Significance of averaging coefficients in stability analysis of shallow wake flows

TLDR: In this paper, the authors show that the development of shallow wakes is different from the wakes in deep water due to the following reasons: 1) The development of three-dimensional instabilities is prevented by limited water depth and 2) bottom friction acts as a stabilizing mechanism for suppressing the transverse growth of perturbations.

Abstract: Flows behind obstacles (such as islands) are shallow if the transverse scale of the flow is much larger than water depth. Field, laboratory and numerical data show that the flow pattern in shallow wakes exhibits a complex eddy‐like motion. Experimental and theoretical analyses provide evidence for the presence of two‐dimensional coherent structures in shallow water flows and show that the development of shallow wakes is different from the wakes in deep water due to the following reasons: first, the development of three‐dimensional instabilities is prevented by limited water depth and second, bottom friction acts as a stabilizing mechanism for suppressing the transverse growth of perturbations. Several authors have used the linear and weakly nonlinear stability theory in order to understand when shallow flows become unstable. Two‐dimensional depth‐averaged Saint‐Venant equations are usually used for the analysis. One of the main assumptions in shallow water theory is the independence of the veloci...