Mars: The Effects of Topography on Baroclinic Instability

Blumsack, Steven L.; Gierasch, P. J.

doi:10.1175/1520-0469(1972)029<1081:mteoto>2.0.co;2

Cited by 115 publications

(133 citation statements)

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“…Interestingly, the boundary current in the model is found to become more stable as the bottom slope is decreased. This is in opposite sense to what would be expected for a horizontally homogeneous baroclinic flow over a sloping bottom (e.g., Blumsack and Gierasch 1972), where a bottom slope of this sense stabilizes the flow.…”

Section: Introductioncontrasting

confidence: 57%

Lateral Coupling in Baroclinically Unstable Flows

Spall

Pedlosky

2008

Journal of Physical Oceanography

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A two-layer quasigeostrophic model in a channel is used to study the influence of lateral displacements of regions of different sign mean potential vorticity gradient (⌸ y ) on the growth rate and structure of linearly unstable waves. The mean state is very idealized, with a region of positive ⌸ y in the upper layer and a region of negative ⌸ y in the lower layer; elsewhere ⌸ y is zero. The growth rate and structure of the model's unstable waves are quite sensitive to the amount of overlap between the two regions. For large amounts of overlap (more than several internal deformation radii), the channel modes described by Phillips' model are recovered. The growth rate decreases abruptly as the amount of overlap decreases below the internal deformation radius. However, unstable modes are also found for cases in which the two nonzero ⌸ y regions are separated far apart. In these cases, the wavenumber of the unstable waves decreases such that the aspect ratio of the wave remains O(1). The waves are characterized by a large-scale barotropic component that has maximum amplitude near one boundary but extends all the way across the channel to the opposite boundary. Near the boundaries, the wave is of mixed barotropic-baroclinic structure with cross-front scales on the order of the internal deformation radius. The perturbation heat flux is concentrated near the nonzero ⌸ y regions, but the perturbation momentum flux extends all the way across the channel. The perturbation fluxes act to reduce the isopycnal slopes near the channel boundaries and to transmit zonal momentum from the region of ⌸ y Ͼ 0 to the region on the opposite side of the channel where ⌸ y Ͻ 0. These nonzero perturbation momentum fluxes are found even for a mean state that has no lateral shear in the velocity field.

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Section: Introductioncontrasting

confidence: 57%

Lateral Coupling in Baroclinically Unstable Flows

Spall

Pedlosky

2008

Journal of Physical Oceanography

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“…There exist numerous linear stability analyses of baroclinic currents flowing over sloping topography which are based on layered models (Mysak, 1977;Mysak et al, 1981;Gula and Zeitlin, 2014;Poulin et al, 2014) or continuous stratification (Blumsack and Gierasch, 1972;Mechoso, 1980;Lozier et al, 2002;Lozier and Reed, 2005;Isachsen, 2011). In the framework of quasi-geostrophic (QG) models, both the two-layer model and the continuously stratified Eady model show that when the isopycnals and the topographic slopes tilt in opposite directions, a sloping topography reduces the growth rate of baroclinic modes with respect to a flat bottom case.…”

Section: Introductionmentioning

confidence: 99%

Meanders and eddy formation by a buoyant coastal current flowing over a sloping topography

2017

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Abstract. This study investigates the linear and non-linear instability of a buoyant coastal current flowing along a sloping topography. In fact, the bathymetry strongly impacts the formation of meanders or eddies and leads to different dynamical regimes that can both enhance or prevent the crossshore transport. We use the Regional Ocean Modeling System (ROMS) to run simulations in an idealized channel configuration, using a fixed coastal current structure and testing its unstable evolution for various depths and topographic slopes. The experiments are integrated beyond the linear stage of the instability, since our focus is on the non-linear end state, namely the formation of coastal eddies or meanders, to classify the dynamical regimes. We find three nonlinear end states, whose properties cannot be deduced solely from the linear instability analysis. They correspond to a quasi-stable coastal current, the propagation of coastal meanders, and the formation of coherent eddies. We show that the topographic parameter T p , defined as the ratio of the topographic Rossby wave speed over the current speed, plays a key role in controlling the amplitude of the unstable crossshore perturbations. This result emphasizes the limitations of linear stability analysis to predict the formation of coastal eddies, because it does not account for the non-linear saturation of the cross-shore perturbations, which is predominant for large negative T p values. We show that a second dimensionless parameter, the vertical aspect ratio γ , controls the transition from meanders to coherent eddies.We suggest the use of the parameter space (T p , γ ) to describe the emergence of coastal eddies or meanders from an unstable buoyant current. By knowing the values of T p and γ for an observed flow, which can be calculated from hydrological sections, we can identify which non-linear end state characterizes that flow -namely if it is quasi-stable, meanders, or forms eddies.

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“…The case of linear baroclinic instability in horizontally-uniform QG flow over a flat bottom was solved by Phillips (1951) with 2 vertical layers and by Eady (1949) with a continuous vertical coordinate. Blumsack & Gierasch (1972) extended the Eady model to include a sloping bottom boundary. Mechoso (1980) similarly extended the Phillips model, and systematically investigated the influence of a sloping bottom boundary in both models.…”

Section: Introductionmentioning

confidence: 99%

“…Blumsack & Gierasch (1972) found that the wavelength of the most rapidly growing mode was lower (higher) for negative (positive) δ, compared to the wavelength at δ = 0, and that the mean flow was stable to all disturbances for δ > 1. Mechoso (1980) reported the same result for the analogous case in a 2-layer model.…”

Section: Introductionmentioning

confidence: 99%

Baroclinic instability of axially symmetric flow over sloping bathymetry

2016

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Observations and models of deep ocean boundary currents show that they exhibit complex variability, instabilities and eddy shedding, particularly over continental slopes that curve horizontally, for example around coastal peninsulas. In this article the authors investigate the source of this variability by characterizing the properties of baroclinic instability in mean flows over horizontally curved bottom slopes. The classical 2-layer quasi-geostrophic solution for linear baroclinic instability over sloping bottom topography is extended to the case of azimuthal mean flow in an annular channel. To facilitate comparison with the classical straight channel instability problem of uniform mean flow, the authors focus on comparatively simple flows in an annulus, namely uniform azimuthal velocity and solid-body rotation. Baroclinic instability in solid-body rotation flow is analytically analogous to the instability in uniform straight channel flow due to several identical properties of the mean flow, including vanishing strain rate and vorticity gradient. The instability of uniform azimuthal flow is numerically similar to straight channel flow instability as long as the mean barotropic azimuthal velocity is zero. Nonzero barotropic flow generally suppresses the instability via horizontal curvatureinduced strain and Reynolds stresses work. An exception occurs when the ratio of the bathymetric to isopycnal slopes is close to (positive) one, as is often observed in the ocean, in which case the instability is enhanced. A non-vanishing mean barotropic flow component also results in a larger number of growing eigenmodes and in increased non-normal growth. The implications of these findings for variability in deep western boundary currents are discussed.

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Mars: The Effects of Topography on Baroclinic Instability

Cited by 115 publications

References 0 publications

Lateral Coupling in Baroclinically Unstable Flows

Lateral Coupling in Baroclinically Unstable Flows

Meanders and eddy formation by a buoyant coastal current flowing over a sloping topography

Baroclinic instability of axially symmetric flow over sloping bathymetry

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