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# A Numerical Study of the Steady Circulation in an Open Bay

Ya Hsueh and Chich-Yuan Peng

## Abstract

The steady-state circulation in a rectangular bay is studied numerically in a model of homogeneous water and vertical coasts. The competing influences of the surface winds and longshore currants flowing by the open side of the bay and the effect of the bathymetry are emphasized. For a wind-stress field that does not vary along the coast but decays linearly inshore from the open side of the bay, the mass-transport streamfunction contours form a gyre rotating in the sense of the wind-stress curl. A uniform continental shelf slope distorts the gyre by creating depth variations that cause vortex stretching. Consequently, the streamlines become more packed to the right of the down-slope direction. The nonlinearity tends to destroy symmetry by crowding streamlines in the direction of the induced current. The influence of large-scale ocean currents along the open side is normally confined to the outer half of the bay. When the wind is blowing against these currents, the influence of the wind creates two gyres, one each at the inshore corners of the bay.

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# Calculation of Pressure in Ocean Simulations

William K. Dewar, Ya Hsueh, Trevor J. McDougall, and Dongliang Yuan

## Abstract

Many state-of-the-art numerical ocean models calculate pressure using the hydrostatic balance, or an equation derived from it. The proper form of this deceptively simple-looking equation, ∂p/∂z = −(S, T, p) (where notation is standard), is nonlinear in the pressure p. In contrast, most numerical models solve the linear equation ∂p/∂z = −(S, T, z). This modification essentially replaces the total pressure, which includes a time-dependent signal, with an approximate time-independent pressure associated with the depth of a model grid point. In this paper, the authors argue that the inclusion of the total pressure when solving the hydrostatic equation can generate a depth-dependent baroclinic pressure gradient equivalent to a geostrophic velocity of several centimeters per second. Further, this effective velocity can increase with depth and is largest in dynamically important areas like western boundary currents. These points suggest that the full feedback of pressure on density should be included in numerical models. Examples of the effect using oceanic data and output from a typical primitive equation model run are discussed. Finally, algorithms for both rigid-lid and free surface models that explicitly include full pressure are derived, and some related numerical issues are discussed.

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# Numerical Model Studies of the Winter-Storm Response of the West Florida Shelf

Ya Hsueh, G. O. Marmorino, and Linda L. Vansant

## Abstract

The wintertime, wind-driven Ocean circulation on the West Florida Continental Shelf is studied within the framework of a linearized storm-surge model. The model bathymetry incorporates a realistic shelf, extending from New Orleans to the southern tip of Florida, and a deep ocean region. The boundary condition at the coast is that there is no normal flow. At the open boundaries, located off the shelf in deep water, the adjusted sea level is fixed at zero.

It is found that 1) a coastally trapped response is achieved within one local inertial period following the imposition of the wind; 2) the curved coast forces a mass exchange between the coastal water and the deep ocean; 3) this exchange leads to the generation of a series of mesoscale eddies along the shelf edge; and 4) these eddies give rise to long-period, shelf-wide oscillations that persist beyond the local spin-up time.

A hindcast of the wind-driven flow on the West Florida Shelf for a particular period (11–25 March 1978) that contains the passage of a distinct cold front produces coastal sea-level and current fluctuations that are in reasonable agreement with observations.

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# An Analysis of Loop Current Frontal Eddies in a ⅙° Atlantic Ocean Model Simulation

Haosheng Huang, Nan D. Walker, Ya Hsueh, Yi Chao, and Robert R. Leben

## Abstract

The Loop Current frontal eddies (LCFEs) refer to cyclonic cold eddies moving downstream along the outside edge of the Loop Current in the eastern Gulf of Mexico. They have been observed by in situ measurements and satellite imagery, mostly downstream of the Campeche Bank continental shelf. Their evolution, simulated by a primitive equation ⅙° and 37-level Atlantic Ocean general circulation numerical model, is described in detail in this study. Some of the simulated LCFEs arise, with the passage through the Yucatan Channel of a Caribbean anticyclonic eddy, as weak cyclones with diameters less than 100 km near the Yucatan Channel. They then grow to fully developed eddies with diameters on the order of 150–200 km while moving along the Loop Current edge. Modeled LCFEs have a very coherent vertical structure with isotherm doming seen from 50- to ~1000-m depth. The Caribbean anticyclone and LCFE are two predominant features in this numerical model simulation, which account for 22% and 10%, respectively, of the short-term (period less than 100 days) temperature variance at 104.5 m in the complex empirical orthogonal function (CEOF) analysis. The source water inside the LCFEs that are generated by Caribbean anticyclonic eddy impingement can be traced back, using a backward-in-time Lagrangian particle-tracking method, to the western edge of the Caribbean Current in the northwest Caribbean Sea and to coastal waters near the northern Yucatan Peninsula. The model results indicating a pairing of anticyclonic and cyclonic eddies within and north of the Yucatan Channel are supported by satellite altimetry measurements during February 2002 when several altimeters were operational.

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