A Spectral Technique for Estimating Turbulent Stress, Scalar Flux Magnitude, and Eddy Viscosity in the Ocean Boundary Layer under Pack Ice

Abstract

The hypothesis is tested that, for the planetary boundary layer, turbulent vertical velocity (w) spectral density, normalized by u2?/k (u2? is Reynolds stress magnitude and k is wavenumber: 2π times frequency divided by mean flow speed), is a ?universal? function of nondimensional wavenumber k/kmax, where kmax is the wavenumber at the peak in the area-preserving log?log w spectrum. Data from clusters of turbulence-measuring instruments deployed through the ocean boundary layer beneath pack ice during the yearlong Surface Heat Budget of the Arctic (SHEBA) project were analyzed by averaging spectra in 3-h bins, then nondimensionalizing weighted w spectral density by directly measured Reynolds stress magnitude and wavenumber by kmax. In the outer boundary layer, normalized spectra were remarkably uniform, suggesting that (i) the fundamental turbulence scale is inversely proportional to kmax and (ii) the w wavenumber spectrum by itself may be used to estimate local stress magnitude and eddy viscosity. The arguments are extended to a scalar variable (temperature) using a combination of the w and scalar spectra, in a way somewhat analogous to the inertial dissipation method used for the atmospheric surface layer. Spectral estimates of turbulent heat flux agreed reasonably well with direct covariance estimates. The structure of the vertical velocity spectrum in the outer boundary layer implies that, in a neutrally stratified, homogeneous flow, production of turbulent kinetic energy (TKE) exceeds dissipation by a significant factor, with the balance provided mainly by vertical TKE turbulent flux divergence.