Abstract:
Observational work by Thompson (1977) and others has demonstrated
that free topographic Rossby waves propagate northward
up the continental rise south of New England. To study the
dynamical implications of these waves as they approach the
shelf, Beardsley, Vermersch, and Brown conducted an experiment
in 1976 (called NESS76) in which some moored instruments were
strategically placed across the New England continental margin
to measure current, temperature, and bottom pressure for about
six months.
An analytical model has been constructed to study the propagation
of free topographic Rossby waves in an infinite wedge filled with a uniformly stratified fluid. The problem is found after some coordinate transformations to be identical to the
corresponding surface gravity wave problem in a homogeneous fluid, but with the roles of the surface and bottom boundaries interchanged. Analytical solutions are thus available for both
progressive and trapped waves, forming continuous and discrete
spectra in the frequency space. The separation occurs at a
nondimensional frequency δ = S, defined as (N/f) tanθ*, where
N and f are the Brunt-Väisälä and inertial frequencies, and
tanθ* is the bottom slope. Since an infinite wedge has no
intrinsic length scales, the only relevant nondimensiona1
parameters are the frequency δ and the Burger number S. Thus,
stratification and bottom slope play the same dynamical role,
and the analysis is greatly simplified. Asymptotic solutions
for the progressive waves have been obtained for both the far
field and small S which enable us to examine the parameter
dependence of some of the basic wave properties in the far
field, and the spatial evolution of the wave amplitude and
phase as they approach the apex when S is small. The general
solution is then presented and discussed in some detail. The
eigenfrequencies of the trapped modes decrease when S decreases
and reduce to the short wave limit of Reid's (1958) second
class, barotropic edge waves when S approaches zero. The modal
structure broadens as S increases to some critical value above
which no such coastally-trapped modes exist.
To simulate more closely the dynamical processes occurring
near the continental margin, a numerical model incorporating a
more realistic topography than an infinite wedge has been constructed.
With stratification imposing an additional harrier,
the model suggests that the maximum energy flux transmission
coefficient obtained in Kroll and Niiler's barotropic model
(1976) is likely an upper bound. Also in the presence of the
finite slope changes, the baroclinic fringe waves generated
near the slope-rise junction may form an amphidromic point at
some mid-depth and locally reverse the direction of the phase
propagation above it. These baroclinic fringe waves also cause
an offshore heat flux over the continental rise which, combined with the onshore heat flux generated over the slope region in a
frictionless model, induces, across the transect, a mean flow
pattern of two counter-rotating gyres with downwelling occurring
near the slope-rise junction. Bottom friction always generates
an offshore heat flux and therefore modifies this mean
flow pattern over the slope region. The induced longshore mean
flow is approximately geostrophically balanced and generally
points to the left facing the shoreline, but its direction can
be reversed where the baroclinic fringe waves dominate. The
mean thermal wind relation implies a generally denser slope
water than that farther offshore.
Some of the model predictions are compared with the data
taken from NESS76. The comparisons are generally consistent,
suggesting that topographic Rossby wave dynamics may play an
important role for the low frequency motions near continental
margins.