Dynamical models for sand ripples beneath surface waves

We introduce order parameter models for describing the dynamics of sand ripple patterns under oscillatory flow. A crucial ingredient of these models is the mass transport between adjacent ripples, which we obtain from detailed numerical simulations for a range of ripple sizes. Using this mass transport function, our models predict the existence of a stable band of wavenumbers limited by secondary instabilities. Small ripples coarsen in our models and this process leads to a sharply selected final wavenumber, in agreement with experimental observations.Comment: 9 pages. Shortened version of previous submissio

Practical sand transport formula for non-breaking waves and currents

Open Access funded by Engineering and Physical Sciences Research Council Under a Creative Commons license Acknowledgements This work is part of the SANTOSS project (‘SANd Transport in OScillatory flows in the Sheet-flow regime’) funded by the UK's EPSRC (GR/T28089/01) and STW in The Netherlands (TCB.6586). JW acknowledges Deltares strategic research funding under project number 1202359.09. Richard Soulsby is gratefully acknowledged for valuable discussions and feedback on the formula during the SANTOSS project.Peer reviewedPostprin

Localized turbulent flows on scouring granular beds

In many applications a sustained, localized turbulent flow scours a cohesionless granular bed to form a pothole. Here we use similarity methods to derive a theoretical formula for the equilibrium depth of the pothole. Whereas the empirical formulas customarily used in applications contain mumerous free exponents, the theoretical formula contains a single one, which we show can be determined via the phenomenological theory of turbulence. Our derivation affords insight into how a state of dynamic equilibrium is attained between a granular bed and a localized turbulent flow.published or submitted for publicationis peer reviewe