Parameterization of oscillating boundary layers in lakes and coastal oceans

Abstract

Oscillating turbulent bottom boundary layers (BBLs) occur in lakes and coastal oceans. At the mesoscale level, their kinematics are usually characterized by assuming either laminar or steady turbulent flow, and applying analytical solutions or semi-empirical correlations; e.g. log-law, Stokes’ second problem, inertial dissipation method (IDM), Batchelor fitting to temperature microstructure method (TMM). To investigate the ability of these models to capture oscillating turbulent BBLs, we have performed large eddy simulations (LES) and direct numerical simulations (DNS) for Reynolds numbers (Reδs; based on the Stokes layer thickness) between 20 and 3600. The velocity profiles showed logarithmic behavior throughout the cycle, in fully turbulent flows (error less than 2% for Reδs>3000), but the log-law was only accurate during turbulent bursts in the later stage of the acceleration phase for Reδs<550. Stokes’ second problem predicted the velocity profile in laminar or disturbed laminar flow (errors less than 10% for Reδs<500). At high Reynolds number (Reδs=3600), LES shows that the dissipation of turbulent kinetic energy from the IDM is more accurate than that from the log-law, particularly during changes in flow direction. The difference between the dissipation estimated from field observations (using IDM and TMM) and from idealized LES, however, suggest that measurement errors may predominate over uncertainties in simulation of boundary conditions and methodological errors in field applications.