Stability of a stratified shear flow for the modelling of estuary bed

Abstract

To improve the understanding of mud resuspension and the behaviour of mud flow in estuaries, a parametric stability analysis of a shear flow is carried out with a model of two miscible fluid layers of different properties. The shear layer is modelled by asymmetric erf(z) vertical profiles of the same thickness for each quantities. The upper layer, composed of water, is considered as a Newtonian fluid. The lower layer mud flow is also considered as a Newtonian fluid of high density and high viscosity. A linear stability study, realized with the code LiSa developed at IMFT (Institut de Mecanique des Fluides de Toulouse), explores the influence of the principal control parameters: the Richardson number, the Reynolds number and viscosity ratio between the two fluids. Direct numerical simulations (DNS) performed with the code JADIM of IMFT are used to compute the temporal evolution of these flows and are compared with the linear stability study. Both approaches describe consistently the development of the bidimensional primary instability. The computed critical Richardson number is close to 0.25. Results show that for high Reynolds numbers, evaluated at the interface, there is no influence of the viscosity ratio with respect to the primary instability. For Reynolds number lower than 10, the viscosity has a destabilizing effect: a bigger difference of viscosity leads to a more important growth rate. This property can result in higher instability growth rates for highly viscous mud flows when submitted to a velocity shear in real estuaries. Secondary instabilities and the other processes leading to an eventual three-layer flow are documented through DNS simulations. Different secondary instabilities are observed depending on the Reynolds number at the interface. Likely outcomes of this study are new parameterizations of the bed sediment flux in realistic modelling of estuaries.