LAGRANGIAN FREQUENCY-SPECTRA OF VERTICAL VELOCITY AND VORTICITY IN HIGH-REYNOLDS-NUMBER OCEANIC TURBULENCE

Lagrangian properties of oceanic turbulent boundary layers were measur ed using neutrally buoyant floats. Vertical acceleration was computed from pressure (depth) measured on the floats. An average vertical vort icity was computed from the spin rate of the float. Forms for the Lagr angian frequency spectra of acceleration, phi(a)(omega), and the Lagra ngian frequency spectrum of average vorticity are found using dimensio n analysis. The how is characterized by a kinetic energy dissipation r ate, epsilon, and a large-eddy frequency, omega(0). The float is chara cterized by its size. The proposed non-dimensionalization accurately c ollapses the observed spectra into a common form. The spectra differ f rom those expected for perfect Lagrangian measurements over a substant ial part of the measured frequency range owing to the finite size of t he float. Exact theoretical forms for the Lagrangian frequency spectra are derived from the corresponding Eulerian wavenumber spectra and a wavenumber-frequency distribution function used in previous numerical simulations of turbulence. The effect of finite float size is modelled as a spatial average. The observed non-dimensional acceleration and v orticity spectra agree with these theoretical predictions, except for the high-frequency part of the vorticity spectrum, where the details o f the float behaviour are important, but inaccurately modelled. A corr ection to the exact Lagrangian acceleration spectra due to measurement by a finite-sized float is thus obtained. With this correction, a fre quency range extending from approximately one decade below omega(0) to approximately one decade into the inertial subrange can be resolved b y the data. Overall, the data are consistent with the proposed transfo rmation from the Eulerian wavenumber spectrum to the Lagrangian freque ncy spectrum. Two parameters, epsilon and omega(0), are sufficient to describe Lagrangian spectra from several different oceanic turbulent f lows. The Lagrangian Kolmogorov constant for acceleration, beta(a) equ ivalent to psi(a)/epsilon, has a value between 1 and 2 in a convective ly driven boundary layer. The analysis suggests a Lagrangian frequency spectrum for vorticity that is white at all frequencies in the inerti al subrange and below, and a Lagrangian frequency spectrum for energy that is white below the large-eddy scale and has a slope of -2 in the inertial subrange.