Mixture Theory Model of Vortex Sand Ripple Dynamics

Introduction: Our lack of understanding of the evolution of seabed roughness (e.g., sand ripples) in sandy coastal regions inhibits our ability to accurately forecast waves and currents and ultimately large-scale morphodynamics. Most wave and circulation models input a constant bottom roughness value (i.e., friction factor) or fixed bed profile that parameterizes the effects of seabed roughness, ignoring any temporal or spatial response of the bed to changing wave and sediment conditions. However, seabed roughness length scales may span three orders of magnitude (e.g., from grain-scale variations to sand ripples), causing significant differences in boundary layer turbulence, wave energy dissipation, coastal circulation, and sediment transport. The constant evolution of the seabed also has significant implications for naval operations (e.g., ocean acoustics, mine hunting missions, littoral navigation). All bathymetric change ultimately results from sediment entrainment and deposition occurring at the fluid-sediment interface inside the wave bottom boundary layer (WBBL). Despite the apparent accessibility of the phenomena, highly turbulent, sedimentladen flow remains poorly understood and difficult to quantify mainly because of our failure to understand the fundamental interaction forces driving sediment transport. However, with recent advances in high performance computing, it is now possible to perform highly resolved simulations of fluid-sediment dynamics in the WBBL that accurately model the evolution of seabed roughness for sandy substrates. The highresolution model described here (SedMix3D) is based on mixture theory. Although the approach is well known and understood for industrial and biological applications, it has never before been applied to coastal sediment dynamics.