Tidal‐induced large‐scale regular bed form patterns in a three‐dimensional shallow water model

TLDR

The study assumes a horizontal elliptical flow over a flat bottom as the basic state. The paper uses a 3‑D model to investigate how tidal currents generate wave‑like bottom patterns. The authors model tide–topography coupling and apply linear stability analysis to examine bed‑form dynamics. Vertical flow structure is essential for reproducing all known large‑scale regular bottom features, and the linear stability analysis reveals mode growth resembling tidal sand banks and sand waves, with predictions matching observations.

Abstract

The three‐dimensional model presented in this paper is used to study how tidal currents form wave‐like bottom patterns. Inclusion of vertical flow structure turns out to be necessary to describe the formation, or absence, of all known large‐scale regular bottom features. The tide and topography are treated as a coupled system, and the potential free instabilities in this system are investigated. A linear stability analysis is used to study the dynamics of bed forms. This yields information on the role of physical mechanisms; such information cannot be obtained by direct numerical nonlinear simulation. The basic state represents a horizontal elliptical flow, veering in vertical direction, over a flat bottom. It is shown that in such a system, modes can grow which have characteristics of both tidal sand banks and sand waves. The model predictions are compared with observations and show good agreement.