Two-Dimensional Wavenumber Spectra on the Horizontal Submesoscale and Vertical Finescale

Abstract

Horizontal and vertical wavenumbers (k_x, k_z) immediately below the Ozmidov wavenumber (N³/ε)^1/2 are spectrally distinct from both isotropic turbulence (k_x, k_z > 1 cpm) and internal waves as described by the Garrett-and-Munk (GM) model spectrum (k_z < 0.1 cpm). Towed CTD chain, augmented with concurrent EM-APEX profiling float microstructure measurements and shipboard ADCP surveys, are used to characterize 2D wavenumber (k_x, k_z) spectra of isopycnal slope, vertical strain and isopycnal salinity-gradient on horizontal wavelengths of 50 m - 250 km and vertical wavelengths of 2 - 48 m. For k_z < 0.1 cpm, 2D spectra of isopycnal slope and vertical strain resemble GM. Integrated over the other wavenumber, the isopycnal slope 1D k_x spectrum exhibits a roughly + 1/3 slope for k_x > 3 × 10⁻³ cpm, and the vertical strain 1D k_z spectrum a −1 slope for k_z > 0.1 cpm, consistent with previous 1D measurements, numerical simulations and anisotropic stratified turbulence theory. Isopycnal salinity-gradient 1D k_x spectra have a + 1 slope for k_x > 2 × 10⁻³ cpm, consistent with nonlocal stirring. Turbulent diapycnal diffusivities inferred in the (i) internal-wave subrange using a vertical strain-based finescale parameterization are consistent with those inferred from finescale horizonal wavenumber spectra of (ii) isopycnal slope and (iii) isopycnal salinity-gradients using Batchelor model spectra. This suggests that horizontal submesoscale and vertical finescale subranges participate in bridging the forward cascade between weakly nonlinear internal waves and isotropic turbulence, as hypothesized by anisotropic turbulence theory. Horizontal and vertical wavenumbers (k_x, k_z) immediately below the Ozmidov wavenumber (N³/ε)^1/2 are spectrally distinct from both isotropic turbulence (k_x, k_z > 1 cpm) and internal waves as described by the Garrett-and-Munk (GM) model spectrum (k_z < 0.1 cpm). Towed CTD chain, augmented with concurrent EM-APEX profiling float microstructure measurements and shipboard ADCP surveys, are used to characterize 2D wavenumber (k_x, k_z) spectra of isopycnal slope, vertical strain and isopycnal salinity-gradient on horizontal wavelengths of 50 m - 250 km and vertical wavelengths of 2 - 48 m. For k_z < 0.1 cpm, 2D spectra of isopycnal slope and vertical strain resemble GM. Integrated over the other wavenumber, the isopycnal slope 1D k_x spectrum exhibits a roughly + 1/3 slope for k_x > 3 × 10⁻³ cpm, and the vertical strain 1D k_z spectrum a −1 slope for k_z > 0.1 cpm, consistent with previous 1D measurements, numerical simulations and anisotropic stratified turbulence theory. Isopycnal salinity-gradient 1D k_x spectra have a + 1 slope for k_x > 2 × 10⁻³ cpm, consistent with nonlocal stirring. Turbulent diapycnal diffusivities inferred in the (i) internal-wave subrange using a vertical strain-based finescale parameterization are consistent with those inferred from finescale horizonal wavenumber spectra of (ii) isopycnal slope and (iii) isopycnal salinity-gradients using Batchelor model spectra. This suggests that horizontal submesoscale and vertical finescale subranges participate in bridging the forward cascade between weakly nonlinear internal waves and isotropic turbulence, as hypothesized by anisotropic turbulence theory.