ALBERT

Description: The stability of lens-shaped vortices is revisited in the context of an idealized quasigeostrophic model. We compute the stability characteristics with higher accuracy and for a wider range of Burger numbers (Bu) than what was previously done. It is found that there are four distinct Bu regions of linear instability. Over the primary region of interest (0.1 〈 Bu 〈 10), we confirm that the first and second azimuthal modes are the only linearly unstable modes, and they are associated with vortex tilting and tearing, respectively. Moreover, the most unstable first azimuthal mode is not precisely captured by the linear stability analysis because of the extra condition that is imposed at the vortex center, and accurate calculations of the second azimuthal mode require higher resolution than was previously considered. We also study the nonlinear evolution of lens-shaped vortices in the context of this model and present the following results. First, vortices with a horizontal length scale a little less than the radius of deformation (Bu 〉 1) are barotropically unstable and develop a wobble, whereas those with a larger horizontal length scale (Bu 〈 1) are baroclinically unstable and often split. Second, the transfer of energy between different horizontal scales is quantified in two typical cases of barotropic and baroclinic instability. Third, after the instability the effective Bu is closer to unity.

Description: In this paper, we analyse the results from a numerical model at high resolution. We focus on the formation and maintenance of subsurface equatorial currents in the Gulf of Guinea and we base our analysis on the evolution of potential vorticity (PV). We highlight the link between submesoscale processes (involving mixing, friction and filamentation), mesoscale vortices and the mean currents in the area. In the simulation, eastward currents, the South and North Equatorial Undercurrents (SEUC and NEUC respectively) and the Guinea Undercurrent (GUC), are shown to be linked to the westward currents located equatorward. We show that east of 20° W, both westward and eastward currents are associated with the spreading of PV tongues by mesoscale vortices. The Equatorial Undercurrent (EUC) brings salty waters into the Gulf of Guinea. Mixing diffuses the salty anomaly downward. Meridional advection, mixing and friction are involved in the formation of fluid parcels with PV anomalies in the lower part and below the pycnocline, north and south of the EUC, in the Gulf of Guinea. These parcels gradually merge and vertically align, forming nonlinear anticyclonic vortices that propagate westward, spreading and horizontally mixing their PV content by stirring filamentation and diffusion, up to 20° W. When averaged over time, this creates regions of nearly homogeneous PV within zonal bands between 1.5° and 5° S or N. This mean PV field is associated with westward and eastward zonal jets flanking the EUC with the homogeneous PV tongues corresponding to the westward currents, and the strong PV gradient regions at their edges corresponding to the eastward currents. Mesoscale vortices strongly modulate the mean fields explaining the high spatial and temporal variability of the jets.

Description: The stability properties of a vortex lens are studied in the quasi geostrophic (QG) framework using the generalized stability theory. Optimal perturbations are obtained using a tangent linear QG model and its adjoint. Their fine-scale spatial structures are studied in details. Growth rates of optimal perturbations are shown to be extremely sensitive to the time interval of optimization: The most unstable perturbations are found for time intervals of about 3 days, while the growth rates continuously decrease towards the most unstable normal mode, which is reached after about 170 days. The horizontal structure of the optimal perturbations consists of an intense counter-shear spiralling. It is also extremely sensitive to time interval: for short time intervals, the optimal perturbations are made of a broad spectrum of high azimuthal wave numbers. As the time interval increases, only low azimuthal wave numbers are found. The vertical structures of optimal perturbations exhibit strong layering associated with high vertical wave numbers whatever the time interval. However, the latter parameter plays an important role in the width of the vertical spectrum of the perturbation: short time interval perturbations have a narrow vertical spectrum while long time interval perturbations show a broad range of vertical scales. Optimal perturbations were set as initial perturbations of the vortex lens in a fully non linear QG model. It appears that for short time intervals, the perturbations decay after an initial transient growth, while for longer time intervals, the optimal perturbation keeps on growing, quickly leading to a non-linear regime or exciting lower azimuthal modes, consistent with normal mode instability. Very long time intervals simply behave like the most unstable normal mode. The possible impact of optimal perturbations on layering is also discussed.

Description: The stability of mixed Rossby gravity (MRG) waves has been investigated numerically using three-dimensionally consistent high-resolution simulations of the continuously stratified primitive equations. For short enough zonal wavelength, the westward phase propagating MRG wave is strongly destabilized by barotropic shear instability leading to the formation of zonal jets. The large-scale instability of the zonally short wave generates zonal jets because it consists primarily of sheared meridional motions, as shown recently for the short barotropic Rossby wave problem. Simulations were done in a variety of domain geometries: a periodic re-entrant channel, a basin with a short MRG wave forced in its western part and a very long channel initialized with a zonally localized MRG wave. The characteristics of the zonal jets vary with the geometry. In the periodic re-entrant channel, barotropic zonal jets dominate the total flow response at the equator and its immediate vicinity. In the other cases, the destabilization leads to zonal jets with quite different characteristics, especially in the eastward group propagating part of the signal. The most striking result concerns the formation of zonal jets at the equator, alternating in sign in the vertical, with vertical scale short compared to the scale of the forcing or initial conditions. A stability analysis of a simplified perturbation vorticity equation is formulated to explain the spatial scale selection and growth rate of the zonal jets as functions of the characteristics of the basic state MRG wave. For both types of zonal jets, the model predicts that their meridional scales are comparable to the zonal scale of the MRG wave basic state, while their growth rates scale as μ ∝ Fr k , where Fr is the Froude number of the meridional velocity component of the basic state and k its non-dimensional zonal wavenumber. The vertical scale of the baroclinic zonal jets corresponds to the dominant harmonic ppeak of the basic state in the fastest growing mode, given by ppeak ≈0.55 k2. Thus, the shorter the zonal wavelength of the basic state MRG wave, the narrower the meridional scale of the zonal jets, both barotropic and baroclinic, with the vertical scale of the baroclinic jets being tied to their meridional scale through the equatorial radius of deformation, which decreases as the square root of the vertical wavenumber. The predictions of the spatial scales are in both qualitative and quantitative agreement with the numerical simulations, where shorter vertical scale baroclinic zonal jets are favoured by shorter-wavelength longer-period MRG wave basic states, with the vertical mode number increasing as the square of the MRG wave period. An Appendix deals with the case of zonally long and intermediate wavelength MRG waves, where a weak instability regime causes a moderate adjustment involving resonant triad interactions without leading to jet formation. For eastward phase propagating waves, adjustment does not lead to significant angular momentum redistribution. © 2008 Cambridge University Press.

Description: The linear instability of several rotating, stably stratified, interior vertical shear flows U.z/ is calculated in Boussinesq equations. Two types of baroclinic, ageostrophic instability, AI1 and AI2, are found in odd-symmetric U.z/ for intermediate Rossby number (Ro). AI1 has zero frequency; it appears in a continuous transformation of the unstable mode properties between classic baroclinic instability (BCI) and centrifugal instability (CI). It begins to occur at intermediate Ro values and horizontal wavenumbers (k; l) that are far from lD0 or k D0, where the growth rate of BCI or CI is the strongest. AI1 grows by drawing kinetic energy from the mean flow, and the perturbation converts kinetic energy to potential energy. The instability AI2 has inertia critical layers (ICL); hence it is associated with inertia-gravity waves. For an unstable AI2 mode, the coupling is either between an interior balanced shear wave and an inertia-gravity wave (BG), or between two inertia-gravity waves (GG). The main energy source for an unstable BG mode is the mean kinetic energy, while the main energy source for an unstable GG mode is the mean available potential energy. AI1 and BG type AI2 occur in the neighbourhood of ASD0 (a sign change in the difference between absolute vertical vorticity and horizontal strain rate in isentropic coordinates; see McWilliams et al., Phys. Fluids, vol. 10, 1998, pp. 3178-3184), while GG type AI2 arises beyond this condition. Both AI1 and AI2 are unbalanced instabilities; they serve as an initiation of a possible local route for the loss of balance in 3D interior flows, leading to an efficient energy transfer to small scales. © 2014 Cambridge University Press.

Description: Evidence of persistent layering, with a vertical stacking of sharp variations in temperature, has been presented recently at the vertical and lateral periphery of energetic oceanic vortices through seismic imaging of the water column. The stacking has vertical scales ranging from a few metres up to 100 m and a lateral spatial coherence of several tens of kilometres comparable with the vortex horizontal size. Inside this layering, in situ data display a [k〈inf〉h〈/inf〉-5/3 k〈inf〉h〈/inf〉-2] scaling law of horizontal scales for two different quantities, temperature and a proxy for its vertical derivative, but for two different ranges of wavelengths, between 5 and 50 km for temperature and between 500 m and 5 km for its vertical gradient. In this study, we explore the dynamics underlying the layering formation mechanism, through the slow dynamics captured by quasi-geostrophic equations. Three-dimensional high-resolution numerical simulations of the destabilization of a lens-shaped vortex confirm that the vertical stacking of sharp jumps in density at its periphery is the three-dimensional analogue of the preferential wind-up of potential vorticity near a critical radius, a phenomenon which has been documented for barotropic vortices. For a small-Burger (flat) lens vortex, baroclinic instability ensures a sustained growth rate of sharp jumps in temperature near the critical levels of the leading unstable modes. Such results can be obtained for a background stratification which is due to temperature only and does not require the existence of salt anomalies. Aloft and beneath the vortex core, numerical simulations well reproduce the [k〈inf〉h〈/inf〉-5/3 k〈inf〉h〈/inf〉-2] scaling law of horizontal scales for the vertical derivative of temperature that is observed in situ inside the layering, whatever the background stratification. Such a result stems from the tracer-like behaviour of the vortex stretching component and previous studies have shown that spectra of tracer fields can be steeper than -1, namely in -5/3 or -2, if the advection field is very compact spatially, with a -5/3 slope corresponding to a spiral advection of the tracer. Such a scaling law could thus be of geometric origin. As for the kinetic and potential energy, the k〈inf〉h〈/inf〉-5/3} scaling law can be reproduced numerically and is enhanced when the background stratification profile is strongly variable, involving sharp jumps in potential vorticity such as those observed in situ. This raises the possibility of another plausible mechanism leading to a -5/3 scaling law, namely surface-quasi-geostrophic (SQG)-like dynamics, although our set-up is more complex than the idealized SQG framework. Energy and enstrophy fluxes have been diagnosed in the numerical quasi-geostrophic simulations. The results emphasize a strong production of energy in the oceanic submesoscales range and a kinetic and potential energy flux from mesoscale to submesoscales range near the critical levels. Such horizontal submesoscale production, which is correlated to the accumulation of thin vertical scales inside the layering, thus has a significant slow dynamical component, well-captured by quasi-geostrophy. ©2013 Cambridge University Press.

Description: Oceanic large- and meso-scale flows are nearly balanced in forces between Earth's rotation and density stratification effects (i.e. geostrophic, hydrostatic balance associated with small Rossby and Froude numbers). In this regime advective crossscale interactions mostly drive energy toward larger scales (i.e. inverse cascade). However, viscous energy dissipation occurs at small scales. So how does the energy reservoir at larger scales leak toward small-scale dissipation to arrive at climate equilibrium? Here we solve the linear instability problem of a balanced flow in a rotating and continuously stratified fluid far away from any boundaries (i.e. an interior jet). The basic flow is unstable not only to geostrophic baroclinic and barotropic instabilities, but also to ageostrophic instabilities, leading to the growth of small-scale motions that we hypothesize are less constrained by geostrophic cascade behaviours in a nonlinear regime and thus could escape from the inverse energy cascade. This instability is investigated in the parameter regime of moderate Rossby and Froude numbers, below the well-known regimes of gravitational, centrifugal, and Kelvin-Helmholtz instability. The ageostrophic instability modes arise with increasing Rossby number through a near-degeneracy of two unstable modes with coincident phase speeds. The near-degeneracy occurs in the neighbourhood of an identified criterion for the non-integrability of the 'isentropic balance equations' (namely A - S = 0 with A the absolute vertical vorticity and S the horizontal strain rate associated with the basic flow), beyond which development of an unbalanced component of the flow is expected. These modes extract energy from the basic state with large vertical Reynolds stress work (unlike geostrophic instabilities) and act locally to modify the basic flow by reducing the isopycnal Ertel potential vorticity gradient near both its zero surface and its critical surface (phase speed equal to basic flow speed). © 2012 Cambridge University Press.

Description: This paper investigates the stability of an axisymmetric pancake vortex with Gaussian angular velocity in radial and vertical directions in a continuously stratified-rotating fluid. The different instabilities are determined as a function of the Rossby number Ro, Froude number Fh, Reynolds number Re and aspect ratio α. Centrifugal instability is not significantly different from the case of a columnar vortex due to its short-wavelength nature: it is dominant when the absolute Rossby number /Ro/ is large and is stabilized for small and moderate /Ro/ when the generalized Rayleigh discriminant is positive everywhere. The Gent-McWilliams instability, also known as internal instability, is then dominant for the azimuthal wavenumber m = 1 when the Burger number Bu = α2Ro2=(4Fh/ is larger than unity. When Bu ≤ 0.7Ro + 0.1, he Gent-McWilliams instability changes into a mixed baroclinic-Gent-McWilliams instability. Shear instability for m=2 exists when Fh=α is below a threshold depending on Ro. This condition is shown to come from confinement effects along the vertical. Shear instability transforms into a mixed baroclinic-shear instability for small Bu. The main energy source for both baroclinic-shear and baroclinic-Gent-McWilliams instabilities is the potential energy of the base flow instead of the kinetic energy for shear and Gent-McWilliams instabilities. The growth rates of these four instabilities depend mostly on Fh=α and Ro. Baroclinic instability develops when Fh/α/1 + 1/Ro/≥1.46 in qualitative agreement with the analytical predictions for a bounded vortex with angular velocity slowly varying along the vertical. © 2016 Cambridge University Press.

Description: The 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.