Prescriptions for Heat Flux and Entrainment Rates in the Upper Ocean during Convection

A. Anis College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

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J. N. Moum College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon

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Abstract

A detailed investigation of the upper ocean during convection reveals

  1. • the vertical structure of potential temperature, θ, to be steady in time, and

  2. • the current shear to vanish in the bulk of the mixed layer.

These imply that a “slab”-type model may be an adequate representation of the convective ocean boundary layer (OBL). In contrast, when convection is not the dominant forcing mechanism, the OBL is stratified and can support a significant current shear. This indicates the inadequacy of “slab” models for the nonconvective OBL.

Two independent estimates of the vertical heat flux profile in the convective OBL were made. The first estimate results from heat conservation and the steadiness of the vertical structure of potential temperature. The second estimate is based on the turbulent kinetic energy (TKE) balance and the vertical profiles of TKE dissipation rate. The estimates are consistent and suggest that the nondimensional vertical heat flux due to turbulence has a linear depth dependence of the form 1 + ah(z/D), where z is the depth, D is the mixed layer depth, and ah is a constant with a mean value of 1.13, consistent with numerical and laboratory results and with observations in the convective atmospheric boundary layer. An estimate of the entrainment rate, derived from observed quantities, is ∼1 × 10−5 m s−1. This is within a factor of 2 of estimates derived from alternative formulations.

Abstract

A detailed investigation of the upper ocean during convection reveals

  1. • the vertical structure of potential temperature, θ, to be steady in time, and

  2. • the current shear to vanish in the bulk of the mixed layer.

These imply that a “slab”-type model may be an adequate representation of the convective ocean boundary layer (OBL). In contrast, when convection is not the dominant forcing mechanism, the OBL is stratified and can support a significant current shear. This indicates the inadequacy of “slab” models for the nonconvective OBL.

Two independent estimates of the vertical heat flux profile in the convective OBL were made. The first estimate results from heat conservation and the steadiness of the vertical structure of potential temperature. The second estimate is based on the turbulent kinetic energy (TKE) balance and the vertical profiles of TKE dissipation rate. The estimates are consistent and suggest that the nondimensional vertical heat flux due to turbulence has a linear depth dependence of the form 1 + ah(z/D), where z is the depth, D is the mixed layer depth, and ah is a constant with a mean value of 1.13, consistent with numerical and laboratory results and with observations in the convective atmospheric boundary layer. An estimate of the entrainment rate, derived from observed quantities, is ∼1 × 10−5 m s−1. This is within a factor of 2 of estimates derived from alternative formulations.

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