917

APRIL 2003

HENCH AND LUETTICH

U2

s

The principal sexdiurnal overtide, *M * 6 , is primarily

f *U*s

g

0,

(5)

generated by nonlinear bottom friction (Parker 1991).

t

n

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 *U*s(*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 *M*10 (not shown) show spatial patterns

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., *U*n 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% 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

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.