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James C Mcwilliams - One of the best experts on this subject based on the ideXlab platform.

  • baroclinic instability of Axially Symmetric Flow over sloping bathymetry
    Journal of Fluid Mechanics, 2016
    Co-Authors: Aviv Solodoch, Andrew L Stewart, James C Mcwilliams
    Abstract:

    Under consideration for publication in J. Fluid Mech. Baroclinic instability of Axially-Symmetric Flow over sloping bathymetry Aviv Solodoch 1 †, Andrew L. Stewart 1 and James C. McWilliams 1 Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA 90095, USA (Received xx; revised xx; accepted xx) 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 curvature- induced 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. 1. Introduction Baroclinic instability is one of the main energy conversion processes to and from the mesoscale in the ocean (McWilliams 2008). The baroclinic source of energy, available potential energy due to tilting of isopycnals (constant density surfaces), is ubiquitous. Studies based on high-resolution altimetry (Chelton et al. 2011) reveal that virtually all areas of the world’s oceans are sources of mesoscale eddies, and therefore may be baroclinically unstable. A few of the many roles mesoscale eddies play in the ocean are: supporting the forward and inverse turbulent energy cascades, relaxing isopycnal slopes and thus restratifying the ocean, vertical transfer of momentum via the eddy form stress and transport, and ventilation and subdaction of tracers (McWilliams 2008; Dong et al. Baroclinic eddy variability peaks in the ocean near strong persistent currents (Chelton et al. 2011), such as large boundary currents (e.g., the Gulf Stream). The task of measuring and characterizing eddy generation mechanisms is more challenging for deep † Email address for correspondence: asolodoch@atmos.ucla.edu

  • baroclinic instability of Axially Symmetric Flow over sloping bathymetry
    Journal of Fluid Mechanics, 2016
    Co-Authors: Aviv Solodoch, Andrew L Stewart, James C Mcwilliams
    Abstract:

    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 two-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. Non-zero barotropic Flow generally suppresses the instability via horizontal curvature-induced strain and Reynolds stress 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.

Aviv Solodoch - One of the best experts on this subject based on the ideXlab platform.

  • baroclinic instability of Axially Symmetric Flow over sloping bathymetry
    Journal of Fluid Mechanics, 2016
    Co-Authors: Aviv Solodoch, Andrew L Stewart, James C Mcwilliams
    Abstract:

    Under consideration for publication in J. Fluid Mech. Baroclinic instability of Axially-Symmetric Flow over sloping bathymetry Aviv Solodoch 1 †, Andrew L. Stewart 1 and James C. McWilliams 1 Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA 90095, USA (Received xx; revised xx; accepted xx) 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 curvature- induced 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. 1. Introduction Baroclinic instability is one of the main energy conversion processes to and from the mesoscale in the ocean (McWilliams 2008). The baroclinic source of energy, available potential energy due to tilting of isopycnals (constant density surfaces), is ubiquitous. Studies based on high-resolution altimetry (Chelton et al. 2011) reveal that virtually all areas of the world’s oceans are sources of mesoscale eddies, and therefore may be baroclinically unstable. A few of the many roles mesoscale eddies play in the ocean are: supporting the forward and inverse turbulent energy cascades, relaxing isopycnal slopes and thus restratifying the ocean, vertical transfer of momentum via the eddy form stress and transport, and ventilation and subdaction of tracers (McWilliams 2008; Dong et al. Baroclinic eddy variability peaks in the ocean near strong persistent currents (Chelton et al. 2011), such as large boundary currents (e.g., the Gulf Stream). The task of measuring and characterizing eddy generation mechanisms is more challenging for deep † Email address for correspondence: asolodoch@atmos.ucla.edu

  • baroclinic instability of Axially Symmetric Flow over sloping bathymetry
    Journal of Fluid Mechanics, 2016
    Co-Authors: Aviv Solodoch, Andrew L Stewart, James C Mcwilliams
    Abstract:

    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 two-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. Non-zero barotropic Flow generally suppresses the instability via horizontal curvature-induced strain and Reynolds stress 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.

Andrew L Stewart - One of the best experts on this subject based on the ideXlab platform.

  • baroclinic instability of Axially Symmetric Flow over sloping bathymetry
    Journal of Fluid Mechanics, 2016
    Co-Authors: Aviv Solodoch, Andrew L Stewart, James C Mcwilliams
    Abstract:

    Under consideration for publication in J. Fluid Mech. Baroclinic instability of Axially-Symmetric Flow over sloping bathymetry Aviv Solodoch 1 †, Andrew L. Stewart 1 and James C. McWilliams 1 Department of Atmospheric and Oceanic Sciences, University of California, Los Angeles, CA 90095, USA (Received xx; revised xx; accepted xx) 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 curvature- induced 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. 1. Introduction Baroclinic instability is one of the main energy conversion processes to and from the mesoscale in the ocean (McWilliams 2008). The baroclinic source of energy, available potential energy due to tilting of isopycnals (constant density surfaces), is ubiquitous. Studies based on high-resolution altimetry (Chelton et al. 2011) reveal that virtually all areas of the world’s oceans are sources of mesoscale eddies, and therefore may be baroclinically unstable. A few of the many roles mesoscale eddies play in the ocean are: supporting the forward and inverse turbulent energy cascades, relaxing isopycnal slopes and thus restratifying the ocean, vertical transfer of momentum via the eddy form stress and transport, and ventilation and subdaction of tracers (McWilliams 2008; Dong et al. Baroclinic eddy variability peaks in the ocean near strong persistent currents (Chelton et al. 2011), such as large boundary currents (e.g., the Gulf Stream). The task of measuring and characterizing eddy generation mechanisms is more challenging for deep † Email address for correspondence: asolodoch@atmos.ucla.edu

  • baroclinic instability of Axially Symmetric Flow over sloping bathymetry
    Journal of Fluid Mechanics, 2016
    Co-Authors: Aviv Solodoch, Andrew L Stewart, James C Mcwilliams
    Abstract:

    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 two-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. Non-zero barotropic Flow generally suppresses the instability via horizontal curvature-induced strain and Reynolds stress 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.

Gunter Gerbeth - One of the best experts on this subject based on the ideXlab platform.

  • stability of Axially Symmetric Flow driven by a rotating magnetic field in a cylindrical cavity
    Journal of Fluid Mechanics, 2001
    Co-Authors: I. Grants, Gunter Gerbeth
    Abstract:

    This paper deals with the stability analysis of an Axially Symmetric liquid metal Flow driven by a rotating magnetic field in a cylinder of finite dimensions. The limit of linear stability with respect to Axially Symmetric perturbations is found for diameter-to-height ratios between 0.4 and 1. This oscillatory instability is shown to be different from the expected Taylor–Gortler vortices. Several linearly unstable steady solutions are found close to the stable basic state. It is shown that small finite-amplitude perturbations in the form of Taylor–Gortler vortices give rise to instability in the linearly stable regime.

Halliday Ian - One of the best experts on this subject based on the ideXlab platform.

  • Chromo-dynamic multi-component lattice Boltzmann equation scheme for axial symmetry
    'IOP Publishing', 2020
    Co-Authors: Spendlove James, Schenkel Torsten, Seaton M, Halliday Ian
    Abstract:

    We validate the chromo-dynamic multi-component lattice Boltzmann equation (MCLBE) simulation for immiscible fluids with a density contrast against analytical results for complex Flow geometries, with particular emphasis on the fundamentals of the method, i.e. compliance with inter-facial boundary conditions of continuum hydrodynamics. To achieve the necessary regimes for the chosen validations, we develop, from a three-dimensional, Axially-Symmetric Flow formulation, a novel, two-dimensional, pseudo Cartesian, MCLBE scheme. This requires the inclusion in lattice Boltzmann methodology of a continuously distributed source and a velocity-dependent force density (here, the metric force terms of the cylindrical Navier–Stokes equations). Specifically, we apply our model to the problem of Flow past a spherical liquid drop in Re = 0, Ca regime and, also, Flow past a lightly deformed drop. The resulting simulation data, once corrected for the simulation’s inter-facial micro-current (using a method we also advance herein, based on freezing the phase field) show good agreement with theory over a small range of density contrasts. In particular, our data extend verified compliance with the kinematic condition from flat (Burgin et al 2019 Phys. Rev. E 100 043310) to the case of curved fluid–fluid interfaces. More generally, our results indicate a route to eliminate the influence of the inter-facial micro-current

  • Chromo-dynamic multi-component lattice Boltzmann equation scheme for axial symmetry
    'IOP Publishing', 2020
    Co-Authors: Spendlove, James Edward, Schenkel Torsten, Seaton, Michael Andrew, Halliday Ian
    Abstract:

    We validate the chromo-dynamic multi-component lattice Boltzmann equation (MCLBE) simulation for immiscible fluids with a density contrast against analytical results for complex Flow geometries, with particular emphasis on the fundamentals of the method, i.e. compliance with inter-facial boundary conditions of continuum hydrodynamics. To achieve the necessary regimes for the chosen validations, we develop, from a three-dimensional, Axially-Symmetric Flow formulation, a novel, two-dimensional, pseudo Cartesian, MCLBE scheme. This requires the inclusion in lattice Boltzmann methodology of a continuously distributed source and a velocity-dependent force density (here, the metric force terms of the cylindrical Navier-Stokes equations). Specifically, we apply our model to the problem of Flow past a spherical liquid drop in Re=$0$, Ca$\rightarrow 0$ regime and, also, Flow past a lightly deformed drop. The resulting simulation data, once corrected for the simulation's inter-facial micro-current (using a method we also advance herein, based on freezing the phase field) show good agreement with theory over a small range of density contrasts. In particular, our data extend verified compliance with the kinematic condition from flat \cite{Burgin} to the case of curved fluid-fluid interfaces. More generally, our results indicate a route to eliminate the influence of the inter-facial micro-current