Rc. Lien et al., LAGRANGIAN FREQUENCY-SPECTRA OF VERTICAL VELOCITY AND VORTICITY IN HIGH-REYNOLDS-NUMBER OCEANIC TURBULENCE, Journal of Fluid Mechanics, 362, 1998, pp. 177-198
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.