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S. J. M. ALLEN

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M. Zerroukat and T. Allen

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The heterogeneity and the singularity of the grid are major factors in the weak scalability of longitude–latitude grid–based atmospheric models on massively parallel machines. Overset grids and, in particular, the Yin–Yang grid, are potential solutions to this problem. Using semi-implicit time marching schemes requires the solution of an elliptic problem on the particular grid. For overset/composite grids to be a viable approach, the solution of the elliptic problem has to be at least as accurate and efficient as using a single grid. This paper proposes combining the overset/Yin–Yang composite elliptic problems in one system using Krylov-type solvers and shows that the solution on overset grids is highly efficient because of the improved grid’s homogeneity.

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Michael M. Whitney and J. S. Allen

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This study examines how coastal banks influence wind-driven circulation along stratified continental shelves. Numerical experiments are conducted for idealized symmetric banks; the standard bank (200 km long and 50 km wide) has dimensions similar to the Heceta Bank complex along the Oregon shelf. Model runs are forced with 10 days of steady winds (0.1 Pa); upwelling and downwelling cases are compared. The bank introduces significant alongshelf variability in the currents and density fields. Upwelling-favorable winds create an upwelling front and a baroclinic jet (flowing opposite coastal-trapped wave propagation) that bend around the standard bank, approximately centered on the 90-m isobath. The upwelling jet is strongest over the upstream bank half, where it advects a tongue of dense water over the bank. There is a current reversal shoreward of the main jet at the bank center. Upwelling is most intense over the upstream part of the bank, while there is reduced upwelling and even downwelling over other bank sections. Downwelling-favorable winds create a near-bottom density front and a baroclinic jet (flowing in the direction of coastal-trapped wave propagation) that bend around the standard bank; the jet core moves from the 150-m isobath to the 100-m isobath and back over the bank. The downwelling jet is slowest and widest over the bank; there are no current reversals. Results over the bank are more similar to 2D results (that preclude alongshelf variability) than in the upwelling case. Downwelling is weakened over the bank. The density field evolution over the bank is fundamentally different from the upwelling case. Most model results for banks with different dimensions are qualitatively similar to the standard run. The exceptions are banks having a radius of curvature smaller than the inertial radius; the main jet remains detached from the coast far downstream from these banks. The lowest-order across-stream momentum balance indicates that the depth-averaged flow is geostrophic. Advection, ageostrophic pressure gradients, wind stress, and bottom stress are all important in the depth-averaged alongstream momentum balance over the bank. There is considerable variability in alongstream momentum balances over different bank sections. Across-shelf and alongshelf advection both change the density field over the bank. Barotropic potential vorticity is not conserved, but the tendency for relative vorticity changes and depth changes to partially counter each other results in differences between the upwelling and downwelling jet paths over the bank. Only certain areas of the bank have significant vertical velocities. In these areas of active upwelling and downwelling, vertical velocities at the top of the bottom boundary layer are due to either the jet crossing isobaths or bottom Ekman pumping.

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Scott M. Durski and J. S. Allen

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A primitive equation model is used to study the finite-amplitude evolution of instabilities associated with the coastal upwelling front. Simulations of increasing complexity are examined that represent idealizations of summer conditions off the Oregon coast, including cases with steady and with time-variable wind in a domain with alongshore-uniform bathymetry and with time-variable wind in a domain with realistic Oregon coast bathymetry. The numerical results indicate that the fastest-growing mode in this system has approximately an 8–10-km alongshore wavelength but that, once the disturbances grow to finite amplitude, the predominant alongfront scale increases rapidly because of nonlinear effects. Separation of the total kinetic energy into contributions from the alongshore average flow and perturbation about that average shows that the initial growth of the perturbation kinetic energy is due to potential energy conversion, but transfer of energy from the kinetic energy of the alongshore average flow becomes important once the disturbances reach large amplitude. The time-variable wind simulations again show initial growth of small-scale instabilities followed by evolution to larger scales. In this case, however, even after larger-scale disturbances have developed on the upwelling front, smaller-scale patterns amplify along the front in response to each upwelling-favorable wind event. Realistic coastal bathymetry introduces additional alongshore topographic scales into the problem, but the formation of instabilities on small scales and evolution to larger scales are still ubiquitous. Where instabilities encounter strong curvature in the upwelling front produced by bathymetric effects, the upwelling front becomes highly contorted and horizontal variability is significantly enhanced.

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Roger M. Samelson and J. S. Allen

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Observations of oppositely directed, monthly mean alongshore currents and wind stress over the continental margin off the Pacific coast of North America motivate the theoretical examination of mean flow generation by topographic lee-wave drag. We formulate a barotropic model for wind-forced shelf-slope flow over variable topography. Our central objective is an analytical expression for mean flow generation in a simple case. We specify a linear cross-shelf slope with sinusoidal alongshore variations and use the approximation of Hart, which yields a system with only parametric cross-shelf dependence when the alongshore scales are short compared to the cross-shelf scales. The inviscid unforced equations have two constants of the motion and reduce to a quartic Hamiltonian system similar to that of Duffing's equation. For weak new-resonant time-periodic forcing, we use the method of averaging to obtain evolution equations for the amplitudes of small oscillations. All steady solutions of the averaged equations, which correspond to steadily oscillating small amplitude currents in the model, have mean current in the direction of the observed currents (poleward on an eastern boundary). Multiple equilibria occur. Mean current generation is most efficient for low frequencies, short wavelength topographic variations, and comparable alongshore and cross-shelf topographic slopes. The mean Lagrangian flow is along isobaths. Numerical solutions of the model equations compare well with the averaging analysis predictions. For certain parameter ranges, all steady solutions of the averaged equations are linearly unstable. In these ranges, numerical solutions of the averaged equations yield limit cycles, period doubling sequences, and chaotic behavior, suggesting that the response of slope flow to atmospheric forcing may be irregular.

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Michael M. Whitney and J. S. Allen

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This study investigates wind-driven circulation in the vicinity of the Heceta Bank complex along the Oregon shelf. Numerical experiments forced with steady winds (0.1 Pa) are conducted; upwelling and downwelling cases are compared. The asymmetric bank bathymetry is the only configurational difference from the symmetric bank runs analyzed in Part I (Whitney and Allen). Upwelling-favorable winds generate an upwelling front and southward baroclinic jet. Model results indicate the upwelling jet is centered on the 100-m isobath along the straight shelf. The jet follows this isobath offshore around the northern part of the bank but separates from sharply turning isobaths in the southern half and flows over deeper waters. The jet turns back toward the coast farther downstream. Inshore of the main jet, currents reverse and flow back onto the bank. These reversed currents turn southward again (at the bank center) and join a secondary southward coastal upwelling jet. This secondary coastal jet converges with the stronger main jet farther downstream. Upwelling is intense at the northern bank edge near the coast, where a dense water tongue is advected over the bank. Upwelling also is strong on the southern bank half where the flow turns and reverses. Other areas of the bank have reduced upwelling or even downwelling during upwelling-favorable winds. Downwelling-favorable winds drive a near-bottom density front and a northward jet. The slower downwelling jet flows along the 130-m isobath over the straight shelf. The jet departs from isobaths over the southern bank half and follows a straighter path over shallower waters. There are no reversed currents over the bank. The bank is an area of reduced downwelling. Some of the differences in the evolution of the current and density fields are linked to fundamental differences between the upwelling and downwelling regimes; these are anticipated by the symmetric bank results of Part I. Other differences arise because of the bank asymmetry and opposite flow directions over the bank.

The lowest-order depth-averaged across-stream momentum balance remains geostrophic over the bank. Advection, ageostrophic pressure gradients, wind stress, and bottom stress all are important in the depth-averaged alongstream momentum balance over the Heceta Bank complex. Both across-shelf and alongshelf density advection are important. Barotropic potential vorticity is not conserved over the bank, but the tendency for relative vorticity changes and depth changes to partially counter each other influences the different paths of the upwelling and downwelling jets. There are several regions of active upwelling and downwelling over the bank. In these areas, vertical velocities at the top of the bottom boundary layer are linked to topographic upwelling and downwelling and Ekman pumping. There is considerable spatial variability in the currents, densities, and dynamics over the Heceta Bank complex.

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Allen C. Kuo and Lorenzo M. Polvani

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Shock-capturing numerical methods are employed to integrate the fully nonlinear, rotating 1D shallow-water equations starting from steplike nongeostrophic initial conditions (a Rossby adjustment problem). Such numerical methods allow one to observe the formation of multiple bores during the transient adjustment process as well as their decay due to rotation. It is demonstrated that increasing the rotation and/or the nonlinearity increases the rate of decay. Additionally, the time required for adjustment to be completed and its dependence on nonlinearity is examined; this time is found to be highly measure dependent. Lastly, the final adjusted state of the system is observed through long time integrations. Although the bores that form provide a mechanism for dissipation, their decay results in a final state in very good agreement with the one computed by well-known (dissipationless) conservation methods.

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J. M. SASSMAN and R. A. ALLEN

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An empirical study is made of the relationship of precipitation occurrence to vertical velocity and dewpoint depression. Based on this work, a method of forecasting precipitation occurrence is developed. The method uses two predictors, the prognostic charts of 500-mb. vertical velocity made by the JNWP Unit with a thermotropic model, and the dewpoint depression. Tests of the method suggest it is widely applicable in the eastern United States.

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C. M. Martell and J. S. Allen

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The effects of alongshore variations in bottom topography on wind-stress-forced barotropic motion over a continental shelf and slope are studied. An idealized channel model with a weakly sloping bottom and with small-amplitude alongshore variations in topography is utilized. Perturbation methods and numerical inversion of Fourier transforms are employed. The effect of a localized alongshore topographic disturbance is examined in the context of an initial-value problem, where a spatially uniform wind stress is applied at t = 0. The wind stress forces a basic unperturbed alongshore velocity V which is constant in space. Shelf waves are forced by the interaction of V with the topographic disturbance. Two types of time variation of the wind stress are considered, a Dirac delta function and a Heaviside unit function. These force, respectively, V = constant and V = tV t, where V t = constant. The effect of the alongshore scale of the topographic feature is examined. For small scales, adjective effects of V are important and lee waves form in cases where V is in a direction opposite to the shelf wave phase velocity c p. Particular attention is paid to a study of the development of lee waves in the time-varying basic flow V = tV t. In that case, the type of lee waves generated depends on the magnitude of V t and on the alongshore scale of the topographic disturbance. If V t is small, a slowly varying lee wavetrain is developed with wavelengths corresponding to the value of V at the time of generation. Approximate analytical solutions are obtainable in this case. If V t is large, lee waves with rapidly varying wavelengths are formed. These waves separate from the disturbance and are advected downstream when |V| > |c p|max.

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B. T. Kuebel Cervantes, J. S. Allen, and R. M. Samelson

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The effects of wind-forced upwelling and downwelling on the continental shelf off Duck, North Carolina, are studied through experiments with a two-dimensional numerical primitive equation model. Moored and shipboard measurements obtained during August–November 1994 as part of the Coastal Ocean Processes (CoOP) Inner Shelf Study (ISS) are used for model–data comparisons. The model is initialized with realistic stratification and forced with observed wind and heat flux data. Both strongly stratified and weakly stratified conditions, found during August and October, respectively, are studied. August is characterized by fluctuating alongshelf wind direction, and October is dominated by downwelling-favorable winds. The across-shelf momentum balance is primarily geostrophic on the continental shelf. The alongshelf momentum balance is mainly between the Coriolis force and vertical diffusion with additional contributions from the local acceleration and nonlinear advection terms. The model solutions are utilized to acquire detailed information on the time- and space-dependent variability of the across-shelf circulation and transport and to investigate the dependence of this circulation on the seasonal change in stratification. When the stratification breaks down, as in October, the across-shelf transport is reduced significantly in comparison with the theoretical Ekman transport for large wind stress values. The paths of individual model water parcels are traced using two methods: calculation of Lagrangian trajectories and time evolution of three Lagrangian label fields. The August period produces complex Lagrangian dynamics because of the switching between upwelling and downwelling winds. The October period illustrates a mean downwelling response that advects parcels across and along the shelf and vertically.

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