Lagrangian Measurements of Waves and Turbulence in Stratified Flows

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Abstract
Stratified flows are often a mixture of waves and turbulence. Here, Lagrangian frequency is used to distinguish these two types of motion. A set of 52 Lagrangian float trajectories from Knight Inlet and 10 trajectories from below the mixed layer in the wintertime northeast Pacific were analyzed using frequency spectra. A subset of 28 trajectories transit the Knight Inlet sill where energetic internal waves and strong turbulent mixing coexist. Vertical velocity spectra show a progression from a nearly Garrett–Munk internal wave spectrum at low energies to a shape characteristic of homogeneous turbulence at high energies. All spectra show a break in slope at a frequency close to the buoyancy frequency N. Spectra from the Knight Inlet sill are analyzed in more detail. For “subbuoyant” frequencies (less than N) all 28 spectra exhibit a ratio of vertical-to-horizontal kinetic energy that varies with frequency as predicted by the linear internal wave equations. All spectra have a shape similar to that of the Garrett–Munk internal wave spectrum at subbuoyant frequencies. These motions are much more like waves than turbulence. For “superbuoyant” frequencies (greater than N) all 28 spectra are isotropic and exhibit the −2 spectral slope of inertial subrange homogeneous turbulence. These motions appear to be turbulent. These data suggest that stratified flows may be modeled as the sum of nearly isotropic turbulence with superbuoyant Lagrangian frequencies and anisotropic internal waves with subbuoyant Lagrangian frequencies. The horizontal velocities are larger than the vertical velocities for the internal wave component but approximately equal for the turbulent component. Vertical kinetic energy is therefore a better indicator of turbulent kinetic energy than is horizontal or total kinetic energy.