M. Jeroen Molemaker

Baroclinic Instability and Loss of Balance

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 ageo...

Balanced and unbalanced routes to dissipation in an equilibrated Eady flow

The oceanic general circulation is forced at large scales and is unstable to mesoscale eddies. Large-scale currents and eddy flows are approximately in geostrophic balance. Geostrophic dynamics is characterized by an inverse energy cascade except for dissipation near the boundaries. In this paper, we confront the dilemma of how the general circulation may achieve dynamical equilibrium in the presence of continuous large-scale forcing and the absence of boundary dissipation. We do this with a forced horizontal flow with spatially uniform rotation, vertical stratification and vertical shear in a horizontally periodic domain, i.e. a version of Eadys flow carried to turbulent equilibrium. A direct route to interior dissipation is presented that is essentially non-geostrophic in its dynamics, with significant submesoscale frontogenesis, frontal instability and breakdown, and forward kinetic energy cascade to dissipation. To support this conclusion, a series of simulations is made with both quasigeostrophic and Boussinesq models. The quasigeostrophic model is shown as increasingly inefficient in achieving equilibration through viscous dissipation at increasingly higher numerical resolution (hence Reynolds number), whereas the non-geostrophic Boussinesq model equilibrates with only weak dependence on resolution and Rossby number.

Effects of turbulence and heterogeneous emissions on photochemically active species in the convective boundary layer

Photochemistry is studied in a convective atmospheric boundary layer. The essential reactions that account for the ozone formation and depletion are included in the chemical mechanism which, as a consequence, contains a wide range of timescales. The turbulent reacting flow is modeled with a large-eddy simulation (LES) code. The deviations from chemical equilibrium that are caused by turbulent motions are investigated in terms of the intensity of segregation. For the studied cases it is found that the volume-averaged concentrations calculated with the LES code agree well with the concentrations calculated with a box model. The reaction rate between RH (a generic hydrocarbon emitted at the surface) and OH is most strongly affected (3% slower than in the box model). However, if RH is emitted nonuniformly at the surface, or if the RH-OH reaction rate is increased, the volume-averaged RH destruction by OH may be slowed down by as much as 30% compared to a box model. Sensitivity studies showed that the intensity of segregation between RH and OH not only depends on the strength and spatial distribution of the RH emissions but also on the way NO is emitted in the model atmosphere. The results obtained indicate that the assumption that localized emissions of reactive hydrocarbons, for example, isoprene or terpenes, are instantaneously mixed may lead to an underestimation of their atmospheric lifetime.

Submesoscale Cold Filaments in the Gulf Stream

AbstractA 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 therm...

Submesoscale Instability and Generation of Mesoscale Anticyclones near a Separation of the California Undercurrent

AbstractThe 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 organizati...

Non-axisymmetric instability of centrifugally stable stratified Taylor-Couette flow

The stability is investigated of the swirling flow between two concentric cylinders in the presence of stable axial linear density stratication, for flows not satisfying the well-known Rayleigh criterion for inviscid centrifugal instability, d(Vr) 2 =d r< 0. We show by a linear stability analysis that a sucient condition for non-axisymmetric instability is, in fact, d(V=r) 2 =d r< 0, which implies a far wider range of instability than previously identied. The most unstable modes are radially smooth and occur for a narrow range of vertical wavenumbers. The growth rate is nearly independent of the stratication when the latter is strong, but it is proportional to it when it is weak, implying stability for an unstratied flow. The instability depends strongly on a nondimensional parameter,S, which represents the ratio between the strain rate and twice the angular velocity of the flow. The instabilities occur for anti-cyclonic flow ( S< 0). The optimal growth rate of the fastest-growing mode, which is non-oscillatory in time, decays exponentially fast as S (which can also be considered a Rossby number) tends to 0. The mechanism of the instability is an arrest and phase-locking of Kelvin waves along the boundaries by the mean shear flow. Additionally, we identify a family of (probably innitely many) unstable modes with more oscillatory radial structure and slower growth rates than the primary instability. We determine numerically that the instabilities persist for nite viscosity, and the unstable modes remain similar to the inviscid modes outside boundary layers along the cylinder walls. Furthermore, the nonlinear dynamics of the anti-cyclonic flow are dominated by the linear instability for a substantial range of Reynolds numbers.

Gulf Stream Dynamics along the Southeastern U.S. Seaboard

AbstractThe 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 ...

Symmetry breaking and overturning oscillations in thermohaline-driven flows

The bifurcation structure of thermohaline-driven flows is studied within one of the simplest zonally averaged models which captures thermohaline transport: a Boussinesq model of surface-forced thermohaline flow in a two-dimensional rectangular basin. Under mixed boundary conditions, i.e. prescribed surface temperature and fresh-water flux, it is shown that symmetry breaking originates from a codimension-two singularity which arises through the intersection of the paths of two symmetry-breaking pitchfork bifurcations. The physical mechanism of symmetry breaking of both the thermally and salinity dominated symmetric solution is described in detail from the perturbation structures near bifurcation. Limit cycles with an oscillation period in the order of the overturning time scale arise through Hopf bifurcations on the branches of asymmetric steady solutions. The physical mechanism of oscillation is described in terms of the most unstable mode just at the Hopf bifurcation. The occurrence of these oscillations is quite sensitive to the shape of the prescribed fresh-water flux. Symmetry breaking still occurs when, instead of a fixed temperature, a Newtonian cooling condition is prescribed at the surface. There is only quantitative sensitivity, i.e. the positions of the bifurcation points shift with the surface heat transfer coefficient. There are no qualitative changes in the bifurcation diagram except in the limit where both the surface heat flux and fresh-water flux are prescribed. The bifurcation structure at large aspect ratio is shown to converge to that obtained by asymptotic theory. The complete structure of symmetric and asymmetric multiple equilibria is shown to originate from a codimension-three bifurcation, which arises through the intersection of a cusp and the codimension-two singularity responsible for symmetry breaking.

Filament Frontogenesis by Boundary Layer Turbulence

AbstractA submesoscale filament of dense water in the oceanic surface layer can undergo frontogenesis with a secondary circulation that has a surface horizontal convergence and downwelling in its center. This occurs either because of the mesoscale straining deformation or because of the surface boundary layer turbulence that causes vertical eddy momentum flux divergence or, more briefly, vertical momentum mixing. In the latter case the circulation approximately has a linear horizontal momentum balance among the baroclinic pressure gradient, Coriolis force, and vertical momentum mixing, that is, a turbulent thermal wind. The frontogenetic evolution induced by the turbulent mixing sharpens the transverse gradient of the longitudinal velocity (i.e., it increases the vertical vorticity) through convergent advection by the secondary circulation. In an approximate model based on the turbulent thermal wind, the central vorticity approaches a finite-time singularity, and in a more general hydrostatic model, the c...

The latmix summer campaign: Submesoscale stirring in the upper ocean

AbstractLateral stirring is a basic oceanographic phenomenon affecting the distribution of physical, chemical, and biological fields. Eddy stirring at scales on the order of 100 km (the mesoscale) is fairly well understood and explicitly represented in modern eddy-resolving numerical models of global ocean circulation. The same cannot be said for smaller-scale stirring processes. Here, the authors describe a major oceanographic field experiment aimed at observing and understanding the processes responsible for stirring at scales of 0.1–10 km. Stirring processes of varying intensity were studied in the Sargasso Sea eddy field approximately 250 km southeast of Cape Hatteras. Lateral variability of water-mass properties, the distribution of microscale turbulence, and the evolution of several patches of inert dye were studied with an array of shipboard, autonomous, and airborne instruments. Observations were made at two sites, characterized by weak and moderate background mesoscale straining, to contrast diff...