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J. C. McWilliams and P. R. Gent

Abstract

Several sets of model equations are presented which represent coupled processes in the tropical atmosphere and ocean. The distribution of ocean surface temperature generates large-scale convective motions in the atmosphere. These winds in turn drive ocean currents which advect ocean temperatures. Under most parametric circumstances, the model solutions have the character of moderately damped oscillations of several year period. This period is characteristic of either ocean particle advection across the zonal extent of the basin or potential energy release associated with the ocean temperature distribution. Less stable model solutions can also occur—limit cycle oscillations, alternative mean climatic balances for fixed parameters—but these are not typical of the parameters selected for application to the tropical Pacific. Simulations of possible El Niño sequences are discussed; in general the responses seem weaker than observed.

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A. R. Robinson and J. C. McWilliams

Abstract

Baroclinic instability is examined in a two-layer, quasi-geostrophic model for linearized mesoscale waves (i.e., with periods of a few months and length scales near the internal deformation radius). The mid-ocean wave environment includes the, β-effect, bottom topography and mean currents, all presumed to vary only on scales much greater than those of the wave. An optimization of the local rate of unstable growth shows the process to be potentially important for mesoscale generation: typically, a vertical velocity shear of 5 cm sec−1 permits an e-folding time of two months. The many processes included in the model allow a great variety of behavior; for example, although both β and topography are generally stabilizing by themselves, their combination can be destabilizing.

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A. M. Treguier and J. C. McWilliams

Abstract

Topographic influences are examined in an eddy-resolving model of oceanic channel flow forced by steady zonal winds. With small explicit lateral friction, transient eddies generated by the baroclinic instability of the mean flow transfer momentum downward to the bottom layer. In the flat-bottom case, bottom friction is the only efficient sink of eastward momentum. When bottom topography is present, the topographic form stress can replace the bottom friction sink in the momentum budget, and a large decrease of the zonal transport results. Large wale topography (of the scale of the forcing) provides the largest form stress. Topographic effects decay with height as suggested by the Prandit scaling, and therefore only topographic scales larger than the Rossby radius can affect the whole water column. In that case, the interfaces are deformed by standing eddies on topographic length scales, and standing eddies replace transient eddies in transferring momentum downward. The bottom-layer mean streamfunction tends to be correlated with the topography as in inviscid solutions. Because of this, only a small part of the flow (the larger scales) contributes to the domain-averaged momentum sink. On smaller scales, the topographic form stress is anticorrelated with the Reynolds stress and has no net effect on the transport. The energy level of the transients is less affected by the topography than is the mean energy. With topography, the space scale of the transients decreases and their time scale increases, and the ratio of potential and kinetic energies is higher.

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W. K. Dewar, J. C. McWilliams, and M. J. Molemaker

Abstract

A regional numerical study of the California Current System near Monterey Bay, California, is conducted using both hydrostatic and nonhydrostatic models. Frequent sighting of strong anticyclones (Cuddies) have occurred in the area, and previous studies have identified Monterey Bay as an apparent region of strong unbalanced flow generation. Here, by means of a downscaling exercise, a domain just downstream of Point Sur is analyzed and argued to be a preferred site of diapycnal mixing. The scenario suggested by the simulations involves the generation of negative relative vorticity in a bottom boundary layer of the California Undercurrent on the continental shelf break. At Point Sur, the current separates from the coast and moves into deep waters where it rapidly develops finite-amplitude instabilities. These manifest as isopycnal overturnings, but in contrast to the normal Kelvin–Helmholtz paradigm for mixing, this study argues that the instability is primarily centrifugal. The evidence for this comes from comparisons of the model with linear results for ageostrophic instabilities. Mixing increases background potential energy. The authors argue the regional potential energy generation near Point Sur in the upper few hundred meters is comparable to that found in open-ocean regions of strong diapycnal mixing, either by abyssal tides and lee waves near topography. This study computes diapycnal fluxes and estimates turbulent diffusivities to argue mixing by centrifugal instability is characterized by diffusivities O(10−4) m2 s−1, although the potential for contamination by explicit diffusivities exists.

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G. Roullet, J. C. McWilliams, X. Capet, and M. J. Molemaker

Abstract

High-resolution simulations of β-channel, zonal-jet, baroclinic turbulence with a three-dimensional quasigeostrophic (QG) model including surface potential vorticity (PV) are analyzed with emphasis on the competing role of interior and surface PV (associated with isopycnal outcropping). Two distinct regimes are considered: a Phillips case, where the PV gradient changes sign twice in the interior, and a Charney case, where the PV gradient changes sign in the interior and at the surface. The Phillips case is typical of the simplified turbulence test beds that have been widely used to investigate the effect of ocean eddies on ocean tracer distribution and fluxes. The Charney case shares many similarities with recent high-resolution primitive equation simulations. The main difference between the two regimes is indeed an energization of submesoscale turbulence near the surface. The energy cycle is analyzed in the (k, z) plane, where k is the horizontal wavenumber. In the two regimes, the large-scale buoyancy forcing is the primary source of mechanical energy. It sustains an energy cycle in which baroclinic instability converts more available potential energy (APE) to kinetic energy (KE) than the APE directly injected by the forcing. This is due to a conversion of KE to APE at the scale of arrest. All the KE is dissipated at the bottom at large scales, in the limit of infinite resolution and despite the submesoscales energizing in the Charney case. The eddy PV flux is largest at the scale of arrest in both cases. The eddy diffusivity is very smooth but highly nonuniform. The eddy-induced circulation acts to flatten the mean isopycnals in both cases.

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E. M. Lane, J. M. Restrepo, and J. C. McWilliams

Abstract

The vortex-force representation of the wave-averaged effects on currents is compared to the radiation-stress representation in a scaling regime appropriate to coastal and shelf waters. Three-dimensional and vertically integrated expressions for the conservative current equations are obtained in both representations. The vortex-force representation decomposes the main wave-averaged effects into two physically understandable concepts—a vortex force and a Bernoulli head. The vortex force is shown to be the dominant wave-averaged effect on currents. This effect can occur at higher order than the apparent leading order for the radiation-stress representation. Excluding nonconservative effects such as wave breaking, the lowest-order radiation or interaction stress can be completely characterized in terms of wave setup, forcing of long (infragravity) waves, and an Eulerian current whose divergence cancels that of the primary wave Stokes drift. The leading-order, wave-averaged dynamical effects incorporate the vortex force together with material advection by Stokes drift, modified pressure-continuity and kinematic surface boundary conditions, and parameterized representations of wave generation by the wind and breaking near the shoreline.

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Richard P. Mied, Gloria J. Lindemann, and James C. McWilliams

Abstract

Numerical simulations have been performed to understand the generation and evolution of mushroom-like patterns observed in remote sensing images of the ocean surface. A two-layer, shallow-water model is employed using a periodic channel on an f-plane. The model is initialized with a unidirectional upper-Ocean momentum patch; the lower layer is at rest, and there is no initial interface displacement. A tracer is used to simulate the presence of passive ocean surface fields advected by the flow. The model thus simulates a nonlinear geostrophic adjustment process at finite Rossby number with a strong radiated wave field and rapid tracer advection. Several types of tracer configuration result, depending upon the size of the Rossby number and the ratio of the patch size to the internal deformation radius. The values of these parameters determine the degree of symmetry of the mushroom pattern, or whether a mushroom tracer distribution even results from the initial flow field. The numerical model is always operated with the ratio of upper layer to lower layer heights small, and analytical calculations using the reduced-gravity, shallow-water equations are used to interpret the numerical results.

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James C. Mcwilliams, Peter R. Gent, and Nancy J. Norton

Abstract

Numerical solutions are examined for nearly axisymmetric geopotential monopole vortices whose vertical structure is essentially confined to the lowest few vertical modes. The vortex environment is a rotating, stratified fluid with spatially variable Coriolis frequency (the β-plane). Solutions are examined with Rossby numbers in an order one range about zero, and therefore the balance equations are and appropriate model. Solutions From the quasi-geostrophic and primitive equations are also examined, and we find that the balance equations are much more accurate than the former and more efficient, both conceptually and computationally, than the latter. The central parameter regime is one of stable vortex propagation, accompanied by week Rossby wave radiation and slow changes in vortex shape, with the latter due more to the radiation than the weak dissipation. Various types of instability—baroclinic, barotropic, and inertial—act to delimit the stable regime for vortices.

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James C. McWilliams, M. J. Molemaker, and E. I. Olafsdottir

Abstract

Near-surface, two-dimensional (2D) baroclinic frontogenesis induced by a barotropic deformation flow enhances the growth of three-dimensional (3D) fluctuations that occur on an ever smaller scale as the front progressively sharpens. The 3D fluctuation growth rate further increases with a larger deformation rate. The fluctuations grow by a combination of baroclinic and barotropic energy conversions from the 2D frontal flow, with the former dominating for most of the situations examined, ranging from small to O(1) values of the Rossby and Froude numbers and nondimensional deformation rate. Averaged 3D fluctuation buoyancy fluxes resist the 2D frontogenesis by a frontolytic tendency. They also augment the buoyancy restratification and potential-to-kinetic energy conversion tendencies of the 2D frontogenesis itself, and the 2D frontogenetic and 3D eddy-induced secondary circulations are mostly reinforcing (unlike in turbulent baroclinic jets). This shows that frontal instability coexists with, and potentially may even overcome, active frontogenesis; this conclusion is contrary to some previous studies. Frontal instability thus can augment frontogenesis in accomplishing a forward cascade of energy from oceanic mesoscale eddies into the submesoscale regime en route to finescale dissipation.

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Sue Ellen Haupt, James C. McWilliams, and Joseph J. Tribbia

Abstract

Modons in shear flow are computed as equilibrium solutions of the equivalent barotropic vorticity equation using a numerical Newton–Kantorovich iterative technique with double Fourier spectral expansion. The model is given a first guess of an exact prototype modon with a small shear flow imposed, then iterated to an equilibrium solution. Continuation (small-step extrapolation of the shear amplitude) is used to produce examples of modons embedded in moderate amplitude background shear flows. It is found that in the presence of symmetric shear, the modon is strengthened relative to the prototype. The best-fit phase speed for this case is significantly greater than the Doppler-shifted speed. Nonsymmetric shear strengthens the poles selectively: positive shear strengthens the low while weakening the high. The diagnosed functional relationship between the streamfunction in the traveling reference frame and the vorticity appears linear for all types of shear studied. The modons in symmetric shear are stable within time integrations, at least for small to moderate shear amplitude. Antisymmetric shear appears to trigger a tilting instability of the stationary state; yet coherence of the modon is maintained. This study strengthens the plausibility of using modons as a model of coherent structures in geophysical flow.

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