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William J. Schmitz Jr. and J. Dana Thompson

Abstract

An adiabatic, primitive equation, eddy-resolving circulation model has been applied to the Gulf Stream System from Cape Hatteras to east of the Grand Banks (30°–48°N, 78°–45°W). A two-layer version of the model was driven both by direct wind forcing and by transport prescribed at inflow ports south of Cape Hatteras for the Gulf Stream and near the Grand Banks of Newfoundland for the deep western boundary current. The mean upper-layer thickness was sufficiently large for interface outcropping not to occur. Numerical experiments previously run at 0.2° horizontal resolution (∼20 km) had some realistic features, but a key unresolved deficiency was that the highest eddy kinetic energies obtained near the Gulf Stream were too low relative to data by a factor of about 2, with inadequate eastward penetration.

A unique set of new numerical experiments has extended previous results to higher horizontal resolution, all other conditions being held fixed. At 0.1° horizontal resolution, eddy kinetic energies in the vicinity of the Gulf Stream realistically increase by a factor of roughly 2 relative to 0.2°. The increase in eddy activity is a result of enhanced energy conversion from mean flow to fluctuations due to barotropic and baroclinic instabilities, with the nature of the instability mixture as well as eddy energy changing with increased resolution. One experiment at 0.05° horizontal resolution (∼5 km) yielded kinetic energies and key energy transfer terms that are within 10% of the equivalent 0.1° case, suggesting that convergence of the numerical solutions has nearly been reached.

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J. Dana Thompson and W. J. Schmitz Jr.

Abstract

A primitive-equation, n-layer, eddy-resolving creation model has been applied to the Gulf Stream System from Cape Hatteras to cast of the Grand Banks (78°–45°W, 30°–48°N). Within the limitations of the model, realistic coastlines, bottom topography, and forcing functions have been used. A two-layer version of the model was driven by observed mean climatological wind forcing and mass transport prescribed at inflow. Outflow was determined by a radiation boundary condition and an integral constraint on the mass field in each layer. Specification of a Deep Western Boundary Current (DWBC) was included in some model runs.

Six numerical experiments, from a series of over fifty integrated to statistical equilibrium, were selected for detailed description and intercomparison with observations. The basic case consisted of a flat bottom regime driven by wind forcing only. Realistic inflow transport in the upper layer was then prescribed and two different outflow specifications at the eastern boundary were studied in experiments 2 and 3. Three additional experiments involved (4) adding bottom topography (including the New England Seamount Chain), (5) adding a DWBC to experiment 4 with 20 Sv (Sv ≡ 106 m3 s−1) total transports and (6) increasing the DWBC, to 40 Sv. A brief discussion of the influence of parameter variations includes modifications of dissipation (lateral eddy diffusion and bottom friction) and stratification.

Results from the sequence of experiments suggest an important role for the DWBC in determining the mean path of the Gulf Stream and consequently the distribution of eddy kinetic energy, and the character of the deep mean flow. The most realistic experiment compares to within a factor of two or better with observations of the amplitude of eddy kinetic energy and rms fluctuations of the thermocline and sea surface height. Abyssal eddy kinetic energy was smaller than observed. The mean flow is characterized by recirculations to the north and south of the Gulf Stream and a deep cyclonic gyre just east of the northern portion of the New England Seamount Chain, as found in the data.

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J. Dana Thompson and James S. O'Brien

Abstract

Linear and nonlinear two-layer ocean circulation models of coastal upwelling on an f-plane are driven by time-dependent winds and solved numerically. Longshore variations in the circulation are neglected and offshore variations in the winds are specified. A technique for generating a realistic broad frequency-band wind stress from a kinetic energy spectrum of wind speed is developed.

When results from the two models are compared, nonlinearities are found to be unimportant in explaining the basic upwelling dynamics. However, they do provide a mechanism for wave-wave interactions which broaden all spectral peaks. In the nonlinear model coherence-squared spectra between the winds and zonal current components in the upwelling zone indicate highest coherence at lowest frequencies for both layers, accompanied by a 180° phase shift from upper to lower layer at frequencies <3 cycles per day. Similar analyses for winds vs meridional current components and winds vs pycnocline height anomalies show a coherence squared maximum for winds of 5-day period. In the frequency band below and including the inertial, remarkable similarities are observed between the results of the nonlinear model and actual ocean current autospectra.

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H. E. Hurlburt and J. Dana Thompson

Abstract

The β effect is found to produce a poleward undercurrent in a wind-driven model of an eastern ocean circulation. The model is on an x, z plane and longshore derivatives of the velocity field are neglected. The nonlinear two-layer model is time-dependent and is solved numerically. Beta is found to exhibit little effect on the vertical mass transport, but exerts a dominant influence on the longshore flow by inducing a north-south sea surface slope.

For an equatorward wind stress and flat bottom topography, the model predicts upwelling adjacent to the coast with a mean vertical velocity of 10−2 to 10−2 cm sec−1 and an e-folding width of about 15 km. The longshore flow is characterized by an equatorward surface jet and a poleward undercurrent. Outside the upwelling zone the longshore flow is weak. The offshore flow in the upper layer is slightly weaker than that predicted by Ekman drift. The compensating onshore flow in the lower layer is balanced by the north-south sea surface slope.

Positive wind stress curl in the coastal upwelling zone tends to diminish the surface jet and to enhance the poleward undercurrent. Bottom topography is shown to modify the dynamics and a secondary upwelling zone is found over the continental slope.

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H. E. Hurlburt and J. Dana Thompson

Abstract

We have sought to simulate and understand consistently observed features of the Somali Current system during the southwest monsoon using a two-layer, nonlinear numerical ocean model driven from rest by a uniform south wind in a flat bottom, rectangular geometry. High spatial resolution in both equatorial and coastal boundary regions was retained in this free-surface model.

The model Somali Current is best classed as a time-dependent, baroclinic inertial boundary current. Analytical solutions to a quasi-steady linear model of the Somali Current are shown to be self-inconsistent with the linear approximation. While linear theory predicts perfect symmetry about the equator, the nonlinear numerical solutions exhibit marked asymmetries in less than a month as the model Somali Current becomes strongly inertial. By day 30 the current has attained its maximum value (140 cm s−1) within a few degrees of the equator, in accord with observations. In this time-dependent case, boundary layer separation occurs at the northern end of the inertial current as the northward advection of the current precedes the adjustment of the mass field. Associated with the northward movement of the baroclinic inertial boundary current is a “great whirl” similar in scale and intensity to that observed. This remarkable whirl is characterized by anti-cyclonic inflow in the upper layer, cyclonic outflow in the lower layer, and a northward translation speed of about 27 cm s−1. At the coast, west of the whirl, is an upwelling maximum also found in the observations.

A consideration of the eastern and equatorial solution shows that the south wind case excites the n=0 mode for equatorially trapped inertia-gravity oscillations. These oscillations are strongly coupled to the eastern boundary layer and excite a poleward propagating train of internal Kelvin waves. Prior to the arrival of the leading edge of the wave train, upwelling (downwelling) occurs south (north) of the equator at the eastern boundary. Due to the symmetry properties of the solution, no internal Kelvin wave of significant amplitude is excited anywhere along the western boundary. The trapped inertia-gravity oscillations are damped as a Yanai wave propagates away from the western boundary. Significantly, in the eastern equatorial ocean the time scale for cessation of vertical motion driven by a meridional wind is the same as that for onset for a zonal wind.

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H. E. Hurlburt and J. Dana Thompson

Abstract

The dynamics of the eddy shedding by the Loop Current in the Gulf of Mexico have been investigated using three nonlinear numerical models: two-layer, barotropic and reduced gravity. The barotropic and reduced gravity models demonstrate the individual behavior of the external and internal modes, and provide insight into how they interact in the two-layer model. Because of the economy of the semi-implicit free surface models, it was possible to perform over 100 experiments to investigate the stability properties of the Loop Current. Typically, the models were integrated 3–5 years to statistical equilibrium on a 1600 km×900 km rectangular domain with a resolution of 20 km×18.75 km. Prescribed inflow through the model Yucatan Channel was compensated by outflow through the Florida Straits.

A long-standing hypothesis is that the Loop Current sheds eddies in response to quasi-annual variations in the inflow. We find that the Loop Current can penetrate into the Gulf, bend westward, and shed realistic anticyclonic eddies at almost an annual frequency with no time variation in the inflow. In this regime, the eddy-shedding rate depends on the internal Rossby wave speed, an eddy diameter derived from conservation of potential vorticity on a β-plane, the angle of the inflow, and to a lesser extent on the Reynolds number. Eddy shedding can be prevented by reducing the Reynolds number sufficiently. However, the Loop Current still spreads far westward. The steady-state solution for a highly viscous case was found to be almost the same as the mean over an eddy cycle for a lower viscosity case which shed discrete eddies of large amplitude. Eddy shedding and westward spreading of the Loop can be prevented at higher Reynolds numbers when the beta Rossby number RB = vc/(βLp 2) > 2, where the appropriate length scale Lp is one-half the port separation distance and vc is the velocity at the core of the current. Differential rotation (β) is also of great importance in determining the diameter and westward speed of the eddies and the penetration of the Loop Current into the Gulf. In a few of the two-layer experiments, baroclinic and mixed instabilities were encountered, but experiments dominated by a horizontal shear instability of the internal mode produced the most realistic results. For sufficiently high Reynolds numbers the shear instability occurred in both the barotropic and reduced gravity models. However, for realistic parameter values eddy shedding occurred in the two-layer and reduced gravity models, but not in the barotropic model.

Consistent with potential vorticity conservation dynamics, the Loop Current and its eddy shedding behavior were quite insensitive to the location and width of the inflow and outflow ports, so long as the western boundary did not interfere with the shedding process and the ports were not separated by much less than 1/???? times a theoretical eddy diameter, i.e., when RB < 2. When the entire eastern boundary was opened, the outflow remained confined to a current adjacent to the southern boundary. Also, while the solution depends on the maximum velocity at inflow, it is relatively insensitive to the shape of the inflow profile.

In the presence of significant deep-water inflow through the Yucatan Straits, bottom topography may prevent Loop Current penetration, westward spreading and eddy shedding. In these cases the interaction between the bottom topography and the pressure field near the Florida Shelf results in a near balance between the pressure torques and the nonlinear terms in the mass transport vorticity equation. When the Yucatan Straits deep-water inflow is reduced or the Florida Shelf is moved to the east, the eddy shedding reappears. A kinematic analysis shows that a sufficiently strong current following f/h contours of the Florida Shelf and intersecting the Loop Current at large angles can locally prevent northward penetration of the Loop Current and effectively reduce the port separation. Thus, the effect of the Florida Shelf is similar to cases in the reduced gravity model where the ports are too close for eddy shedding to occur, i.e., when RB>2. Bottom topography also inhibits development of baroclinic instability, yielding solutions more closely resembling those from the reduced gravity model than from the two-layer flat bottom model. However, movement of the shed eddies is significantly modified by the introduction of topography.

In the presence of realistic time variations in the upper layer inflow, the eddy-shedding period is dominated by the natural period rather than the forcing period, although the influence of the latter is not negligible.

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Robert C. Rhodes, J. Dana Thompson, and Alan J. Wallcraft

Abstract

The large variability of the Gulf of Mexico wind field indicates that high-resolution wind data will be required to represent the weather systems affecting ocean circulation. This report presents methods and results of the calculation of a corrected geostrophic wind data set with high temporal and spatial resolution.

Corrected geostrophic wind was calculated from surface pressure analyses compiled by the Fleet Numerical Oceanography Center. The correction factors for wind magnitude and direction were calculated using linear regressions of observed Gulf buoy winds and geostrophic winds derived at the buoys. The regressions were performed for each month to determine the seasonal variability of the correction factors. The magnitude correction was found to be nearly constant (0.675) throughout the year, but the direction correction varied seasonally from 8.5 to 26.5 degrees.

The corrected geostrophic wind was calculated twice daily store 1967–1982 on a spherical grid over the Gulf, together with the corresponding wind stress and wind stress curl fields. The 12-hourly stress fields show large temporal variations of the wind field for both winter and summer months. Seasonal and monthly climatologies of the stress and corresponding curl show positive curl over the Yucatan and negative curl in the southwest Gulf, which are features not seen in any previous study of Gulf wind stress.

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