Coriolis

925

APRIL 2003

HENCH AND LUETTICH

side is changing cyclonically (turning toward the inlet)

At stronger tide phases (Figs. 11ad) centrifugal accel-

yielding positive rotary acceleration, while anticyclonic

erations are greater than Coriolis at both inlets (Ro

direction change on the east side (also toward inlet)

), particularly close to the headlands. There is more

gives negative rotary acceleration. Very close to the

than two orders of magnitude difference in Ro across

both inlets during maximum ebb ( 20 near headland

headland tips centrifugal acceleration remains impor-

tant; note that the signs have switched from ebb on both

tips, and approaching zero at the inlet centers). Most of

sides reflecting the sign change in Rs , as leftward (right-

this variability is from the radii of curvature, which

ward) curvature switches to rightward (leftward) cur-

range from tens of meters near the headland tips to near

vature on the east (west) side.

infinity at inlet centers where the streamlines are almost

straight. During the brief ( 1 h) period around slack

At Beaufort Inlet the situation is somewhat more com-

tide (see Figs. 11e,f) Rossby numbers are O(1) or less

plex. At the start of flood, the offshore pressure gradient

has acted long enough for the flow along the eastern

throughout most of the domain. For all tide phases Ro

shore outside the inlet to have a clear flood direction,

sharply decreases with distance from the inlet, except

but offshore west of the inlet flood flow is just beginning

within the transient tidal eddies. In comparison to the

(Fig. 10a). High momentum fluid in the ebb jet continues

idealized inlet, Beaufort Inlet shows considerable small-

to spin down (Fig. 10d) southwest of the inlet under the

scale spatial structure associated with flow curvature

``braking'' influence of the adverse pressure gradient

from irregular bathymetry.

(Fig. 10f). Inside the inlet on the west side, the velocities

Ro time series from both inlets (particularly the sym-

have turned to a flood orientation; here the flow is being

metric idealized inlet) indicate that the time period that

fed by the east side sound (Fig. 10a). This may be a

Coriolis is dynamically important is too short to cause

significant mechanism for cross-inlet exchange at Beau-

large asymmetries in the flow field. Even during the

fort Inlet (see discussion). The tides in this system be-

brief periods at slack when Coriolis is larger than cen-

trifugal acceleration, the n-direction momentum balance

have as a damped quasi-progressive wave on both es-

tuarine sides of the inlet, however the differing geom-

is still not geostrophic because this also coincides with

etry and depths on the two sides produce different damp-

the period when local accelerations are significant. This

ing and phase lags. The sound bathymetry on the east

point is clear from the highly symmetric circulation

side is shallower compared to the deeper dredged west

fields (Fig. 3) and Ro contours for the idealized inlet

side, which results in stronger attenuation and retarding

(Fig. 11), but less so for the natural inlet as the effects

of the tide on the east side relative to the west (see Fig.

of bathymetric asymmetries obscure those potentially

4 in Luettich et al. 1999). The differences in sound side

caused by Coriolis. Conceptually one would expect that

lateral phasing drives a lateral exchange across the inlet

Coriolis would act constructively or destructively to the

7 m)

near slack. Model runs with uniform depth (h

centrifugal acceleration and, for example, shift the po-

gave nearly symmetric behavior.

sition of maximum surface elevation across the inlet.

The normal direction momentum balance is domi-

Such an effect is very slight for the idealized inlet, while

nated by the rotary acceleration and pressure gradient

at Beaufort Inlet the effect is entirely obscured by asym-

terms (Figs. 10h,j). The rotary acceleration is largest in

metries due to irregular bathymetry.

the navigation channel where flow is turning anticy-

clonically toward the inlet. The normal direction pres-

5. Discussion

sure gradient is driving this direction change. The cen-

trifugal acceleration is generally small except at the

Dynamical balances for the remainder of the tidal cycle

headland tips (Fig. 10i), and as with the idealized inlet

(not shown because of space considerations) closely fol-

the cross-stream momentum balance is dominated by

low those described above for the ebb. The temporal

linear terms.

evolution of the momentum fields shows that the balances

oscillate between two dynamical states. At maximum

flow and throughout much of the tidal cycle, the nonlinear

d. Coriolis

terms and pressure gradients dominate the momentum

The role of Coriolis in the time-dependent momentum

balance, whereas near slack the balance is dominated by

balances is subtle and merits a more complete discus-

the linear terms. During the transition between the two

sion. To assess the relative importance of Coriolis versus

end states, local acceleration is important, but the rotary

centrifugal acceleration in the cross-stream momentum

acceleration is small as most of the flow direction change

balance, we form a ``curvature'' Rossby number Ro,

occurs during a brief period around slack.

defined in the streamline coordinate system as

As noted in section 3, the idealized inlet and Beaufort

Inlet have different wave characteristics (standing vs

quasi-progressive) and we wondered what effect this has

f Us

(6)

fRs

on inlet momentum balances. We reran the idealized

inlet model with a Sommerfeld type radiation condition

Model momentum fields were used to directly compute

in the sound (to mimic the effect of the extensive sound

Ro at both inlets for three phases of the tide (Fig. 11).

regions surrounding Beaufort Inlet), which yielded near-

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