Gerald S. Janowitz

The effects of alongshore variation in bottom topography on a boundary current—(topographically induced upwelling)

Abstract A theory which describes the constant f -plane flow of a steady inviscid baroclinic boundary current over a continental margin with a bathymetry that varies slowly in the alongshore but rapidly in the offshore directions is developed in the parameter regime (L D /L) 2 ≤ Ro ≪ 1 , where L D is the internal deformation radius, L the horizontal length scale, and Ro the Rossby number. To lowest order in the Rossby number the flow is along isobaths with speed q o = V u (h,z)|Vh|/α , where V u (h,z) is the upstream speed, α the upstream bottom slope at depth h , and Vh the bottom slope downstream at depth h . The lowest order flow produces a variation in the vertical component of relative vorticity along the isobath as the magnitude and direction of Vh vary in the downstream direction. The variation of vorticity requires a vertical as well as a cross-isobath flow at first order in the Rossby number. The first order vertical velocity is computed from the vorticity equation in terms of upstream conditions and downstream variations of the bathymetry. The density, pressure, and cross-isobath flow at first order in the Rossby number are then calculated. It is shown that in the cyclonic region of current ( d/dh(V u /α) > 0 ), if the isobaths diverge in the downstream direction ( (∂/∂s)|Vh| ), then upwelling and onshore flow occur. The theory is applied to the northeastern Florida shelf to explain bottom temperature observations.

Continental shelf circulation induced by a moving, localized wind stress

Abstract A linear, two-dimensional model of a rotating, stratified fluid is constructed to investigate the circulation induced by a moving, localized line of surface stress. This model is used to analyze the effect of moving cold fronts on continental shelf circulation. The nature of the induced circulation depends on the relative magnitude of the translation speed of the storm and the natural internal wave speed. If the surface stress moves slower than the internal wave speed. the disturbance is quasi-geostrophic and moves with the storm. If the storm moves faster than the internal wave speed, two sets of internal-inertial waves are produced. One set of waves is forced by the surface forcing and travels at the speed of the storm. Another set of waves is produced by reflection of the directly forced waves from the coastal wall. We conclude that free surface deflection (slope) is responsible for the low-frequency. quasi-geostrophic currents due to passing cold fronts. The internal response is composed of t...

ABIOTIC FACTORS INFLUENCING THE SPATIAL AND TEMPORAL VARIABILITY OF JUVENILE FISH IN PAMLICO SOUND, NORTH CAROLINA

Abstract We have examined the relationship between the abundance of juvenile spot {Leiostomas xanthurus) in the nursery areas along the western boundary of Pamlico Sound, North Carolina, and the circulation patterns in the Sound. Juvenile fish abundance data are related to wind measurements taken two to three weeks prior to the fish sampling program. When the wind has a significant eastward component, i.e., from the nursery areas toward the inlets during the period preceding the sampling program, juvenile spot are relatively abundant compared with periods when the wind is not in that direction. Our numerical model of circulation in Pamlico Sound indicates that this wind field produces surface currents towards the east, and near-bottom currents towards the nursery areas, i.e., towards the west. The near-bottom currents are driven by the pressure-gradient forces associated with the set up of sealevel in the down-wind direction. It is postulated that the bottom-seeking juvenile spot ride these favorable bottom currents across the sound from the inlets to the nursery areas.

The Effect of a Localized Topographic Irregularity on the Flow of a Boundary Current along the Continental Margin

Abstract A model for the effect of a localized topographic irregularity on a barotropic sheared current flowing along a continental margin with shallow water to the left of the current is developed. The topographic irregularity is assumed to be small and smooth compared to the background water depth and the background bottom slope, respectively. It is shown that the amplitude of the disturbance depends on the volume of the irregularity and its location on the margin. For a certain class of velocity and topographic profiles a closed form solution is obtained. The results show that the current is deflected seaward down- stream of the disturbance with the maximum deflection occurring one-fourth of a wavelength downstream of the irregularity. Closed eddies are formed in shallow water and sometimes in deep water. If the ratio of relative shear to the speed of the approaching current is large at the continental margin, a simple analytical solution is applicable. The model is applied to the Gulf Stream flowing o...

An expanded Eulerian model of phytoplankton environmental response

An Eulerian approach to modeling plankton physiological responses to environmental factors is developed wherein the time history of cell exposure to two external environmental fields over specified time intervals are utilized as independent variables along with position and time to help characterize the cell population. We seek to find the concentration of cells per unit volume as a function of depth, time, and the time histories of exposure to PAR (photosynthetically active radiation) as it influences internal cellular carbon through phototsynthesis and to nitrate as it influences internal cellular nitrogen through nutrient assimilation. The response under consideration here, vertical swimming, is taken to depend on historical exposure to the external PAR and nitrate fields. The model can be readily extended to other external fields and to more than the one historical time scale here associated with each external field. This type of model joins Lagrangian models as most beneficial when phytoplankton physiology responds to environmental factors in a nonlinear fashion, i.e. when the mean response does not depend on the mean exposure. A simple example is discussed and the impact of wind-driven mixing is explored.

On the effects of buoyancy flux on continental shelf circulation

Abstract The effects of surface buoyancy flux. atmospheric wind stress and bottom topography on the horizontal and vertical structure of the density and alongshore velocity fields over a continental shelf are investigated within the context of a two-dimensional steady-state model. Using an iterative procedure, similarity solutions are obtained which include the important nonlinear advective effects in the density diffusion equation. In the absence of a wind stress, a reasonable value for the surface buoyancy flux produces alongshore velocities on the order of 20 cm s−1 and an upwelling-like vertical plane circulation. The depth variation across the shelf significantly affects the vertical structure of the density and velocity fields. The introduction of upwelling favorable winds decreases the horizontal density gradient and its associated baroclinic current. A simple physical explanation for this effect, based on heat conservation, is presented.

The Scattering of Continental Shelf Waves by an Isolated Topographic Irregularity

Abstract A model for the scattering of a continental shelf wave by a small, isolated and smooth topographic irregularity is developed. It is found that a wave of frequency ω, incident on a bump of a sufficiently small horizontal extent such that the solution for a delta-function bump will apply, will trigger all other allowable modes of the same frequency with the highest modes having the largest amplitudes. Further, the higher the mode of the incoming wave, the more strongly will it be scattered. Thus, for a continuous spectrum of continental shelf waves propagating over complicated and extended topography, one would expect a net cascading process toward the higher wavenumber end of the spectrum due solely to the effects of topography. It is noted, however, that if the solution is integrated over a bump of large horizontal extent, the behavior of the forward-scattered and backscattered waves could be entirely different from that of a delta function bump.

Steady, three-dimensional circulation on a cuspate continental shelf

Abstract A three-dimensional diagnostic model is constructed to investigate the steady circulation on a cuspate continental shelf. The curvature of the coastline and variable bottom topography are included in the analysis. The model is forced by alongshore wind stress, offshore wind stress, wind stress curl, wind stress divergence, and the spatial variations of the density field. Because of the coastline curvature the component of the wind stress parallel to the coast varies in the alongshore direction even if the wind stress itself is spatially uniform. This leads to asymmetrical distribution of the sea level gradients and to variations in the mass flux normal to the coast. The effects of nonuniform wind forcing introduced by the coastal curvature and those purely due to the effects of the wind stress curl and divergence with no flux normal to the coast are compared and discussed.

A model of the effects of horizontal density gradients on mixing processes in the oceanic surface layer

A diurnal Eulerian model of the upper mixed layer incorporating the effects of horizontal density gradients is developed based on that of Janowitz and Kamykowski [1991] and is utilized to study the effects of wind-driven cross-isopycnal transport on mixing processes in the layer. Four runs of the model are conducted for a constant horizontal density gradient of 2.5 × 10−5 kg m−4 with wind directions at 0°, 90°, 180°, and 270° to this gradient. Two runs are conducted with half this density gradient and wind directions 90° to the left and right of the gradient and one run with no density gradient. In all cases the model is first run with a constant heat loss rate of 150 W m−2 through the sea surface for 11 hours to simulate nighttime cooling and to provide initial conditions for daytime runs. The model is then run for 24 hours with a constant wind speed of 7 m s−1 and a maximum solar radiation of 900 W m−2 during the first 13 hours of the 24-hour simulation. The results show that the shallowest mixed layer occurs when the wind direction is 90° to the left of the density gradient and the deepest layer occurs with the wind direction 90° to the right of the gradient. After 24 hours, the ratio of the deepest to the shallowest mixed layer depth is 2.35 for the stronger gradient and 1.83 for the weaker gradient. These results are explained by the effect of vertical shear of the wind-driven advection of horizontal density variations, which changes the vertical density gradient and can destabilize or stabilize the mixed layer. The results indicate that wind-driven, cross-isopycnal transport can have significant effects on mixing processes in the layer. Dimensionless parameters are developed to estimate the relative importance of cross-isopycnal, wind-driven transport on mixed layer properties.

Baroclinically driven estuarine flow: A perturbation approach

The residual circulation and density in a shallow estuary of constant depth and width and flowing at high Rayleigh number (Ra) and small internal Froude number (Fr), based on riverine flow (U∞) and the horizontal density variation, are studied. Criteria under which direct tidal effects on the residual flow can be neglected are established. The effects of varying the bottom boundary condition on the velocity field from free slip to no slip are examined using a linear bottom stress boundary condition. The governing equations are nondimensionalized, expanded in a power series in the small parameter, and the zeroth- and first-order equations governing the density field are solved; these solutions yield the zeroth- and first-order results for the velocity field. The equation governing the density field at lowest order is nonlinear and is solved numerically. The results show that for sufficiently large Ra, the mean transport of salt is balanced by baroclinic advection near the mouth and by horizontal turbulent transport farther upstream. For these large Ra the horizontal structure as well as the vertical structure of the flow is strongly affected by the bottom boundary condition with the salinity disturbances determined under the free-slip condition extending twice as far upstream as the no-slip results. For smaller Ra, though still large compared to 1, the mean transport is balanced by horizontal mixing throughout the system, and the bottom boundary condition does not affect the horizontal structure. The penetration distance of oceanic waters, with the internal Fr fixed, increases as Ra increases above 24, reaches a maximum upstream penetration distance of Kh/U∞ when Ra reaches 65, and decreases as Ra increases further. The ratio of entrained oceanic waters to riverine inflow is inversely proportional to the internal Fr to the 2/3 power for very large Ra and becomes proportional to Ra as the latter decreases.