Abstract: Method of multiple scales is used in the paper in order
to derive an amplitude evolution equation for the most unstable mode
from two-dimensional shallow water equations under the rigid-lid
assumption. It is assumed that shallow mixing layer is slightly curved
in the longitudinal direction and contains small particles. Dynamic
interaction between carrier fluid and particles is neglected. It is
shown that the evolution equation is the complex Ginzburg-Landau
equation. Explicit formulas for the computation of the coefficients of
the equation are obtained.