Numerical problems in simulating tidal flows with a frictional‐velocity‐dependent eddy viscosity and the influence of stratification

Abstract

AbstractThe paper deals with the accurate determination of tidal current profiles in both homogeneous and stratified regions when a no‐slip condition is used at the seabed with a flow‐dependent eddy viscosity related to the depth‐mean current or the bed frictional velocity.Calculations show that it is essential to accurately resolve the high‐shear region which occurs at the bed and across the pycnocline/thermocline in the case of stratified flow. A computationally accurate and economic method of resolving these regions is demonstrated using the Galerkin method with a set of basis functions designed to accurately reproduce the high‐shear layers which occur in these regions.With a flow‐independent eddy viscosity a stability analysis can be readily performed and an unconditionally stable algorithm developed. However, with a flow‐dependent viscosity, in particular a viscosity computed from the frictional velocity, a non‐linear numerical instability can occur. A method of maintaining numerical stability in this case is also described.The importance of near‐bed resolution to the computed value of the frictional velocity is demonstrated and its influence on the total tidal velocity profile is illustrated by a number of idealized calculations using various eddy viscosity formulations.The influence of stratification on the computed tidal profiles is shown in the latter part of the paper.