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On the Turbulent Mixing Length in the Oceanic Boundary Layer

Miles G. McpheeMcPhee Research Company Naches Washington

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Abstract

Turbulence measurements from under drifting pack ice illustrate the distribution of turbulent mixing length in the well-mixed layer of the upper ocean. Mixing length (λ ≡ K/u*, where K and u* are the local eddy viscosity and square root of Reynolds stress, respectively) is found to vary inversely with wavenumber at the peak in the weighted vertical velocity variance spectrum: λ = cλ/kmax. This relation provides an empirical tool for making local estimates of eddy viscosity if the Reynolds stress is known, or alternatively, deriving fluxes via the inertial-dissipation method in the outer part of the rotational boundary layer. The vertical structure of λ is described for conditions of (i) neutral stratification (negligible surface buoyancy flux) under thick ice. (ii) stable stratification under rapidly melting ice, and (iii) statically unstable conditions from intense freezing. The last example, obtained during the 1992 Lead Experiment, included dime measurements of turbulent salinity flux, 〈wS′〉. As an analog to Monin-Obukhov similarity for the atmospheric surface layer, a simple algorithm is developed for calculating λ in the mixed layer in term of displacement from the interface, z; boundary values of friction velocity, u*0, and buoyancy flux, 〈wb′〉0; the planetary length scale, u*0/|fr| (for neutral and stable conditions); and mixed layer depth, |zml (unstable conditions). A simple numerical model demonstrates the algorithm by simulating a hypothetical example of intense wind stirring in the wintertime Weddell Sea.

Abstract

Turbulence measurements from under drifting pack ice illustrate the distribution of turbulent mixing length in the well-mixed layer of the upper ocean. Mixing length (λ ≡ K/u*, where K and u* are the local eddy viscosity and square root of Reynolds stress, respectively) is found to vary inversely with wavenumber at the peak in the weighted vertical velocity variance spectrum: λ = cλ/kmax. This relation provides an empirical tool for making local estimates of eddy viscosity if the Reynolds stress is known, or alternatively, deriving fluxes via the inertial-dissipation method in the outer part of the rotational boundary layer. The vertical structure of λ is described for conditions of (i) neutral stratification (negligible surface buoyancy flux) under thick ice. (ii) stable stratification under rapidly melting ice, and (iii) statically unstable conditions from intense freezing. The last example, obtained during the 1992 Lead Experiment, included dime measurements of turbulent salinity flux, 〈wS′〉. As an analog to Monin-Obukhov similarity for the atmospheric surface layer, a simple algorithm is developed for calculating λ in the mixed layer in term of displacement from the interface, z; boundary values of friction velocity, u*0, and buoyancy flux, 〈wb′〉0; the planetary length scale, u*0/|fr| (for neutral and stable conditions); and mixed layer depth, |zml (unstable conditions). A simple numerical model demonstrates the algorithm by simulating a hypothetical example of intense wind stirring in the wintertime Weddell Sea.

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