J.L. Hench et al. / Continental Shelf Research 22 (2002) 26152631
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Rs1 is the length scale at which the centrifugal and
for 20 inlets were taken from the literature and
combined with those for the four inlets analyzed in
known as the inertial radius). We now want to
this study (see list in Fig. 7). The inlets chosen are
compare Rs1; the length scale set by the dynamics,
not an exhaustive list, but should be representative
with the inlet geometric length scales. We define
of many inlets found in nature. The velocity scales
the dynamic length and dynamic width as
were chosen from published values for maximum
ebb or flood. In some cases, parameter values were
L=2
W =2
L
W
11
;
estimated from published figures when the actual
Rs1
Rs1
numbers were not cited, so the values used here
where the inlet length and width scales, L and W ;
may not be exact.
The inlet classification diagram using L versus
are divided by two because of symmetry. The
physical interpretations of L and W are
W is shown in Fig. 7. For the 24 inlets analyzed
the parameter space for both L and W spans
straightforward. First consider flow curving
over an order of magnitude. Since f varies only by
around headlands at a very wide inlet (or taken
to the limit, around a single headland, i.e.
a factor of 3 among the inlets, most of the variance
in L and W is due to differences in flow speed
W N). Adjacent to either of the headlands
(varies by a factor of 10) and geometry (L varies by
one would expect the momentum balance to be
a factor of 15, W by a factor of 80). The clustering
cyclostrophic. However, with increasing distance
of data around a line L W suggests that in
from a headland the centrifugal acceleration
nature there is a tendency for the aspect ratio of
diminishes, and the water surface relaxes into a
cross-stream balance with Coriolis. Here the inlet
dynamic lengths to widths to be close to one. The
correlation between L and W may be a
width does not constrain the lateral dynamics, and
W is large. Thus if the inlet is much wider than
consequence of flow having feedback with a
the inertial radius, flow around each headland is
topography. However many of these inlets are
not in strong dynamic communication with the
fictitious (idealized) and others have been modified
opposing headland. Now consider a narrower
by jetties and dredging. We tentatively picked 0.1
inlet. The balance at each of the opposing head-
as the dividing line between ``narrow'' and ``wide'',
lands is still cyclostrophic, but here the inlet width
and between ``short'' and ``long''; based on the
is too narrow for the water surface in the middle of
results of our numerical experiments, this appears
the inlet to relax to geostrophy. Rather, the
to be roughly where the transition takes place.
These lines should provide a rough guide of which
balanced by opposing pressure gradients, forming
dynamical regime one might expect an inlet to fall
a ``dome'' of water across the inlet. Since the
within.
barotropic pressure gradient is uniform with
depth, flow around each headland is effectively
constrained to one side of the inlet, in much the
same way as the solid outside boundary pushes
6. Discussion and conclusions
against the flow around a river bend. In this case
W is small and the flows around each headland
Our analysis of inlet dynamics has shown that
momentum balances can vary significantly over
are in strong dynamic communication. A similar
sub-kilometer scales. Near the inlet headlands, and
dynamical situation exists along the length of the
often over the entire inlet, the first-order balances
channel. When the inertial radius is greater than
the geometric length (small L) then the balance is
are the pressure gradient and a combination of
different nonlinear terms. A common assumption
cyclostrophic along the entire length of the inlet.
Conversely, a large L would indicate that a
in one-dimensional inlet analyses is that the
streamwise pressure gradient is balanced by non-
geostrophic region exists within the inlet straits.
linear bottom friction. Our two-dimensional re-
We use these two parameters to classify and
sults indicate this assumption is only valid within
compare inlets from previous studies. Parameters