B. R. Sutherland,
J. Phys. Oceanogr., 26, pp 2398--2419 (1996).
It is proposed that shear instability of the upper flank of the equatorial
undercurrent may generate, under a broad range of conditions,
downward propagating internal gravity waves (IGW) of large amplitude.
The generation mechanism is shown to require only that the
background stratification is weak where the shear is large
(i.e. in the mixing region) and that the
stratification is sufficiently
large in the far field (i.e. near the thermocline).
In a series of studies, the generation of IGW from unstable
shear flows is examined.
is used to predict under what circumstances the generation of IGW may
be large and fully nonlinear simulations restricted to two dimensions
are employed to provide estimates of the degree of vertical mixing
and of the vertical transport of horizontal momentum by IGW.
In particular, the simulations demonstrate that when
large amplitude IGW are generated by
the mean flow itself is significantly
decelerated in the mixing region.
The momentum flux
associated with the radiating IGW
is large and it is proposed that these may
act in part as a momentum source to the deep equatorial countercurrents.
B. R. Sutherland,
Phys. Fluids, 8, pp 430--441 (1996).
It is shown by way of nonlinear numerical
simulations of flow restricted to two dimensions
a compact wavepacket of
large-amplitude internal gravity waves
incident upon a weakly stratified region in
which the buoyancy frequency is less
than the frequency of the wavepacket may partially transmit
energy into this region through the generation of a wavepacket
of lower frequency.
In part, the transmission of waves occurs
due to the transient nature of
the forcing by the incident wavepacket, but if the amplitude of the
wavepacket is moderately large,
weakly nonlinear effects may act to significantly increase the proportion
of the wavepacket that is transmitted.
For a range of simulations
initialised with wavepackets of different amplitude and vertical
extent, the characteristics of the reflected and transmitted waves are
reflection coefficients are calculated.
An explanation for how the nonlinear transmission mechanism operates
is given by
demonstrating that the wave induced mean-flow,
which is shown to be approximately equal to the horizontal wave
expressed in Eulerian variables,
acts to adjust the frequency of the incident waves.
B. R. Sutherland and A. E. Jacobs,
Complex Systems, 8 (6), pp 385--405 (1994).
that self-organization may provide a mechanism
by which power-law cluster distributions of mobile prey
(e.g. fish, phytoplankton) may develop; in contrast,
such distributions have often been attributed to
scaling of the background environment.
Evidence supporting our proposal is provided by examining
the dynamics of a cellular automaton-like model of a predator-prey system.
The model, which is discrete in space and time,
is robust and evolves to a state with oscillatory, phase-shifted populations
for a large range of parameter values, namely the predator and
prey breeding times and the predator starvation time.
The distribution function D(s) of the prey cluster sizes s
has roughly power-law form, s^(-alpha), over
a range of moderately large sizes but is
cut off at large s.
The exponent alpha ~= 1.35 +/- 0.10
depends only weakly on the parameters of the model.
B. R. Sutherland, C. P. Caulfield, and W. R. Peltier,
J. Atmos. Sci, 51, pp 3261--3280 (1994).
Two mechanisms are proposed whereby
internal gravity waves (IGW) may radiate from a
linearly unstable region of Boussinesq parallel flow that is
characterized in the far field by constant horizontal velocity and
Through what is herein referred to as ``primary generation'',
IGW may be directly
excited by linear instability of the initial state parallel shear flow.
Characteristically, these waves propagate with horizontal phase speed and
wave number equal to that of the most unstable mode of linear stability
Through the second mechanism, referred to as ``secondary generation'',
IGW may be excited via nonlinear modification of the initial
instability into a form that couples strongly to a large
amplitude outgoing internal wave field.
We propose that the primary generation of IGW may occur provided a
penetration condition, which we derive on the basis on linear theory,
is satisfied. The penetration condition provides
a limit on the growth rate of a
disturbance of any particular frequency that is capable of propagating
into the far field.
This hypothesis is supported by a sequence of representative
nonlinear numerical simulations in two spatial dimensions for
both free mixing layer and jet
flows with horizontal velocity profiles U(z)=tanh(z) and
U(z)=sech^2(z), respectively. For the purpose
of these analyses, the fluid density is taken to be such
that the square of the Brunt-Vaisala frequency
is given by N^2(z)=J tanh^2(z/R).
allows both for the development of large-scale eddies in the
region of low static stability and, in the far field
where N^2 ~= J is positive and approximately constant,
for the radiation of a broad frequency spectrum of IGW.
B. R. Sutherland and W. R. Peltier,
Phys. Fluids, 6 (3), pp 1267--1284 (1994).
The nonlinear evolution of an unstable symmetric
jet in incompressible, density stratified fluid is simulated
When N^2 is constant and near zero, like-signed
vortices pair by way of an instability of the mean flow to a subharmonic
disturbance with wavelength twice that of the most unstable
mode of linear theory.
For small but finite and constant values of N^2,
however, the individual vortex cores are
strained and vorticity is generated at small scales
by the action of baroclinic
torques. In this case, the mean flow of the fully evolved jet
is stable to subharmonic disturbances.
The linear stability of the two-dimensional nonlinear basic
states to three dimensional perturbations is examined in detail.
stability analysis it is inferred that jet flow with stratification
characterized by constant N^2 is a poor
candidate for IGW generation.
the existence of an efficient mechanism whereby
IGW may be radiated to infinity from the jet core is demonstrated
via simulations initialized with a density profile such that
This mechanism is expected to be an important contributor to the
wave field observed in a variety of geophysical circumstances.
B. R. Sutherland and W. R. Peltier,
Geophys. Astrophys. Fluid Dyn., 66, pp 101--131 (1992).
We study numerically the two dimensional linear instabilities of
an incompressible, inviscid, density stratified, symmetric
jet as a function of a width parameter, D.
In the limit of infinite D, the maximum growth rate of temporal
approaches that of the shear flow on either flank of the jet.
The growth rate need not
approach this limit monotonically, however.
For some stratified flows it is possible that the
odd (varicose) mode of a jet with sufficiently large width
may grow more rapidly than the even (sinuous) mode.
We also examine spatiotemporal instabilities of the
Bickley profile, focusing specifically upon the identification of the regime
of parameter space in which
the flow is absolutely or convectively unstable.
Finally, our methods of spatiotemporal linear stability analysis are applied
to a more realistic asymmetric jet which mimics the internal wave related
flow that develops
in the lee of a topographic obstacle when ``breaking'' occurs.
This analysis appears to bear
strongly upon the interaction that occurs subsequent to wave breaking
that leads to intense wave, mean-flow interaction.
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Bruce R. Sutherland, Jan 96,