Abstract:
The structure of the inertial peak in deep ocean kinetic energy
spectra is studied here. Records were obtained from Polymode arrays
deployed in the Western North Atlantic Ocean (40°W to 70°W, 15°N
to 42°N). The results are interpreted both in terms of local sources
and of turning point effects on internal waves generated at lower
latitudes.
In most of the data, there is a prominent inertial peak slightly
above f; however, the peak height above the background continuum varies
with depth and geographical environment. Three classes of environment
and their corresponding spectra emerge from peak height variations:
class 1 is the 1500 m level near the Mid-Atlantic Ridge, with the
greatest peak height of 18 db; class 2 includes (a) the upper ocean
(depth less than 2000 m), (b) the deep ocean (depth greater than 2000 m)
over rough topography, and (c) the deep ocean underneath the Gulf
Stream, with intermediate peak height of 11.5 db; class 3 is the deep
ocean over smooth topography, with the lowest peak height of 7.5 db.
Near f, the horizontal coherence scale is 0(60 km) at depths from 200 m
to 600 m, and the vertical coherence scale is O(200 m) just below the
main thermocline.
A one turning point model is developed to describe inertial waves at
mid-latitudes, based on the assumption that inertial waves are randomly
generated at lower latitudes (global generation) where their frequency-wavenumber
spectrum is given by the model of Garrett and Munk (1972 a,
1975). Using the globally valid wave functions obtained by Munk and
Phillips (1968), various frequency spectra near f are calculated
numerically. The model yields a prominent inertial peak of 7 db in the
horizontal velocity spectrum but no peaks in the temperature spectrum.
The model is latitudinally dependent: the frequency shift and bandwidth
of the inertial peak decrease with latitude; energy level near f is
minimum at about 30° and higher at low and high latitudes. The
observations of class 3 can be well-described by the model; a low zonal
wavenumber cutoff is required to produce the observed frequency shift of
the inertial peak.
The differences between the global generation model and the
observations of class 1 and class 2 are interpreted as the effects of
local sources. A locally forced model is developed based on the
latitudinal modal decomposition of a localized source function.
Asymptotic eigensolutions of the Laplace's tidal equation are therefore
derived and used as a set of expansion functions. The forcing is through
a vertical velocity field specified at the top or bottom boundaries of
the ocean. For white noise forcing, the horizontal velocity spectrum of
the response has an inertial peak which diminishes in the far-field.
With the forcing located at either the surface or the bottom, several
properties of the class 2 observations can be described qualitatively by
a combination of the global and local models.
The reflection of inertial waves from a turbulent benthic boundary
layer is studied by a slab model of given depth. Frictional effects are
confined to the boundary layer and modelled by a quadratic drag law. For
given incident waves, reflection coefficients are found to be greater
than 0.9 for the long waves which contain most of the energy. This
result suggests that energy-containing inertial waves can propagate over
great distance as is required by the validity of the model of global
generation.