Abstract:
Oceanic profiles of temperature, salinity, horizontal velocity, rate of
dissipation of turbulent kinetic energy (ε) and rate of dissipation of thermal
variance (χ) are used to examine the parameterization of turbulent mixing
in the ocean due to internal waves. Turbulent mixing is quantified through
eddy diffusivity parameterizations of the mass (Kρ; Osborn, 1980) and heat
fluxes (Kτ; Osborn and Cox, 1972) in turbulent production/dissipation
balances. Turbulence in the ocean is generally held to result from the
occurrence of shear instability in regions where the Richardson number is
locally supercritical (i.e. Ri ≤ 1/4), permitting the growth of small-scale
waves which break and result in turbulent mixing. The occurrence of
shear instability results from the local intensification of the shear in the
internal wave field. The energy dissipated in such events is provided by the
energy flux to higher wavenumber due to nonlinear wave/wave interactions
on scales of 10's to 100's of meters. In turn, the strength of the wave/wave
interactions depends generally on the energy content of the internal wave
field, which can vary considerably over even larger scales due to the presence
of topography or background flows. The magnitude of turbulent mixing
is linked to internal wave dynamics by equating the turbulent dissipation
with the energy flux through the vertical wavenumber spectrum under
the priviso that the model spectrum which forms the basis for the analysis
is statistically stationary with respect to the nonlinear interactions.
Dynamical models (McComas and Muller, 1981; Henyey et al., 1986) indicate
that the Garrett and Munk (GM; Munk, 1981) spectrum is stationary.
Observations from the far field of a seamount in a region of negligible
large-scale flow were examined to address the issue of the buoyancy scaling
of ε. These data exhibited large variations in background stratification with
depth, but the internal wave characteristics were not substantially differentiable
from the GM prescription. The magnitude of ε and its functional
dependence upon internal wave energy levels (E) and buoyancy frequency
(N) was best described by the dynamical model ofHenyey et al. (1986) (ε ~ E2N2). The Richardson number scaling model of Kunze et al. (1990)
produced consistent estimates. A second dynamical model, McComas and
Muller (1981), predicted an appropriate (E,N) scaling, but overestimated the observed dissipation rates by a factor of five. Two kinematical dissipation
parameterizations (Garmett and Holloway (1984) and Munk (1981)) predicted
buoyancy scalings of N3/2 which were inconsistent with the observed scaling.
Data from an upper-ocean front, a warm core ring and a region of
steep topography were analyzed in order to examine the parameter
dependence of E in internal wave fields which exhibited potentially nonstationary
characteristics. Evidence was provided which implied the
internal wave field in an upper ocean front was interacting with and
modified by the background flow. Inhomogeneity and anisotropy of the
internal wave field were noted in that data set. The model of Gregg (1989),
which in turn was based upon the model of Henyey et al., effectively
collapsed the observed diffusivity estimates from the front. The warm core
ring profiles were noted to be anisotropic, dominated by near-inertial
frequencies and to have a peaked vertical wavenumber shear spectrum.
The data from a region of steep topography were noted to have a peaked
vertical wavenumber spectrum and were characterized by higher than GM
frequency motions. For the latter two data sets, application of a frequency
based correction to the Henyey et al. model (Henyey, 1991) reduced more
than an order of magnitude scatter in the parameterized estimates of E to
less than a factor of four. Of the possible non-equilibrium conditions in the
internal wave field, the (E,N) scaled dissipation rates were most sensitive to
deviations in wave field frequency content.
On the basis of a number of theoretical Richardson number
probability distributions (Ri = N2/S2, where S2 is the sum of the squared
vertical derivatives of horizontal velocity), the nominal dissipation scaling
of the Kunze et al. model was determined to be E2N3. This scaling is altered
to the observed ε ~ E2N2 scaling by a statistical dependence between N2 and
S2 which reduces the occurrence of supercritical Ri values. This statistical
dependence is hypothesized to be an effect of the turbulent momentum and
buoyancy fluxes on the internal wave shear and strain profiles caused by
shear instability. The statistical dependence between N2 and S2 exhibited a
buoyancy scaling which was interpreted as resulting from the decreasing
ratio between the time scale of the shear instability mechanism [T- 2π/N]
and the adiabatic time scale [T - 2π/(Nf)1/2] of the internal wave field (f is the
Coriolis parameter). This phenomenology is interpreted in light of
saturated spectral theories which suggest that the magnitude and shape of
the vertical wavenumber spectrum is controlled by instability mechanisms
at large wavenumber ( ≥ .1 cpm). We argue that saturated spectral theories
are valid only in the limit where a separation exists between the two time
scales, i.e. for large N, low internal wave frequency content, and small f.
These results have immediate implications for oceanic mixing
driven by internal wave motions. First, background diffusivities are small:
at GM energy levels, Kρ - .03x10-4 m2/s (Kρ = .25ε/N2). Secondly, since Kρ is
independent of N at constant E, some process or collection of processes
must be responsible for heightened E values in the abyss if internal waves
cause the 0(1-10x10-4 m2/s) diffusivities generally inferred from deep ocean
hydrographic data. We view internal wave reflection and/or internal wave
generation associated with topographic features to be likely candidates.