917
APRIL 2003
HENCH AND LUETTICH
U2
s
The principal sexdiurnal overtide, M 6 , is primarily
f Us
g
0,
Us
(5)
generated by nonlinear bottom friction (Parker 1991).
t
n
Rs
l
ocal
centrifugal
Coriolis
normal
rotary
acceleration
acceleration
direction
ent. At the idealized inlet M 6 is largest within the inlet
acceleration
pressure
throat, where flow speeds are largest. For Beaufort Inlet,
gradient
the largest M 6 is not in the inlet throat, but rather in the
force
shallow sound just east of the inlet, where flow speeds
where Us(x, y, t) is the streamwise velocity, (x, y, t)
are highest and depths are shallow. The higher har-
is the streamline angle (the angle between the positive
monics of M 8 and M10 (not shown) show spatial patterns
x axis and the local flow vector), and Rs(x, y, t) is the
similar to M 4 and M 6 , respectively, but were at least a
streamwise radius of curvature. With this choice of co-
factor of 210 smaller than both and thus contribute
ordinate system there is, by definition, no normal com-
little to the total velocity signal.
ponent to the flow (i.e., Un 0 everywhere at all times).
Nonlinear flow also generates Eulerian residual cur-
Therefore the Coriolis term is zero in the s equation, as
rents and both inlets exhibit quadrapole residual fields
is the bottom friction term in the n equation. Moreover,
(Figs. 3g,h). The idealized inlet field is nearly sym-
the advective acceleration terms collapse to a single term
metric, while Beaufort Inlet shows a pronounced off-
in each equation: streamwise in the s equation and cen-
shore anticyclonic residual eddy west of the inlet and a
trifugal in the n equation. For both the idealized and
rather weak eastside eddy. One might expect this asym-
Beaufort inlet models, momentum was conserved to
metry to be due to Coriolis enhancing the westside eddy
within one percent before and after the transformation.
and diminishing the eastside eddy. However, inspection
The horizontal diffusion terms were generally an order
of the idealized inlet shows this is a minimal effect, as
of magnitude smaller than the other terms, and for sim-
0. Another possible
did a Beaufort Inlet run with f
plicity are omitted from Eqs. (4) and (5) as well as from
asymmetry source is phase differences in the offshore
the discussion below. Results are presented in terms of
open boundary forcing. However, the maximum differ-
momentum fluxes (obtained by multiplying each term
ence in M 2 elevation phase along the open boundary is
by H ) to provide a more physically intuitive picture of
less than 1.6 (about a 6-min phase lag). Rerunning the
the momentum balances.
model with uniform phases (set to the mean values)
yielded results nearly the same as those using the actual
forcing (e.g., residual speed and direction changed by
3. Circulation
3% in the immediate vicinity of the inlet). These re-
Modeled inlet circulation fields are shown in Fig. 3
sults suggest that the asymmetries are principally due
in terms of major tidal constituents. For both inlets, M 2
to bathymetric and geometric effects. In the throat of
tidal ellipses are largest in the inlet throat and rapidly
Beaufort Inlet there is a net inflow on the east side and
diminish within several kilometers from the inlet (Figs.
outflow on the west side. East and west of the inlet on
3a,b). On both the sound and ocean sides, M 2 ellipse
the sound side are counterrotating eddies, which appear
orientations are directed toward the inlets, and maxi-
to be significantly constrained by the land boundaries.
mum velocities are adjacent to the headland tips rather
than at the inlet centers. The M 2 ellipses are highly
rectilinear in the inlet throat and become more rotary
4. Momentum balances
with increasing distance from the inlet.
Momentum balances were computed at each model
The strong nonlinear nature of inlet flow generates
time step over a complete semidiurnal tidal cycle. An-
significant overtides and tidal residuals. Lateral shear in
imations of these results revealed that the most salient
an inlet is generated during both ebb and flood so the
time-varying features can be seen by examining three
principal quarter-diurnal overtide, M 4 , should coincide
phases of the tide: maximum ebb, midebb, and slack
(at least qualitatively) with advective acceleration pat-
before flood. Figure 4 shows the phases of the tide to
terns (Parker 1991). For the idealized inlet M 4 ellipses
be discussed for both inlets. For the idealized inlet, ve-
are largest adjacent to the headlands features and weak-
locity and elevation fields at the inlet center are nearly
est in the inlet throat, where streamlines become straight
90 out of phase, indicative of a standing wave. The
(Fig. 3c). At Beaufort Inlet, M 4 ellipses are also largest
corresponding figure for Beaufort Inlet indicates more
near the headland tips, but in contrast to the idealized
of a progressive wave, with velocity leading elevation
inlet there are significant regions offshore with large M 4
by about 1.5 h. The more progressive nature of the tide
(Fig. 3d). Beaufort Inlet model runs with uniform flat
7 m) show that natural topography
at Beaufort Inlet is due to the extensive shallow sound
bathymetry (h
that is less reflective than the sound in the idealized inlet
(and thus differential bottom friction) generates a con-
model. In the analysis below, the phase of the tide is
siderable part of the lateral shear and this suggests that
defined relative to a point at the geometric center of
topography is the source of enhanced M 4 relative to the
each inlet.
idealized inlet.
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