An Analytical Model With a Critical Richardson Number Closure for Sediment‐Stratified Open Channel Flow

Abstract

AbstractAn analytical model is developed for sediment‐stratified open channel flow, with an objective to explore the parameter regime where the self‐induced stratification controls the vertical structure. The model exploits a critical Richardson number closure motivated by a suite of numerical experiments. It is shown that, with Rouse number (relative settling speed) below one, a buoyancy length scale LB, defined as the Monin‐Obukhov length scaled by a factor of 0.1, separates the water column into two regions. Below LB, the buoyancy destruction by sediment stratification is of secondary importance (as indicated by the factor 0.1), and the concentration and velocity closely resemble the unstratified Rousean and logarithmic distributions; Above LB, the sediment feedback in the turbulence kinetic energy balance helps maintain a critically stratified state, and the vertical profiles deviate markedly from the unstratified scaling. Incorporating this closure then leads to analytical expressions for concentration and velocity that compare well with the numerical model and prior studies. The influence of sediment stratification on vertical structure is governed by a dimensionless height LB/h (h is water depth). A smaller LB/h reflects a greater portion of critically stratified water column, indicative of a stronger stratification control. Large near‐bottom buoyancy destruction, as indicated by a large bottom Richardson number, and slow vertical decay, as indicated by a small Rouse number, lead to an expansion of critically stratified region and thus favor sediment stratification. It is shown further that, in sediment‐stratified regime, different concavities of concentration profiles are possible.