Methods of weakly nonlinear theory are used in the present paper in order to study the development of instability in shallow water for the case where the flow is assumed to be slightly non‐parallel. An asymptotic scheme where slow divergence of the base flow is taken into account is applied to shallow water equations with averaging coefficients. An amplitude evolution equation for the most unstable mode is derived. First Published Online: 14 Oct 2010
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Kolyshkin et al. (2007) studied this question.