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Richard W. Garvine

Abstract

The paper develops and analyzes a model of frontal-scale dynamics applicable to established, persistent upper ocean density fronts. The effects of interfacial friction and mass entrainment arising from turbulent dissipative processes are incorporated as well as the effects of earth rotation and wind stress. The model is of hydrodynamic character in that the circulation is not permitted to do its own mixing. The equations of motion are solved after their integration over the vertical from the pycnocline bottom to the sea surface. Two independent frontal length scales are found. one is L t , the dissipative length scale, defined as the ratio of the asymptotic pycnocline depth to the magnitude of the interfacial entrainment coefficient; the other is the baroclinic Rossby radius, the internal wave phase speed divided by the Coriolis parameter. The ratio of these length scales forms the fundamental parameter of the model dynamics, P r , called the rotation parameter. For large values of P r the frontal length scale is the Rossby radius alone and the model dynamics show features in common with the inertial, inviscid Gulf Stream theories. For small values of P r the frontal zone can have a double structure with the inner region corresponding to the nonrotational dynamics explored in a previous paper. For values of order one both dissipative and rotational effects enter the dynamics.

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Richard W. Garvine

Abstract

Plumes of buoyant water produced by inflow from rivers and estuaries are common on the continental shelf. Typically they turn anticyclonically to flow alongshelf as buoyancy-driven coastal currents. During this passage, mixing with ambient shelf water gradually erodes the plume buoyancy so that its alongshelf penetration is finite. This paper addresses the extent of this penetration and how it is determined by fundamental dimensionless flow parameters.

A three-dimensional numerical model is applied to an idealized flow regime. Ambient shelf conditions include tidal motion, but neither wind stress nor ambient alongshelf current. The alongshelf extent of penetration is evaluated after the plume reaches a stationary condition downshelf. A total of 66 model experiments are conducted, including variations in buoyant source and ambient shelf properties. Five dimensionless parameters determine the alongshelf and across-shelf penetration, the latter the coastal current width. The most critical of these is τ, the source volume transport scaled by the associated source geostrophic transport. For fixed shelf bottom slope and no tides, similarity forms are found for both alongshelf and across-shelf penetration for a wide range of τ. Increased shelf bottom slope and increased shelf tidal amplitude shorten the alongshelf penetration.

The vertical turbulent closure scheme itself contributes one of the five model parameters, the background eddy viscosity or diffusivity. This background viscosity ν is added to the viscosity determined from the Mellor–Yamada level 2.5 closure scheme to give N, the vertical viscosity used by the model. Where the local Richardson number exceeds about 0.2, as in most buoyant plumes, the Mellor–Yamada scheme “switches off,” forcing N to default to ν. Plume penetration properties thus are found to depend significantly on ν. At present one must choose ν arbitrarily, thus introducing uncertainty into the model results.

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Richard W. Garvine

Abstract

The constraints imposed upon a coastal upwelling zone by the steady-state wind-driven dynamics of the interior of an ocean basin are examined. A parameter is found which measures the strength of the bottom boundary layer in the interior. Oceanic conditions correspond to small values of this parameter and, thus, the bottom boundary layer is weak. For these conditions the meridional mass flux can be prescribed at the boundary of the interior in terms of local variables. The zonal mass flux is developed for a meridional eastern boundary. A mean meridional pressure gradient is shown to be impressed on the eastern boundary upwelling region by the interior dynamics. Restrictions imposed upon the upwelling region motion by the assumption of an f-plane and a two-dimensional interior are discussed.

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Richard W. Garvine

Abstract

An integral model of the steady-state dynamics of a shallow, small-scale oceanic front is developed. Such fronts have been observed at the boundaries of river plumes discharging into coastal sea water. They share with larger scale oceanic fronts the features of persistence in time, despite sharp horizontal gradients in properties, and strong horizontal convergence at the surface front with consequent sinking. For a steady state to exist in a reference frame moving with the front, the model shows that interfacial friction and/or upward mass entrainment is required to balance the net pressure gradient produced by the sloping sea surface and frontal interface in the light water pool. Maintenance of this balance dictates that the Richardson number be of order unity; thus, friction and entrainment coefficients are kept low allowing sharp property gradients in the steady state. Strong surface convergence is also a prominent feature of the model dynamics. Comparisons are made with the observations of Garvine and Monk and show acceptable qualitative agreement.

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Richard W. Garvine

Abstract

The influence of bathymetry upon the wind-driven, steady-state coastal upwelling motion of homogeneous water is investigated. The motion occurs in two principal layers, a divergent surface Ekman layer and a subsurface return flow. The restriction that the surface layer depth be always a small fraction of the total depth permits the retention of the surface layer solution developed in a previous paper by the author where bathymetry was not treated. The subsurface motion is affected by bathymetry, but the governing equations can he simplified for bottom topographies of slopes characteristic of continental slopes and shelves. The velocity and pressure fields are deduced by a combination of analytic and numerical means. The principal physical effects of bathymetry are two-fold. Shoaling uplifts and compresses the streamline field in the return flow. The resulting acceleration of the flow toward shore induces a jet in the longshore velocity field for the subsurface layer. This motion occurs in the direction of the longshore wind component and exceeds the surface layer longshore movement in mass flux.

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Richard W. Garvine

Abstract

An analytic model of long, propagating free-wave perturbations to an established upper ocean density front is developed. The primary purpose of the model is to illuminate basic frontal wave mechanisms for possible subsequent use in more sophisticated numerical models. The models is of the barotropic class but has ageostrophic dynamics because of the basic state adopted, essentially Stommel's model of the Gulf Stream with uniform potential vorticity and order one Rossby number. The model assumes inviscid dynamics apart from a narrow dissipative zone adjacent to the surface front. The latter exerts a bulk effect on the large inviscid zone, especially in generating small, bur finite, cross-stream flow in the basic state. For zero cross-flow the resulting waves are stable, have downstream phase speeds that are slow compared to the current speed and that increase with frequency, and have anomalous dispersion. The phase speeds compare well with the analysis of observations of propagating Gulf Stream meanders buy Halliwell and Mooers. For finite cross-flow the waves grow slowly in the downstream direction when flow is out of the current and decay when flow is into the current. The rates of growth or decay are independent of wavelength. Corresponding net growth or decay in the wave kinetic energy is produced by action of the cross-correlation wave Reynolds stress against the lateral shear of the basic state current.

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Richard W. Garvine

Abstract

As a step in understanding the complicated dynamics of coastal upwelling areas, a simple theoretical model is examined. The motion is driven by surface wind stress acting on homogeneous water of constant depth adjacent to a long straight coastline. Order-of-magnitude analysis is used to argue that the upwelling is induced by the horizontal divergence of a lateral, frictional boundary layer. A vertical integration of the equations of motion shows the necessity of retaining the pressure gradient term in the longshore direction even though the velocity field is two-dimensional. The motion in the lower return layer and upper Ekman layer is analyzed. It is found that the surface layer motion may he deduced independently of the return flow layer. The mass flux pumped into it should not be affected by bathymetry or stratification, provided that the depth is much greater than the Ekman layer depth. Streamlines are shown for different surface wind stress orientations. The results show that some upwelling occurs regardless of the direction in which the wind blows.

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Richard W. Garvine

Abstract

Recent observations of particle paths in the Gulf Stream show clear evidence of strong vertical motion with upwelling approaching anticyclonic turns and sinking approaching cyclonic turns. In a recent paper a simple model of propagating long waves on oceanic fronts was developed based on Stommel's model of the Gulf stream and its wave propagation properties compared with observations. In this paper properties of the associated model flow field, especially the vertical velocity, are examined for comparison with the observations of Rossby et al. Similar phase and amplitude results are found.

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Richard W. Garvine

Abstract

The physical characteristics of a model of an upper ocean density front are examined and compared to observations. The model was developed and analyzed in a companion paper. It applies to the mean circulation and hydrography of established, persistent fronts. The results for a case where turbulent transport and earth rotational effects are both important are examined in detail. The circulation then contains a jet for the velocity parallel to the front including a cyclonic shear zone but with speeds that are below geostrophic values. The circulation normal to the front shows strong two-sided convergence and sinking near the surface front. The question of upward versus downward mass entrainment is examined in terms of its impact on the model circulation. Five frontal cases are examined and compared to field observations. These cover a wide range of frontal scales from a river plume front to the Gulf Stream front. The river plume front nearly corresponds to a limiting case for the model where rotation is negligible and turbulent dissipative effects dominant, while the Gulf Stream front corresponds nearly to the opposite limiting model case where dissipation is negligible and rotation dominant. The other cases fall between these two limits.

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Richard W. Garvine

Abstract

A layer model that treats fronts as discontinuities is developed to study the steady state behavior of shallow estuary plumes on the continental shelf. The complete range of earth rotation effect is evaluated from small-scale or nonrotating plumes (Kelvin number equal zero) to large-scale, rotating plumes (Kelvin number equal order one). Supercritical flow is assumed in the outlet channel and the method of characteristics is used to compute the flow downstream. Nonrotating plumes have strong boundary fronts and concentrate their greatest layer depth and mass transport offshore near the front, but form no coastal current. Rotating plumes have boundary fronts that weaken soon after discharge, form a turning region where Coriolis action deflects the flow toward shore, and subsequently set up a coastal current. Soon after its formation this coastal current is bounded offshore by a strong front called the coastal front, across which the momentum balance changes from nearly inertial in the turning region upstream to nearly geostrophic in the coastal current itself. In traversing this front the flow loses total energy, but gains potential vorticity. Farther downstream the coastal front weakens, and meanders of the coastal current begin. Their wavelengths are short, about two Rossby radii, and their amplitudes grow, doubling after about 20 Rossby radii. The presence of supercritical speeds and fronts generates a plume dynamics that is remote from any linear description but shows analogous behavior to supersonic, compressible gas flow with shock waves.

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