Mixing in an Internal Wave Bottom Boundary Layer: A Simple Model Predicts Entrainment above a Sloping Bed during the Stabilizing Phase of Strain-Induced Periodic Stratification
Year: 2025
Type: article
Abstract: Mixed layer models have been applied to diverse environments, yet a complete parameterization does not exist for cases with significant boundary-parallel density gradients, where strain-induced periodic stratification (SIPS) influences mixed layer thickness. We developed a parameterization for entrainment into an internal wave bottom boundary layer above a sloping bed. This parameterization accounts for two turbulent buoyancy fluxes. The first flux (Fe) is proportional to entrainment, whereas the second (Fs) redistributes buoyancy as required to maintain a mixed layer in the presence of stabilizing SIPS. The turbulent energy loss associated with Fs reduces entrainment, with reduction proportional to the ratio h/LMO, where h is the mixed layer thickness and LMO is a Monin–Obukhov length defined using Fs. This ratio resembles the Simpson number often used to analyze SIPS in estuaries. Entrainment is almost unaffected by Fs when h/LMO ≪ 1, whereas entrainment halts when h/LMO ∼ 1. The entrainment parameterization was used to close boundary layer–averaged equations of momentum and buoyancy. The resulting model accurately described the thickening, velocity, and buoyancy of mixed layers observed above a sloping lakebed. Accounting for Fs improved predictions. Therefore, the simple parameterization improves model skill and provides a scaling quantifying the importance of SIPS to near-bed mixing. Significance Statement Mixing near sloping topography is important for the transport of heat, chemicals, and organisms in oceans and lakes. For example, near-bed mixing may influence mean vertical circulation, even very far from ocean or lake boundaries. Through the process of “strain-induced periodic stratification” (SIPS), oscillating upslope and downslope flows associated with internal waves and tides cause major fluctuations in near-bed stratification and mixing. This study derives a very simple model that conserves momentum and buoyancy, while accounting for SIPS. The model accurately described the thickening, velocity, and buoyancy of a mixed layer observed above a sloping lakebed. Parameterization of SIPS improves model skill and provides a scaling determining the importance of SIPS to near-bed mixing.
Source: Journal of Physical Oceanography
Authors: Jeffrey R. Nielson, Stephen M. Henderson
Institutions: Utah State University, Washington State University Vancouver
Language: English
Subfield: Oceanography
Field: Earth and Planetary Sciences
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4410888697