Stability of slowly diverging flows in shallow water

Abstract

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.

Key words:

• momentum correction coefficients
• shallow wake flows
• asymptotic analysis

Notes

This work has been partly supported by the European Social Fund within the National Programme “Support for the carrying out doctoral study programs and post‐doctoral researches” project “Support for the development of doctoral studies at Riga Technical University” and the Latvian Council of Science under the Project No. 04.1239.