above complicated bottom relief, which can be presented as superposition of small sections, for which the wave celerity changes as c(x) ~ [x.sup.1] or c(x) ~ [x.sup.4/3].
We also define a local wave celerity
of a local wave event of the wave field by
These conditions made it possible to demonstrate experimentally that the crest of the steepest wave slows down while growing due to nonlinear focusing, so its velocity falls notably below the wave celerity