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M. Jeroen Molemaker and Henk A. Dijkstra

Abstract

Geostrophic eddies in a stratified liquid are susceptible to baroclinic instabilities. In this paper, the authors consider these instabilities when such an eddy is simultaneously cooled homogeneously from above. As a linear stability analysis shows, the developing convection modifies the background stratification, the stability boundaries, and the patterns of the dominant modes. The coupling between the effects of convection and the large-scale flow development of the eddy is studied through high-resolution numerical simulations, using both nonhydrostatic and hydrostatic models. In the latter models, several forms of convective adjustment are used to model convection. Both types of models confirm the development of the dominant modes and indicate that their nonlinear interaction leads to localized intense convection. By comparing nonhydrostatic and hydrostatic simulations of the flow development carefully, it is shown that convective adjustment may lead to erroneous small-scale variability. A simple alternative formulation of convective adjustment is able to give a substantial improvement.

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James C. McWilliams and M. Jeroen Molemaker

Abstract

In a large-scale deformation flow, lateral and vertical buoyancy gradients sharpen through baroclinic frontogenesis near the surface boundary. A “thermally direct” ageostrophic secondary circulation cell arises during frontogenesis to maintain geostrophic, hydrostatic (thermal wind) momentum balance for the alongfront flow. Unstable three-dimensional fluctuations can grow during frontogenesis by baroclinic instability of the alongfront shear flow that converts frontal potential energy to fluctuation energy. At finite amplitude, the fluctuations provide alongfront-averaged eddy momentum and buoyancy fluxes that arrest the frontal sharpening even while the deformation flow persists. The frontal ageostrophic secondary circulation reverses to become a “thermally indirect” cell in the center of the front. This allows an approximate opposition between ageostrophic advection and eddy-flux divergence in the frontal buoyancy gradient variance (i.e., frontal strength) balance equation, implying frontal equilibration. During the approximately equilibrated phase, the energy exchange rates among the deformation flow, front, and fluctuations are all reduced in comparison with a solution without eddy-flux feedback on the frontal evolution. The mean stratification is enhanced by both frontogenesis and eddy vertical buoyancy flux. The thermally indirect secondary circulation arises from eddy fluxes acting to force a departure in thermal-wind balance for the alongfront flow, overwhelming the single-cell thermally direct circulation induced by the deformation flow. The equilibrated thermal-wind imbalance in the frontal flow is appreciable, and its magnitude is set by the cross-front eddy flux of alongfront vorticity. This demonstrates an essentially inviscid, baroclinic, dynamical process for frontogenetic arrest through frontal instability.

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Jonathan Gula, M. Jeroen Molemaker, and James C. McWilliams

Abstract

The Gulf Stream strongly interacts with the topography along the southeastern U.S. seaboard, between the Straits of Florida and Cape Hatteras. The dynamics of the Gulf Stream in this region is investigated with a set of realistic, very high-resolution simulations using the Regional Ocean Modeling System (ROMS). The mean path is strongly influenced by the topography and in particular the Charleston Bump. There are significant local pressure anomalies and topographic form stresses exerted by the bump that retard the mean flow and steer the mean current pathway seaward. The topography provides, through bottom pressure torque, the positive input of barotropic vorticity necessary to balance the meridional transport of fluid and close the gyre-scale vorticity balance. The effect of the topography on the development of meanders and eddies is studied by computing energy budgets of the eddies and the mean flow. The baroclinic instability is stabilized by the slope everywhere except past the bump. The flow is barotropically unstable, and kinetic energy is converted from the mean flow to the eddies following the Straits of Florida and at the bump with regions of eddy-to-mean conversion in between. There is eddy growth by Reynolds stress and downstream development of the eddies. Interaction of the flow with the topography acts as an external forcing process to localize these oceanic storm tracks. Associated time-averaged eddy fluxes are essential to maintain and reshape the mean current. The pattern of eddy fluxes is interpreted in terms of eddy life cycle, eddy fluxes being directed downgradient in eddy growth regions and upgradient in eddy decay regions.

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M. Jeroen Molemaker and Jordi Vilà-Guerau de Arellano

Abstract

The influence of convective turbulence on chemical reactions in the atmospheric boundary layer is studied by means of direct numerical simulation (DNS). An archetype of turbulent reacting flows is used to study the reaction zones and to obtain a description of the turbulent control of chemical reactions. Several simulations are carried out and classified using a turbulent Damköhler number and a Kolmogorov Damköhler number. Using a classification based on these numbers, it is shown that it is possible to represent and to solve adequately all relevant scales of turbulence and chemistry by means of DNS. The simulations show clearly that the reaction zones are located near the boundaries where the species are introduced. At the lower boundary of the convective boundary layer, the reaction takes place predominantly in the core of the updrafts, whereas in the upper part of the domain the chemical reaction is greatest in the center of the downdrafts. In the bulk of the boundary layer the chemical reaction proceeds very slowly, due to the almost complete segregation of the chemical species. From the point of view of chemistry, the mixing across the interface between updrafts and downdrafts in the bulk of the convective boundary layer plays only a minor role.

The amount of chemical reaction in relation to the degree of turbulence is quantified by the introduction of an effective Damköhler number. This dimensionless number explicitly takes into account the reduction of the reaction rate due to the segregation of the chemical species. It is shown that the number approaches an asymptotic value that is O(1) for increasingly fast reaction rates. This shows explicitly that the timescale of the chemical reactions is limited by the integral turbulent timescale. It is suggested how a parameterization could be used to include this effect into one-dimensional atmospheric models.

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M. Jeroen Molemaker, James C. McWilliams, and Irad Yavneh

Abstract

Under the influences of stable density stratification and the earth’s rotation, large-scale flows in the ocean and atmosphere have a mainly balanced dynamics—sometimes called the slow manifold—in the sense that there are diagnostic hydrostatic and gradient-wind momentum balances that constrain the fluid acceleration. The nonlinear balance equations are a widely successful, approximate model for this regime, and mathematically explicit limits of their time integrability have been identified. It is hypothesized that these limits are indicative, at least approximately, of the transition from the larger-scale regime of inverse energy cascades by anisotropic flows to the smaller-scale regime of forward energy cascade to dissipation by more nearly isotropic flows and intermittently breaking inertia–gravity waves. This paper analyzes the particular example of an unbalanced instability of a balanced, horizontally uniform, vertically sheared current, as it occurs within the Boussinesq equations. This ageostrophic, anticyclonic, baroclinic instability is investigated with an emphasis on how it relates to the breakdown of balance in the neighborhood of loss of balanced integrability and on how its properties compare with other examples of ageostrophic anticyclonic instability of rotating, stratified, horizontally sheared currents. It is also compared with the more familiar types of instability for a vertically sheared current: balanced (geostrophic) baroclinic instability, centrifugal instability, and Kelvin–Helmholtz instability.

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James C. McWilliams, Jonathan Gula, and M. Jeroen Molemaker

Abstract

Eastward zonal jets are common in the ocean and atmosphere, for example, the Gulf Stream and jet stream. They are characterized by atypically strong horizontal velocity, baroclinic vertical structure with an upward flow intensification, large change in the density stratification meridionally across the jet, large-scale meanders around a central latitude, narrow troughs and broad crests, and a sharp and vertically sloping northern (poleward) “wall” defined by horizontal maxima in the lateral gradients of both velocity and density. Measurements and realistic oceanic simulations show these features in the Gulf Stream downstream from its western boundary separation point. A diagnostic theory based on the conservative balance equations is developed to calculate the 3D velocity field associated with the dynamic height field. When applied to an idealized representation of a meandering jet, it explains the spatial structure of the associated ageostrophic secondary circulation around the jet and the positive frontogenetic tendency along the northern wall in the meander sector located upstream from the trough. This provides a basis for understanding why submesoscale instabilities and cross-wall intrusion and streamer events are more prevalent along the sector downstream from the trough and at the crest where there is not such a frontogenetic tendency. An important attribute for this frontogenesis pattern is the 3D shape of the jet, whose idealization is summarized above.

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Jonathan Gula, M. Jeroen Molemaker, and James C. McWilliams

Abstract

Frontal eddies are commonly observed and understood as the product of an instability of the Gulf Stream along the southeastern U.S. seaboard. Here, the authors study the dynamics of a simulated Gulf Stream frontal eddy in the South Atlantic Bight, including its structure, propagation, and emergent submesoscale interior and neighboring substructure, at very high resolution (dx = 150 m). A rich submesoscale structure is revealed inside the frontal eddy. Meander-induced frontogenesis sharpens the gradients and forms very sharp fronts between the eddy and the adjacent Gulf Stream. The strong straining increases the velocity shear and suppresses the development of barotropic instability on the upstream face of the meander trough. Barotropic instability of the sheared flow develops from small-amplitude perturbations when the straining weakens at the trough. Small-scale meandering perturbations evolve into rolled-up submesoscale vortices that are advected back into the interior of the frontal eddy. The deep fronts mix the tracer properties and enhance vertical exchanges of tracers between the mixed layer and the interior, as diagnosed by virtual Lagrangian particles. The frontal eddy also locally creates a strong southward flow against the shelf leading to topographic generation of submesoscale centrifugal instability and mixing. In eddy-resolving models that do not resolve these submesoscale processes, there is a significant weakening of the intensity of the upwelling in the core of the frontal eddies, and their decay is generally too fast.

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M. Jeroen Molemaker, James C. McWilliams, and William K. Dewar

Abstract

The California Undercurrent (CUC) flows poleward mostly along the continental slope. It develops a narrow strip of large negative vertical vorticity through the turbulent boundary layer and bottom stress. In several downstream locations, the current separates, aided by topographic curvature and flow inertia, in particular near Point Sur Ridge, south of Monterey Bay. When this happens the high-vorticity strip undergoes rapid instability that appears to be mesoscale in “eddy-resolving” simulations but is substantially submesoscale with a finer computational grid. The negative relative vorticity in the CUC is larger than the background rotation f, and Ertel potential vorticity is negative. This instigates ageostrophic centrifugal instability. The submesoscale turbulence is partly unbalanced, has elevated local dissipation and mixing, and leads to dilution of the extreme vorticity values. Farther downstream, the submesoscale activity abates, and the remaining eddy motions exhibit an upscale organization into the mesoscale, resulting in long-lived coherent anticyclones in the depth range of 100–500 m (previously called Cuddies) that move into the gyre interior in a generally southwestward direction. In addition to the energy and mixing effects of the postseparation instability, there is are significant local topographic form stress and bottom torque that retard the CUC and steer the mean current pathway.

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Tao Wang, Roy Barkan, James C. McWilliams, and M. Jeroen Molemaker

Abstract

Submesoscale currents (SMCs), in the forms of fronts, filaments, and vortices, are studied using a high-resolution (~150 m) Regional Oceanic Modeling System (ROMS) simulation in the Mississippi River plume system. Fronts and filaments are identified by large horizontal velocity and buoyancy gradients, surface convergence, and cyclonic vertical vorticity with along-coast fronts and along-plume-edge filaments notably evident. Frontogenesis and arrest/destruction are two fundamental phases in the life cycle of fronts and filaments. In the Mississippi River plume region, the horizontal advective tendency induced by confluence and convergence plays a primary role in frontogenesis. Confluent currents sharpen preexisting horizontal buoyancy gradients and initiate frontogenesis. Once the fronts and filaments are formed and the Rossby number reaches O(1), they further evolve frontogenetically mainly by convergent secondary circulations, which can be maintained by different cross-front momentum balance regimes. Confluent motions and preexisting horizontal buoyancy gradients depend on the interaction between wind-induced Ekman transport and the spreading plume water. Consequently, the direction of wind has a significant effect on the temporal variability of SMCs, with more active SMCs generated during a coastally downwelling-favorable wind and fewer SMCs during an upwelling-favorable wind. Submesoscale instabilities (~1–3 km) play a primary role in the arrest and fragmentation of most fronts and filaments. These instabilities propagate along the fronts and filaments, and their energy conversion is a mixed barotropic–baroclinic type with horizontal-shear instabilities dominating.

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Jonathan Gula, M. Jeroen Molemaker, and James C. McWilliams

Abstract

A set of realistic, very high-resolution simulations is made for the Gulf Stream region using the oceanic model Regional Oceanic Modeling System (ROMS) to study the life cycle of the intense submesoscale cold filaments that form on the subtropical gyre, interior wall of the Gulf Stream. The surface buoyancy gradients and ageostrophic secondary circulations intensify in response to the mesoscale strain field as predicted by the theory of filamentogenesis. It can be understood in terms of a dual frontogenetic process, along the lines understood for a single front. There is, however, a stronger secondary circulation due to the amplification at the center of a cold filament. Filament dynamics in the presence of a mixed layer are not adequately described by the classical thermal wind balance. The effect of vertical mixing of momentum due to turbulence in the surface layer is of the same order of magnitude as the pressure gradient and Coriolis force and contributes equally to a so-called turbulent thermal wind balance. Filamentogenesis is disrupted by vigorous submesoscale instabilities. The cause of the instability is the lateral shear as energy production by the horizontal Reynolds stress is the primary fluctuation source during the process; this contrasts with the usual baroclinic instability of submesoscale surface fronts. The filaments are lines of strong oceanic surface convergence as illustrated by the release of Lagrangian parcels in the Gulf Stream. Diabatic mixing is strong as parcels move across the filaments and downwell into the pycnocline. The life cycle of a filament is typically a few days in duration, from intensification to quasi stationarity to instability to dissipation.

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