Local Characteristics of Sand Wave Patterns Are Governed by Underlying Sand Bank: A Linear Stability Approach

Abstract Tidal sand waves are dynamic bedforms, observed in shelf seas. In some cases they co‐exist with tidal sand banks, larger‐scale bed features. Sand wave characteristics then vary over the sand bank, migrating anti‐cyclonically around the bank. Yet, little is known about the processes behind sand wave formation on a sand bank characterized by a spatially non‐uniform flow pattern. Here, we extend an existing linear stability model to assess the effects of an underlying sand bank on sand wave formation. Specifically, we allow for a spatially varying basic state, representing the topography of the bank as well as the typical 3D tidal and residual flow patterns over it. The eigenmodes of the system then turn out to be spatially varying too, that is, showing a sand wave pattern only on certain parts of the bank (trough, crest or one of the flanks). Therefore, sand wave characteristics across the sand bank are given by multiple modes, and not only by the fastest growing mode (FGM). This is a major difference with respect to previous studies, focusing on sand wave formation on a horizontal bed with a spatially uniform flow field. There, the pattern of each mode covered the entire domain, so the FGM was the single mode that represented the preferred sand wave pattern. Model results further show sand waves anti‐cyclonically migrating around the sand bank, and crestline veering toward the sand bank crest. These results are in qualitative agreement with observations.