David C. Chapman

Numerical Treatment of Cross-Shelf Open Boundaries in a Barotropic Coastal Ocean Model

Abstract Using a barotropic coastal ocean model with a straight coastline and uniform cross-shelf bottom slope, seven different cross-shelf open boundary conditions (four of which are applied in either implicit or explicit form) are compared in three numerical experiments. 1) A mound of water is allowed to collapse and radiate waves toward the open boundaries. 2) A uniform alongshelf wind stress is applied at zero time over the entire shelf and held constant for the duration of the experiment. 3) A uniform cross-shelf wind stress is applied at zero time over the entire shelf and held constant for the duration of the experiment. The boundary condition which is most transparent to waves consists of a sponge at the outer edge of the model domain with an Orlanski radiation condition at the outer edge of the sponge. Several open boundary conditions perform adequately in the wind stress experiments, but the Orlanski radiation condition alone (without a sponge) appears to give the best total performance (of thes...

A Simple Theory for the Fate of Buoyant Coastal Discharges

Abstract A simple theory that predicts the vertical structure and offshore spreading of a localized buoyant inflow onto a continental shelf is formulated. The theory is based on two competing mechanisms that move the buoyant fluid offshore: 1) the radial spread of the lighter water over the ambient water, being deflected by the Coriolis force and producing an anticyclonic cyclostrophic plume, and 2) offshore transport of buoyant water in the frictional bottom boundary layer that moves the entire plume offshore while maintaining contact with the bottom. The surface expression of the cyclostrophic plume moves offshore a distance ys = 2(3g′h0 + υ 2i)/(2g′h0 + υ 2i)1/2f,where g′ is reduced gravity based on the inflow density anomaly, h0 is the inflow depth, υi is the inflow velocity, and f is the Coriolis parameter. The plume remains attached to the bottom to a depth given by hb = (2Lυih0f/g′)1/2,where L is the inflow width. Both scales are based solely on parameters of the buoyant inflow at its source. There...

Trapping of a Coastal Density Front by the Bottom Boundary Layer

Abstract The dynamics of a surface-to-bottom density front on a uniformly sloping continental shelf and the role of density advection in the bottom boundary layer are examined using a three-dimensional, primitive equation numerical model. The front is formed by prescribing a localized freshwater inflow through the coastal boundary. The resulting freshwater plume turns anticyclonically and moves along the coast, generating offshore transport in the bottom boundary layer, which advects freshwater offshore and creates a sharp surface-to-bottom density front with a surface-intensified alongshelf jet over the front. The offshore buoyancy flux in the bottom boundary layer moves the front offshore until it reaches a depth where the vertical shear within the front leads to a reversal in the cross-shelf velocity at the shoreward edge of the front. Consequently, the offshore buoyancy flux in the bottom boundary layer vanishes shoreward of the front. Within the front, a steady balance is established in the bottom bo...

On the Origin of Shelf Water in the Middle Atlantic Bight

Abstract Based on a limited set of available oxygen isotope measurements, it is hypothesized that the mean now in the Middle Atlantic Bight is part of a 5000 km-long buoyancy-driven, coastal current which originates along the southern coast of Greenland. This idea is consistent with most features of the known circulation of the region.

The Nantucket Shoals Flux Experiment (NSFE79). Part I: A Basic Description of the Current and Temperature Variability

Abstract The Nantucket Shoals Flux Experiment (NSFE79) was conducted across the continental shelf and upper slope south of Nantucket from March 1979 to April 1980 to study the flow of shelf water from the Georges Bank/Gulf of Maine region into the Middle Atlantic Bight. The experiment included a moored array of current meters and bottom instrumentation deployed at six locations across the shelf and upper slope spanning a depth range from 46 to 810 m, and supporting hydrographic observations. A basic description of the moored current and temperature data is given here with an emphasis on the low-frequency variability. In the summer period (April–August) when the local vertical stratification reached a maximum due to increased surface heating and reduced wind mixing, the mean flow over the shelf at all instruments was primarily along 1ocal isobaths towards the west. The subtidal current fluctuations were coherent both horizontally and vertically over the shelf, but not with current fluctuations observed ove...

A numerical study of dense water formation and transport on a shallow, sloping continental shelf

The circulation and transport of dense water generated by an idealized coastal polynya is studied using a three-dimensional primitive equation model. Starting with a homogeneous, quiescent ocean, a constant negative buoyancy flux is imposed at the surface over a half-elliptical region adjacent to the coastal boundary on a gently sloping continental shelf. The flow response can be divided into the following three phases: geostrophic adjustment, instability, and offshore eddy transport. During geostrophic adjustment the fluid within the forcing region becomes denser and the flow at the edge of the forcing region accelerates in response to the strong density gradient there. Eventually, the flow at the leading edge of the forcing region (relative to Kelvin wave propagation) becomes unstable and a train of counterrotating eddies develops. These eddies then form a complex three-dimensional flow field and rapidly transport dense water offshore, across isobaths. The density within the forcing region reaches a maximum which remains fairly constant after the eddies begin to transport the dense fluid offshore. The results are qualitatively insensitive to weakening of the negative buoyancy forcing and to changing the bottom slope. Eddy scales and velocities are consistent with observations in the Arctic. The results suggest that instability processes and eddy fluxes are important in transporting dense water off continental shelves and into marginal seas.

Formation of Taylor caps over a tall isolated seamount in a stratified ocean

Abstract A primitive equation numerical model is used to examine various aspects of the formation of Taylor caps over a tall isolated seamount in a steady, rotating, nearly inviscid, stratified flow. The flow is characterized by four nondimensional parameters: the Rossby number, R0 = U/fL; the Burger number, S = NH/fL; the fractional seamount height, δ = hm/H; and the aspect ratio, Δ = H/L. Here U is the uniform inflow velocity, f the Coriolis parameter, L the horizontal length scale of the seamount, N the initial buoyancy frequency, H the ocean depth away from the seamount, and h m the maximum height of the seamount above the otherwise flat bottom. For both unstratified (S = 0) and stratified (S= 1) flows over a tall seamount which ultimately form a Taylor cap, the initial response is similar to that found in previous studies which considered short seamounts (δ ≪ 1) in weakly nonlinear flows (R0 ≪ 1). Two eddies form over the seamount and co-rotate clockwise around the seamount until one is swept away wi...

On the Continuity of Mean Flow between the Scotian Shelf and the Middle Atlantic Bight

Abstract Oxygen-isotope tracer data combined with results from two linear barotropic coastal models are used to argue that the observed equatorward mean alongshelf flow in the Middle Atlantic Bight is a downstream extension of the mean alongshelf flow over the Scotian Shelf. Qualitative agreement between model results and observations supports the concept that the alongshelf pressure gradient associated with the mean alongshelf flow in the Middle Atlantic Bight has an upstream or downstream and not an offshelf origin. The role of the local large-scale general circulation is apparently to help keep the shelf water on the shelf rather than to drive the shelf mean flow.

The Importance of Nonlinear Cross-Shelf Momentum Flux during Wind-Driven Coastal Upwelling*

A simple theory is proposed for steady, two-dimensional, wind-driven coastal upwelling that relates the dynamics and the structure of the cross-shelf circulation to the stratification, bathymetry, and wind stress. The new element is an estimate of the nonlinear cross-shelf momentum flux divergence due to the wind-driven crossshelf circulation acting on the vertically sheared geostrophic alongshelf flow. The theory predicts that the magnitude of the cross-shelf momentum flux divergence relative to the wind stress depends on the Burger number S 5 aN/ f, where a is the bottom slope, N is the buoyancy frequency, and f is the Coriolis parameter. For S K 1 (weak stratification), the cross-shelf momentum flux divergence is small, the bottom stress balances the wind stress, and the onshore return flow is primarily in the bottom boundary layer. For S 1 or larger (strong stratification), the cross-shelf momentum flux divergence balances the wind stress, the bottom stress is small, and the onshore return flow is in the interior. Estimates of the cross-shelf momentum flux divergence using moored observations from four coastal upwelling regions (0.2 # S # 1.5) are substantial relative to the wind stress when S 1 and exhibit a dependence on S that is consistent with the theory. Two-dimensional numerical model results indicate that the cross-shelf momentum flux divergence can be substantial for the time-dependent response and that the onshore return flow shifts from the bottom boundary layer for small S to just below the surface boundary layer for S 1.5‐2.

The Role of Stratification in the Formation and Maintenance of Shelf-Break Fronts

Abstract A mechanism is described for the formation or a front at the edge of a continental shelf in an initially linearly stratified fluid lacking horizontal density gradients. A primitive equation numerical model is used with a specified vertically uniform inflow imposed at the upstream boundary, and the flow is allowed to evolve alongshelf under the influence of bottom friction. As the flow progresses downstream, the shelf water moves steadily offshore due to the Ekman flux concentrated in the bottom boundary layer. This offshore flow transports light water under heavier water, which leads to convective overturning and ultimately a vertically well-mixed density field over the shelf. Large cross-shelf density gradients appear along the bottom at the shelf break where the vertically well-mixed shelf water abuts the linearly stratified water on the upper slope. At the shelf break, the bottom boundary layer detaches and continues offshore along upward sloping isopycnals. Neutrally buoyant particles in the ...