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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 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

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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H. E. Hurlburt, John C. Kindle, and James J. O'Brien

Abstract

El Niño may be defined oceanographically as a massive influx of warm water into the coastal region of Ecuador and Peru. We have tested the hypothesis that these rare events occur after a substantial reduction of the atmospheric trade winds over the central Pacific Ocean. An idealized nonlinear, two-layer, equatorial beta-plane ocean is spun-up with easterly winds for 50 days after which the wind is relaxed over several days. The relaxation of the wind initiates internal Kelvin wave fronts at both sides of the ocean at the equator. The eastern wave fronts propagate poleward and the western ones eastward. Internal Rossby waves are generated which propagate westward from the eastern boundary. As the Kelvin wave fronts move poleward along the eastern boundary, strong downwelling occurs and the coastal currents reverse direction and become poleward. The rapid downwelling and the sudden reversal of the coastal current are consistent with observations during El Niño. This downwelling is much more rapid than the upwelling which occurred during spin-up due to nonlinear Kelvin wave dispersion. The dispersion results in the development of a frontal character at the leading edge of the waves. When the western Kelvin wave fronts reach the eastern boundary, the downwelling ceases and the poleward currents separate from the coast, propagating westward as Rossby waves. Thus we suggest the pulsating nature of El Niño is related to the occurrence of major equatorial wind changes and the dynamics of internal Kelvin waves whose nonlinear attributes may greatly sharpen the pulses.

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R. M. Clancy, J. D. Thompson, H. E. Hurlburt, and J. D. Lee

Abstract

A time-dependent, two-dimensional numerical model is constructed by coupling a four-layer atmosphere to a two-layer ocean through fluxes of heat and momentum. Idealized experiments are performed to investigate the oceanic response to sea breeze forcing, changes induced in the sea breeze by coastal upwelling, and air-sea feedback during periods of active coastal upwelling. This problem is motivated by the fact that the time scale of the coastal upwelling response is short compared to most oceanic response times and is comparable to the sea breeze time scale.

When forced with a longshore wind stress, the model ocean reproduces several features commonly observed in coastal upwelling regimes, including an equatorward surface jet, a poleward undercurrent, and a region of low sea surface temperatures near the coast. For the cases considered here, the sea breeze contributes significantly to the mean longshore wind stress and, consequently, plays a role in driving the coastal upwelling circulation. It also substantially increases the kinetic energy of the nearshore ocean by forcing inertial oscillations and internal gravity waves with a diurnal period.

When the sea surface temperature is held constant and the land temperature is varied diurnally, the model atmosphere cyclically reproduces a realistic simulation of the sea breeze-land breeze circulation which includes such features as the sea breeze forerunner and the sea breeze front. However, a rapid decrease in sea surface temperature near the coast characteristic of coastal upwelling produces important alterations of the sea breeze-land breeze circulation. Low-level cooling of the atmosphere over the cold water leads ultimately to the formation of a shallower, sharper, faster and longer lasting sea breeze front that penetrates more than twice as far inland than it would without the upwelling. In general, the cold water causes an increase in the low-level sea breeze intensity landward of ∼6 km inland but a decrease seaward of this point. The cold water decreases the land-sea thermal contrast at night and weakens the low-level land breeze everywhere.

Since the cold water in the upwelling zone perturbs the atmosphere on a horizontal scale that is small compared to the internal radius of deformation for the atmosphere, the increase in the longshore geostrophic wind it induces near the coast is small. Furthermore, the reduction in low-level sea breeze amplitude over the cold water compensates the effect of slightly increased mean longshore wind such that the change in mean longshore wind stress is negligible. Thus, although the sea breeze affects the upwelling and the upwelling affects the sea breeze, the air-sea feedback loop to the coastal upwelling process is exceedingly weak.

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