Preprint A111/2001
Apparent diffusion due to mountain microstructure in shallow waters

Knut Solna | Nachbin, Andre

**Keywords: **
waves in random media | asymptotic theory | scientific computing

Wave propagation in disordered (random) media is the underlying theme.
We study the effective behaviour of long coastal waves
that travel over rough topographies.
The topographies analyzed contain a smooth slowly varying profile
together with disordered small-scale features.
The mathematical model is a
Conservation Law with random coefficients.
The main (stochastic theory) asymptotic result is that
the medium fluctuations cause the propagating pulse to
broaden as it travels.
The so called {\em apparent diffusion}
(or pulse shaping) depends only on the traveling
distance and the {\em statistics} of the random medium fluctuations.
Thus, the broadening can be described in a deterministic
way independently of the particular medium realization.
This is confirmed numerically.
Numerical experiments also show that the theory
describing pulse shaping is very robust.
Nonlinear shallow water simulations show that small
amplitude pulse shaping is not affected by higher order terms.
The robustness of the theory is observed numerically for a wide
parameter regime.
We vary both the microscale fluctuation level as well as the
horizontal length scales of the topography.
The numerical experiments produce very good results
regarding the prediction for the wavefront attenuation.