Quasi-geostrophic Research Articles

An enhanced ensemble‐based method for computing CNOPs using an efficient localization implementation scheme and a two‐step optimization strategy: formulation and preliminary tests

The ensemble‐based methods for computing conditional nonlinear optimal perturbations (CNOPs) often contain a localization implementation scheme; its computer implementation is very expensive because of huge memory usage or costly repeated calculations. As a result, the lack of efficient algorithms limits the applications of CNOP. To address this issue, an efficient new localization implementation scheme is proposed in this article. The main ideas are to utilize the correlation matrix and to approximate it by a set of selected Gaussian random samples. An enhanced ensemble‐based method is then proposed using the new localization scheme and a newly proposed two‐step optimization strategy. The proposed approach results in a significant speed‐up for overall optimization algorithms for computing the CNOPs and can be applied to complicated nonlinear models. Numerical experiments with a nonlinear model of the viscous Burgers equation show that the proposed new method produces comparable solutions against an existing ensemble‐based method and an adjoint‐based one for computing the CNOPs. In terms of the net growth ratio of norm square, the proposed method slightly outperforms these two existing methods. On the other hand, our numerical experiments show that the proposed method has an advantage on the memory usage and computational cost, which particularly demonstrates its high potential in predictability or sensitivity studies of operational prediction models. Another group of assimilation experiments conducted using the T21L3 quasi‐geostrophic (QG) model further demonstrates its potential for broader applications.

On Galerkin Approximations of the Surface Active Quasigeostrophic Equations

AbstractThis study investigates the representation of solutions of the three-dimensional quasigeostrophic (QG) equations using Galerkin series with standard vertical modes, with particular attention to the incorporation of active surface buoyancy dynamics. This study extends two existing Galerkin approaches (A and B) and develops a new Galerkin approximation (C). Approximation A, due to Flierl, represents the streamfunction as a truncated Galerkin series and defines the potential vorticity (PV) that satisfies the inversion problem exactly. Approximation B, due to Tulloch and Smith, represents the PV as a truncated Galerkin series and calculates the streamfunction that satisfies the inversion problem exactly. Approximation C, the true Galerkin approximation for the QG equations, represents both streamfunction and PV as truncated Galerkin series but does not satisfy the inversion equation exactly. The three approximations are fundamentally different unless the boundaries are isopycnal surfaces. The authors discuss the advantages and limitations of approximations A, B, and C in terms of mathematical rigor and conservation laws and illustrate their relative efficiency by solving linear stability problems with nonzero surface buoyancy. With moderate number of modes, B and C have superior accuracy than A at high wavenumbers. Because B lacks the conservation of energy, this study recommends approximation C for constructing solutions to the surface active QG equations using the Galerkin series with standard vertical modes.

Can core flows inferred from geomagnetic field models explain the Earth's dynamo?

We test the ability of large scale velocity fields inferred from geomagnetic secular variation data to produce the global magnetic field of the Earth.Our kinematic dynamo calculations use quasi-geostrophic (QG) flows inverted from geomagnetic field models which, as such, incorporate flow structures that are Earth-like and may be important for the geodynamo.Furthermore, the QG hypothesis allows straightforward prolongation of the flow from the core surface to the bulk.As expected from previous studies, we check that a simple quasi-geostrophic flow is not able to sustain the magnetic field against ohmic decay.Additional complexity is then introduced in the flow, inspired by the action of the Lorentz force.Indeed, on centenial time-scales, the Lorentz force can balance the Coriolis force and strict quasi-geostrophy may not be the best ansatz.When the columnar flow is modified to account for the action of the Lorentz force, magnetic field is generated for Elsasser numbers larger than 0.25 and magnetic Reynolds numbers larger than 100.This suggests that our large scale flow captures the relevant features for the generation of the Earth's magnetic field and that the invisible small scale flow may not be directly involved in this process.Near the threshold, the resulting magnetic field is dominated by an axial dipole, with some reversed flux patches.Time-dependence is also considered, derived from principal component analysis applied to the inverted flows.We find that time periods from 120 to 50 years do not affect the mean growth rate of the kinematic dynamos.Finally we notice the footprint of the inner-core in the magnetic field generated deep in the bulk of the shell, although we did not include one in our computations.

Symmetric and Geostrophic Instabilities in the Wave-Forced Ocean Mixed Layer

AbstractHere, the effects of surface waves on submesoscale instabilities are studied through analytical and linear analyses as well as nonlinear large-eddy simulations of the wave-averaged Boussinesq equations. The wave averaging yields a surface-intensified current (Stokes drift) that advects momentum, adds to the total Coriolis force, and induces a Stokes shear force. The Stokes–Coriolis force alters the geostrophically balanced flow by reducing the burden on the Eulerian–Coriolis force to prop up the front, thereby potentially inciting an anti-Stokes Eulerian shear, while maintaining the Lagrangian (Eulerian plus Stokes) shear. Since the Lagrangian shear is maintained, the Charney–Stern–Pedlosky criteria for quasigeostrophic (QG) baroclinic instability are unchanged with the appropriate Lagrangian interpretation of the shear and QG potential vorticity. While the Stokes drift does not directly affect vorticity, the anti-Stokes Eulerian shear contributes to the Ertel potential vorticity (PV). When the Stokes shear and geostrophic shear are aligned (antialigned), the PV is more (less) cyclonic. If the Stokes-modified PV is anticyclonic, the flow is unstable to symmetric instabilities (SI). Stokes drift also weakly impacts SI through the Stokes shear force. When the Stokes and Eulerian shears are the same (opposite) sign, the Stokes shear force does positive (negative) work on the flow associated with SI. Stokes drift also allows SI to extract more potential energy from the front, providing an indirect mechanism for Stokes-induced restratification.

Available potential vorticity and wave-averaged quasi-geostrophic flow

We derive a wave-averaged potential vorticity equation describing the evolution of strongly stratified, rapidly rotating quasi-geostrophic (QG) flow in a field of inertia-gravity internal waves. The derivation relies on a multiple-time-scale asymptotic expansion of the Eulerian Boussinesq equations. Our result confirms and extends the theory of Bühler & McIntyre (J. Fluid Mech., vol. 354, 1998, pp. 609–646) to non-uniform stratification with buoyancy frequency$N(z)$and therefore non-uniform background potential vorticity$f_{0}N^{2}(z)$, and does not require spatial-scale separation between waves and balanced flow. Our interest in non-uniform background potential vorticity motivates the introduction of a new quantity: ‘available potential vorticity’ (APV). Like Ertel potential vorticity, APV is exactly conserved on fluid particles. But unlike Ertel potential vorticity, linear internal waves have no signature in the Eulerian APV field, and the standard QG potential vorticity is a simple truncation of APV for low Rossby number. The definition of APV exactly eliminates the Ertel potential vorticity signal associated with advection of a non-uniform background state, thereby isolating the part of Ertel potential vorticity available for balanced-flow evolution. The effect of internal waves on QG flow is expressed concisely in a wave-averaged contribution to the materially conserved QG potential vorticity. We apply the theory by computing the wave-induced QG flow for a vertically propagating wave packet and a mode-one wave field, both in vertically bounded domains.

Pairwise surface drifter separation in the western Pacific sector of the Southern Ocean

AbstractThe Southern Ocean plays a critical role in global climate, yet the mixing properties of the circulation in this part of the ocean remain poorly understood. Here dispersion in the vicinity of the Southern Antarctic Circumpolar Current Front, one of the branches of the Antarctic Circumpolar Current, is studied using 10 pairs of surface drifters deployed systematically across the frontal jet and its flanks. Drifter pairs were deployed with an initial separation of 13 m and report their position every hour. The separation of the pairs over 7 months, in terms of their Finite‐Scale Lyapunov Exponents (FSLE), dispersion, and diffusivity, is characterized and related to expected behavior from Quasi‐Geostrophic (QG) and Surface Quasi‐Geostrophic (SQG) theories. The FSLE analysis reveals two submesoscale regimes, with SQG‐like behavior at scales below 3.2 km and mixed QG/SQG behavior at scales between 3.2 and 73 km. The dispersion analysis, however, suggests QG‐like behavior for the smallest scales. Both dispersion and diffusivity appear isotropic for scales up to 500 km. Finally, there is no clear indication of a cross‐jet variation of drifter dispersion.

Effect of Prandtl’s ratio on balance in geophysical turbulence

The fluid dynamics of the atmosphere and oceans is to a large extent controlled by the slow evolution of a scalar field called ‘potential vorticity’ (PV), with relatively fast motions such as inertia-gravity waves playing only a minor role. This state of affairs is commonly referred to as ‘balance’. Potential vorticity is a special scalar field which is materially conserved in the absence of diabatic effects and dissipation, effects that are generally weak in the atmosphere and oceans. Moreover, in a balanced flow, PV induces the entire fluid motion and its thermodynamic structure (Hoskins et al., Q. J. R. Meteorol. Soc., vol. 111, 1985, pp. 877–946). While exact balance is generally not achievable, it is now well established that balance holds to a high degree of accuracy in rapidly rotating and strongly stratified flows. Such flows are characterised by both a small Rossby number, $\mathit{Ro}\equiv |{\it\zeta}|_{max}/f$, and a small Froude number, $\mathit{Fr}\equiv |{\bf\omega}_{h}|_{max}/N$, where ${\it\zeta}$ and ${\bf\omega}_{h}$ are the relative vertical and horizontal vorticity components, while $f$ and $N$ are the Coriolis and buoyancy frequencies. In fact, balance can even be a good approximation when $\mathit{Fr}\lesssim \mathit{Ro}\sim \mathit{O}(1)$. In this study, we examine how balance depends specifically on Prandtl’s ratio, $f/N$, in unforced freely evolving turbulence. We examine a wide variety of turbulent flows, at a mature and complex stage of their evolution, making use of the fully non-hydrostatic equations under the Boussinesq and incompressible approximations. We perform numerical simulations at exceptionally high resolution in order to carefully assess the degree to which balance holds, and to determine when it breaks down. For this purpose, it proves most useful to employ an invariant PV-based Rossby number ${\it\varepsilon}$, together with $f/N$. For a given ${\it\varepsilon}$, our key finding is that – for at least tens of characteristic vortex rotation periods – the flow is insensitive to $f/N$ for all values for which the flow remains statically stable (typically $f/N\lesssim 1$). Only the vertical velocity varies in proportion to $f/N$, in line with quasi-geostrophic (QG) scaling for which $\mathit{Fr}^{2}\ll \mathit{Ro}\ll 1$. We also find that as ${\it\varepsilon}$ increases towards unity, the maximum $f/N$ attainable decreases towards 0. No statically stable flows occur for ${\it\varepsilon}\gtrsim 1$. For all stable flows, balance is found to hold to a remarkably high degree: as measured by an energy norm, imbalance never exceeds more than a few per cent of the balance, even in flows where $\mathit{Ro}>1$. The vertical velocity $w$ remains a tiny fraction of the horizontal velocity $\boldsymbol{u}_{h}$, even when $w$ is dominantly balanced. Finally, typical vertical to horizontal scale ratios $H/L$ remain close to $f/N$, as found previously in QG turbulence for which $\mathit{Fr}\sim \mathit{Ro}\ll 1$.

Analytical initial conditions and an analysis of baroclinic instability waves in f ‐ and β‐plane 3D channel models

The article presents a description of idealized, balanced initial conditions for dry 3D channel models with either the hydrostatic or non‐hydrostatic shallow‐atmosphere equation set. Both the analytical expressions for an f‐ and β‐plane configuration are provided and possible variations are discussed. The initialization with an overlaid perturbation is then used for baroclinic instability studies which can serve either as a test case for the numerical discretization or for physical science investigations such as the impact of the Coriolis parameter on the evolution of baroclinic waves.Example results for two channel models are presented: the MCore and the Weather Research and Forecasting (WRF) models. The simulations show that the evolution of the baroclinic wave on the β‐plane is more unstable than the corresponding f‐plane configuration, experiencing a faster linear growth rate of the most unstable wave mode, a shorter most unstable wavelength, a narrower meridional width, and an earlier breaking of the baroclinic wave. A theoretical analysis based on linearized quasi‐geostrophic (QG) theory sheds light on these findings. It is shown that the simulated baroclinic instability waves on both the f‐ and β‐plane closely match the predicted wavelength, shape and linear growth rate obtained from the QG theory, thus validating the model results.

A generalised-Lagrangian-mean model of the interactions between near-inertial waves and mean flow

Wind forcing of the ocean generates a spectrum of inertia–gravity waves that is sharply peaked near the local inertial (or Coriolis) frequency. The corresponding near-inertial waves (NIWs) are highly energetic and play a significant role in the slow, large-scale dynamics of the ocean. To analyse this role, we develop a new model of the non-dissipative interactions between NIWs and balanced motion. The model is derived using the generalised-Lagrangian-mean (GLM) framework (specifically, the ‘glm’ variant of Soward & Roberts, J. Fluid Mech., vol. 661, 2010, pp. 45–72), taking advantage of the time-scale separation between the two types of motion to average over the short NIW period. We combine Salmon’s (J. Fluid Mech., vol. 719, 2013, pp. 165–182) variational formulation of GLM with Whitham averaging to obtain a system of equations governing the joint evolution of NIWs and mean flow. Assuming that the mean flow is geostrophically balanced reduces this system to a simple model coupling Young & Ben Jelloul’s (J. Mar. Res., vol. 55, 1997, pp. 735–766) equation for NIWs with a modified quasi-geostrophic (QG) equation. In this coupled model, the mean flow affects the NIWs through advection and refraction; conversely, the NIWs affect the mean flow by modifying the potential-vorticity (PV) inversion – the relation between advected PV and advecting mean velocity – through a quadratic wave term, consistent with the GLM results of Bühler & McIntyre (J. Fluid Mech., vol. 354, 1998, pp. 301–343). The coupled model is Hamiltonian and its conservation laws, for wave action and energy in particular, prove illuminating: on their basis, we identify a new interaction mechanism whereby NIWs forced at large scales extract energy from the balanced flow as their horizontal scale is reduced by differential advection and refraction so that their potential energy increases. A rough estimate suggests that this mechanism could provide a significant sink of energy for mesoscale motion and play a part in the global energetics of the ocean. Idealised two-dimensional models are derived and simulated numerically to gain insight into NIW–mean-flow interaction processes. A simulation of a one-dimensional barotropic jet demonstrates how NIWs forced by wind slow down the jet as they propagate into the ocean interior. A simulation assuming plane travelling NIWs in the vertical shows how a vortex dipole is deflected by NIWs, illustrating the irreversible nature of the interactions. In both simulations energy is transferred from the mean flow to the NIWs.

Low-Frequency Variability of Monsoon-Driven Circulation with Application to the South China Sea

AbstractThe interannual variability of the upper-ocean circulation forced by seasonally varying monsoonal wind is investigated in a two-layer quasigeostrophic (QG) model, with the aim to understand the low-frequency variability of the South China Sea (SCS) circulation. It is demonstrated that the seasonally varying monsoonal wind can force the upper-ocean circulation with significant internal variability, which is mainly associated with the intrinsic nonlinear dynamics of the summer double-gyre system. This arises from the fact that the intrinsic variability, characterized by the Rossby wave adjustment in the winter single-gyre system, is much weaker than that in the summer double-gyre system driven by the intergyre eddy potential vorticity flux through barotropic instability.

Latitude of Eastward Jet Prematurely Separated from the Western Boundary in a Two-Layer Quasigeostrophic Model

AbstractThis paper investigates the formation of eastward jets extended from western boundary currents, using a simple two-layer quasigeostrophic (QG) model forced by a wind stress curl consistent with the formation of a subtropical gyre. The study investigated the dependency of the latitude of the eastward jet on various parameters and on the meridional distribution of the Ekman pumping velocity. The parameters considered in the present study included the viscous and inertial western boundary layer width, the parameter representing the degree of the partial-slip boundary condition, the ratio of the upper- to lower-layer depth, and the bottom friction. With the parameters used, two types of stable structures are found in the time-mean field. One type of structure represented the “prematurely separated jet case,” in which the eastward extension jet was located far south of the northern boundary of the subtropical gyre, as is the Kuroshio Extension; the other type was the “gyre boundary jet case,” in which the eastward jet occurred along the northern boundary. The initial condition decides which type of structure would occur. When the prematurely separated jet case occurred, the authors found that the latitude of the eastward jet depended very little on the parameters. In addition, this study also observed that the latitude was determined by the meridional distribution of the Ekman pumping velocity. The eastward extension jet was usually located near the latitude that was half of the maximum value of the Sverdrup streamfunction and satisfied an integral condition derived from the QG potential vorticity equation.

Global Wavenumber Spectrum with Corrections for Altimeter High-Frequency Noise

AbstractThe altimetry wavenumber spectra of sea surface height (SSH) provide a unique dataset for testing of geostrophic turbulence. While SSH spectral slopes of k−11/3 and k−5 are expected from theories and numerical simulations, the altimetry spectra from the original unfiltered and instrument noise–corrected data often are too shallow, falling between k−2 and k−3. In this study, the possibility that the flattened spectral slopes are partly due to contamination by unresolved high-frequency (<10 days) motions is tested. A spatiotemporal filter based on empirical orthogonal function expansion (EOF) is used to remove the temporally incoherent signals. The resulting spectral slopes are much steeper than in the previous studies. Over 70% of the revised global spectral estimates, excluding the tropics, are above k−3. Moreover, in high energy regions like the Gulf Stream and Kuroshio, the spectral slopes are about k−5, which is consistent with the classical quasigeostrophic (QG) turbulence. The spectral slopes are validated with the eddy kinetic energy (EKE) spectra from shipboard acoustic Doppler current profiler (ADCP) measurements in the high and low energy regions.

Tracer Stirring around a Meddy: The Formation of Layering

AbstractThe dynamics of the formation of layering surrounding meddy-like vortex lenses is investigated using primitive equation (PE), quasigeostrophic (QG), and tracer advection models. Recent in situ data inside a meddy confirmed the formation of highly density-compensated layers in temperature and salinity at the periphery of the vortex core. Very high-resolution PE modeling of an idealized meddy showed the formation of realistic layers even in the absence of double-diffusive processes. The strong density compensation observed in the PE model, in good agreement with in situ data, suggests that stirring might be a leading process in the generation of layering. Passive tracer experiments confirmed that the vertical variance cascade in the periphery of the vortex core is triggered by the vertical shear of the azimuthal velocity, resulting in the generation of thin layers. The time evolution of this process down to scales of O(10) m is quantified, and a simple scaling is proposed and shown to describe precisely the thinning down of the layers as a function of the initial tracer column’s horizontal width and the vertical shear of the azimuthal velocity. Nonlinear QG simulations were performed and analyzed for comparison with the work of Hua et al. A step-by-step interpretation of these results on the evolution of layering is proposed in the context of tracer stirring.

The Quasigeostrophic Omega Equation: Reappraisal, Refinements, and Relevance

Abstract A two-component study is undertaken of the classical quasigeostrophic (QG) omega equation. First, a reappraisal is undertaken of extant formulations of the equation’s so-called forcing function. It pinpoints shortcomings of various formulations and prompts consideration of alternative forms. Particular consideration is given to the contribution of flow deformation to the forcing function, and to the role of the advection of the geostrophic flow by the thermal wind (the R vector). The latter is closely related to the Q vector, the horizontal component of the ageostrophic vorticity, and the forcing function itself. The reexamination promotes further examination of the physical interpretation and diagnostic use of the omega equation particularly for assessing richly structured subsynoptic flow features. Second, consideration is given to the dynamics associated with the equation and its more general utility. It is shown that the R vector is intrinsic to a quasigeostrophic cascade to finer-scaled flow, and that a fundamental feature of the QG omega equation—the in-phase relationship between cloud-diabatic heating and the attendant vertical velocity—has important potential ramifications for the assimilation of data in numerical weather prediction (NWP) models. Finally, it is shown that, in the context of considering NWP model output, mild generalizations of the quasigeostrophic R vector retain interpretative value for flow settings beyond geostrophy and warrant consideration when addressing some contemporary NWP challenges.

Atmospheric Circulation Regimes in a Nonlinear Quasi-Geostrophic Model

Atmospheric low-frequency variability and circulation regime behavior are investigated in the context of a quasi-geostrophic (QG) three-level T63 model of the wintertime atmospheric circulation over the Northern Hemisphere (NH). The model generates strong interannual and decadal variability, with the domination of the annular mode of variability. It successfully reproduces a satisfactory model climatology and the most important atmospheric circulation regimes. The positive phase of the Arctic Oscillation is a robust feature of the quasi-geostrophic T63 model. The model results based on QG dynamics underlie atmospheric regime behavior in the extratropical NH and suggest that nonlinear internal processes deliver significant contribution to the atmospheric climate variability on interannual and decadal timescales.

LARGE-SCALE QUASI-GEOSTROPHIC MAGNETOHYDRODYNAMICS

We consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the "shallow water" beta-plane approximation is used. We derive a single equation for the slow large length scale dynamics. The range of validity of this equation fits the MHD of the lighter fluid at the top of Earth's outer core. The form of this equation is similar to the quasi-geostrophic (Q-G) equation (for usual ocean or atmosphere), but the parameters are essentially different. Our equation also implies the inverse cascade; but contrary to the usual Q-G situation, the energy cascades to smaller length scales, while the enstrophy cascades to the larger scales. We find the Kolmogorov-type spectrum for the inverse cascade. The spectrum indicates the energy accumulation in larger scales. In addition to the energy and enstrophy, the obtained equation possesses an extra (adiabatic-type) invariant. Its presence implies energy accumulation in the 30° sector around zonal direction. With some special energy input, the extra invariant can lead to the accumulation of energy in zonal magnetic field; this happens if the input of the extra invariant is small, while the energy input is considerable.

Nonlinear evolution of a baroclinic wave and imbalanced dissipation

AbstractWe consider the nonlinear evolution of an unstable baroclinic wave in a regime of rotating stratified flow that is of relevance to interior circulation in the oceans and in the atmosphere: a regime characterized by small large-scale Rossby and Froude numbers, a small vertical to horizontal aspect ratio and no bounding horizontal surfaces. Using high-resolution simulations of the non-hydrostatic Boussinesq equations and companion integrations of the balanced quasi-geostrophic (QG) equations, we present evidence for a local route to dissipation of balanced energy directly through interior turbulent cascades. That is, analysis of simulations presented in this study suggest that a developing baroclinic instability can lead to secondary instabilities that can cascade a small fraction of the energy forward to unbalanced scales whereas the bulk of the energy is confined to large balanced scales. Mesoscale shear and strain resulting from the hydrostatic geostrophic baroclinic instability drive frontogenesis. The fronts in turn support ageostrophic secondary circulation and instabilities. These two processes acting together lead to a quick rise in dissipation rate which then reaches a peak and begins to fall slowly when frontogenesis slows down; eventually balanced and imbalanced modes decouple. A measurement of the dissipation of balanced energy by imbalanced processes reveals that it scales exponentially with Rossby number of the base flow. We expect that this scaling will hold more generally than for the specific set-up we consider given the fundamental nature of the dynamics involved. In other results, (a) a break is seen in the total energy (TE) spectrum at small scales: while a steep $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}k^{-3}$ geostrophic scaling (where $k$ is the three-dimensional wavenumber) is seen at intermediate scales, the smaller scales display a shallower $k^{-5/3}$ scaling, reminiscent of the atmospheric spectra of Nastrom & Gage and (b) at the higher of the Rossby numbers considered a minimum is seen in the vertical shear spectrum, reminiscent of similar spectra obtained using in situ measurements.

Geostrophic Turbulence in the Frequency–Wavenumber Domain: Eddy-Driven Low-Frequency Variability*

Abstract Motivated by the potential of oceanic mesoscale eddies to drive intrinsic low-frequency variability, this paper examines geostrophic turbulence in the frequency–wavenumber domain. Frequency–wavenumber spectra, spectral fluxes, and spectral transfers are computed from an idealized two-layer quasigeostrophic (QG) turbulence model, a realistic high-resolution global ocean general circulation model, and gridded satellite altimeter products. In the idealized QG model, energy in low wavenumbers, arising from nonlinear interactions via the well-known inverse cascade, is associated with energy in low frequencies and vice versa, although not in a simple way. The range of frequencies that are highly energized and engaged in nonlinear transfer is much greater than the range of highly energized and engaged wavenumbers. Low-frequency, low-wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing and friction playing important but secondary roles. In the high-resolution ocean model, nonlinearities also generally drive kinetic energy to low frequencies as well as to low wavenumbers. Implications for the maintenance of low-frequency oceanic variability are discussed. The cascade of surface kinetic energy to low frequencies that predominates in idealized and realistic models is seen in some regions of the gridded altimeter product, but not in others. Exercises conducted with the general circulation model suggest that the spatial and temporal filtering inherent in the construction of gridded satellite altimeter maps may contribute to the discrepancies between the direction of the frequency cascade in models versus gridded altimeter maps seen in some regions. Of course, another potential reason for the discrepancy is missing physics in the models utilized here.

Impact of the SST–wind stress coupling on the dynamics and stability of ocean current inside and outside SST frontal zones

The robust relationship between the sea surface temperature (SST) and wind stress is used to examine the impact of the SST–wind stress coupling on the dynamics and stability of ocean currents inside and outside SST frontal zones based on the wave-activity equations for the semi-geostrophic (SG) and quasi-geostrophic (QG) models.The results show that the coupling has fundamentally different effects on the ocean current inside and outside SST fronts. Outside the frontal zones the coupling only redistributes the surface temperature perturbation but does not change the total pseudo-momentum and pseudo-energy. Therefore the QG pseudo-momentum and pseudo-energy are still conserved under the impact of the coupling, although the pseudo-energy is slightly modified. The stability conditions, more general than the ones obtained by Spall (2007), are obtained from the conservation of the wave-activities. Inside the SST frontal zones, however, the coupling, along with the nonlinear Ekman effect, destroys the conservation of the SG pseudo-momentum and pseudo-energy. Therefore no stability condition is available, indicating that the current inside the frontal zone may be unstabilized by the coupling or nonlinear Ekman transport effect. It is also found that different dynamical features inside and outside frontal zones cause the different modulation of the coupling strength. The drastic differences are closely associated with the different assumptions underlying QG and SG dynamics about the density/temperature gradient and isotropy of motions.The different impacts of the coupling are further illustrated analytically by comparing the normal mode growth rates for the SG and QG Eady models. The comparisons show that ocean current outside the SST frontal zone is stable under any normal mode disturbances when the coupling factor σQG<−U¯s where U¯s is the basic zonal flow at the surface, but it is unstable under certain normal modes when σQG>−U¯s. However the ocean current inside the frontal zone is always unstable under the influence of the SST–wind coupling or nonlinear Ekman effect. It is found that the negative coupling (when surface wind blows from cold water to warm water) tends to generate strong instability. In addition, the growing/decaying normal modes are non-dispersive and propagate only in one direction (eastward) outside the frontal zone, but they are dispersive and can propagate in both directions inside frontal zone.

Toward a stochastic parameterization of ocean mesoscale eddies

A stochastic parameterization of ocean mesoscale eddies is constructed in order to account for the fluctuations in subgrid transport and to represent upscale turbulent cascades. Eddy-resolving simulations to derive the parameterization are performed in a quasi-geostrophic (QG) model in a double-gyre configuration. The coarse-graining of the high-resolution model is giving rise to an eddy source term which represents the turbulent Reynolds stresses. The eddy source term, its mean and fluctuations are analyzed as function of the resolved scales and external parameters.A functional form of the resolved scales, based on a representation of turbulence as a non-Newtonian viscoelastic medium and including the rate of strain, is used to describe the eddy source term mean, variance and decorrelation timescale. Probability density functions (PDFs) of the eddy source term conditional on the resolved scales are then calculated, capturing the fluctuations associated with mesoscale eddies and their impact on the mean flow. Scalings for the mean, standard deviation, skewness, and kurtosis of the conditional PDFs are provided as function of the grid size, forcing, and stratification of the coarse-resolution model.In light of these scalings, no preliminary high-resolution (QG) model runs are necessary to diagnose the subgrid forcing and the implementation of a stochastic closure based on the conditional PDFs requires in principle very little tuning.