Ageostrophic instability in rotating shallow water

Wang, Peng; McWilliams, James C.; Kizner, Ziv

doi:10.1017/jfm.2012.422

Cited by 6 publications

(6 citation statements)

References 33 publications

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“…AAI has been identified in several previous studies (see e.g. Wang et al 2012 and references therein) and these studies show that significant ageostrophic growth rates can occur in the neighborhood of . Even though the maximum growth rates of these ageostrophic modes are smaller than that of the classical geostrophic mode (baroclinic instability), it is important to note that the geostrophic mode is only unstable at length scales larger than the first baroclinic deformation radius which is far from the turbulent dissipation scale, and that at smaller scales the ageostrophic mode is the only unstable one (Müller et al 2005).…”

Section: Loss Of Balancementioning

confidence: 61%

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An Idealized Model Study of Eddy Energetics in the Western Boundary “Graveyard”

Yang

Zhai

Marshall

et al. 2021

Journal of Physical Oceanography

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Recent studies show that the western boundary acts as a ‘graveyard’ for westward-propagating ocean eddies. However, how the eddy energy incident on the western boundary is dissipated remains unclear. Here we investigate the energetics of eddy-western boundary interaction using an idealised MIT ocean circulation model with a spatially variable grid resolution. Four types of model experiments are conducted: (1) single eddy cases, (2) a sea of random eddies, (3) with a smooth topography and (4) with a rough topography. We find significant dissipation of incident eddy energy at the western boundary, regardless of whether the model topography at the western boundary is smooth or rough. However, in the presence of rough topography, not only the eddy energy dissipation rate is enhanced, but more importantly, the leading process for removing eddy energy in the model switches from bottom frictional drag as in the case of smooth topography to viscous dissipation in the ocean interior above the rough topography. Further analysis shows that the enhanced eddy energy dissipation in the experiment with rough topography is associated with greater anticyclonic-ageostrophic instability (AAI), possibly as a result of lee wave generation and non-propagating form drag effect.

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Section: Loss Of Balancementioning

confidence: 61%

“…instabilities, the criteria for AAI can be satisfied even if the magnitude of Rossby number is moderate, and is therefore considered to be one possible route to dissipation for the large-scale ocean general circulation (Wang et al 2012).…”

Section: Loss Of Balancementioning

confidence: 99%

An Idealized Model Study of Eddy Energetics in the Western Boundary “Graveyard”

Yang

Zhai

Marshall

et al. 2021

Journal of Physical Oceanography

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“…At the ocean surface, the dominant (i.e., leading-order) geostrophic velocity can be treated as non-divergent and purely solenoidal. The corresponding ageostrophic velocity corrections to the leading-order fields are 3D, weakly 2D-divergent at the surface, and characterized by small vertical velocities [17][18][19][20][21][22]. At the surface, this flow correction can be treated as divergent (potential) component of the combined 2D velocity field responsible for advection and clustering of material tracers.…”

Section: Russiamentioning

confidence: 99%

Clustering of floating tracers in weakly divergent velocity fields

et al. 2019

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This work focuses on buoyant tracers floating on the ocean surface and treats the geostrophic and ageostriphic surface velocities as the 2D solenoidal (non-divergent) and potential (divergent) flow components, respectively. We consider a random kinematic flow model and study the process of clustering, that is, aggregation of tracers in localized spatial patches. An asymptotic theory exists only for strongly divergent velocity fields and predicts complete clustering, that is, emergence in the large-time limit of spatial singularities containing all available tracers. To extend the theory, we consider combinations of the solenoidal and potential velocity components and explore the corresponding regimes of the clustering process. We have found that, even for weakly divergent flows complete clustering still persists but occurs at a significantly slower rate. For a wide range of parameters, we have analyzed this process, as well as the other type of clustering, referred to as fragmentation clustering, and the coarse-graining effects on clustering, and interpreted the results.For the analyses we have considered ensembles of Lagrangian particles representing the tracer, then, introduced and applied the methodology of statistical topography, which paves the way for systematic studies of clustering in progressively more complicated flows, and for both passive and floating tracers.

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“…In shallow-water equations Hayashi & Young (1987) shows an unstable coupling between Kelvin and inertia-gravity waves for a shear flow on an equatorial beta-plane, and Dritschel & Vanneste (2006) show a coupling between a balanced mode and an inertia-gravity mode for a potential vorticity front. Wang & McWilliams (2012) show resonances between a balanced shear wave and an inertia-gravity wave or between two inertia-gravity waves in shallow-water equations on an f -plane with several continuous profiles for a basic flow far from boundaries. Sakai (1989) analyses Phillips' two-layer flow in a bounded channel and shows the coupling between a Rossby wave in the first layer and a Kelvin wave in the second or between two Kelvin waves.…”

Section: Introductionmentioning

confidence: 95%

Ageostrophic instability in a rotating stratified interior jet

Ménesguen¹,

McWilliams²,

Molemaker³

2012

J. Fluid Mech.

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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).

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Ageostrophic instability in rotating shallow water

Cited by 6 publications

References 33 publications

An Idealized Model Study of Eddy Energetics in the Western Boundary “Graveyard”

An Idealized Model Study of Eddy Energetics in the Western Boundary “Graveyard”

Clustering of floating tracers in weakly divergent velocity fields

Ageostrophic instability in a rotating stratified interior jet

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