Lateral dynamics and Rossby numbers

Model sensitivity - Hench_et_al_CSR_020008

Fig. 6. Computed Rossby number (defined as R0 jUs=fRsj) shaded contours for the four idealized inlets at maximum flood.

Hench_et_al_CSR_02
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J.L. Hench et al. / Continental Shelf Research 22 (2002) 26152631

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with runs where n was set to 2 m2 s1, 4 m2 s1 (the

context of the rotated coordinate system we form

baseline), and 6 m2 s1. The 2 m2 s1 run showed

a ``curvature'' Rossby number

sharper velocity gradients, but was contaminated

by high frequency numerical oscillations in the

R0 s jUs=fRsj:

momentum fields, while the 6 m2 s1 run exhibited

comparatively smooth velocity gradients and

momentum fields. In all three runs the major

Model results were used to directly compute R0

features of the momentum balances were un-

throughout the flow, as shown in Fig. 6 for each of

changed. The model was most sensitive to changes

the idealized inlets. For inlet I, R0 > 1 over the

in depth. Runs where the sound and inlet

entire width and length of the inlet (Fig. 6a). There

bathymetry were set shallower (3 m) and deeper

is a marked asymmetry between the ocean side and

(7 m) were compared with the baseline run with

the sound side of the inlet. The region of high R0

5 m depth. Results were as expected, with the

on the sound side is enhanced by the centrifugal

shallower depth producing stronger streamwise

acceleration of the transient tidal eddies. For inlet

accelerations and bottom friction (both balanced

II (Fig. 6b), the high R0 region still spans the entire

by a steeper streamwise pressure gradient). Spatial

inlet width, but the centrifugal acceleration and R0

structure of the lateral balance was unchanged, but

sharply diminish within the straits. For inlet III

with stronger centrifugal accelerations and lateral

(Fig. 6c), R0 is large in regions adjacent to the inlet

pressure gradients. Increasing the depth had the

headlands and along the entire inlet length, but

opposite effects, but again did not change the

there is a region of low R0 in the inlet center.

major momentum features.

Finally, inlet IV exhibits R0 patterns that are a

combination of inlets II and III (Fig. 6d), with

high R0 only near the inlet headlands. By

4. Lateral dynamics and Rossby numbers

convention R0 is always positive but we note that

it reaches zero in the middle of each of the inlets at

The results of our analysis on the four idealized

the location where the radius of curvature becomes

inlets indicate that at the stronger phases of the

infinite. At these locations the radius of curvature

tide, the flow is near steady state and lateral

changes sign from positive (on the west sides) to

diffusion of momentum is small. Therefore the

negative (on the east sides). Results from a

lateral momentum balance reduces to the sum of

companion study of transient dynamics (Hench

centrifugal and Coriolis accelerations and the

and Luettich, in review) showed that these

lateral pressure gradient

balances hold for much of the tidal cycle but not

Us2

fUs g

during the weaker phases, particularly during the

hour nearest to slack. During those tidal phases,

We now look at the two limiting cases. If

R0{1 but the balances are still not geostrophic as

centrifugal acceleration is negligible then (Eq. 6)

the local acceleration terms are important.

reduces to a geostrophic balance

fUs g

5. Inlet classification scheme

and conversely, if the centrifugal acceleration is

Our analysis of inlet dynamics has identified the

much greater than Coriolis (Eq. 6) can be

dominant force balances for a range of inlet

approximated by a cyclostrophic balance

configurations. In this section, we use this insight

Us2

to develop an inlet classification scheme based on

these underlying dynamics. Previous classification

schemes have been developed for estuarine circula-

We now assess the relative importance of the

tion (Stommel and Farmer, 1952; Hansen and

centrifugal and Coriolis accelerations. In the

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