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Baroclinic Instability

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Leonid L Kitchatinov – 1st expert on this subject based on the ideXlab platform

  • Baroclinic Instability in stellar radiation zones
    The Astrophysical Journal, 2014
    Co-Authors: Leonid L Kitchatinov

    Abstract:

    Surfaces of constant pressure and constant density do not coincide in differentially rotating stars. Stellar radiation zones with Baroclinic stratification can be unstable. Instabilities in radiation zones are of crucial importance for angular momentum transport, mixing of chemical species, and, possibly, for magnetic field generation. This paper performs linear analysis of Baroclinic Instability in differentially rotating stars. Linear stability equations are formulated for differential rotation of arbitrary shape and then solved numerically for rotation nonuniform in radius. As the differential rotation increases, r- and g-modes of initially stable global oscillations transform smoothly into growing modes of Baroclinic Instability. The Instability can therefore be interpreted as stability loss to r- and g-modes excitation. Regions of stellar parameters where r- or g-modes are preferentially excited are defined. Baroclinic Instability onsets at a very small differential rotation of below 1%. The characteristic time of Instability growth is about 1000 rotation periods. Growing disturbances possess kinetic helicity. Magnetic field generation by the turbulence resulting from Baroclinic Instability in differentially rotating radiation zones is therefore possible.

  • Baroclinic Instability in stellar radiation zones
    arXiv: Solar and Stellar Astrophysics, 2014
    Co-Authors: Leonid L Kitchatinov

    Abstract:

    Surfaces of constant pressure and constant density do not coincide in differentially rotating stars. Stellar radiation zones with Baroclinic stratification can be unstable. Instabilities in radiation zones are of crucial importance for angular momentum transport, mixing of chemical species and, possibly, for magnetic field generation. This paper performs linear analysis of Baroclinic Instability in differentially rotating stars. Linear stability equations are formulated for differential rotation of arbitrary shape and then solved numerically for rotation non-uniform in radius. As the differential rotation increases, r- and g-modes of initially stable global oscillations transform smoothly into growing modes of Baroclinic Instability. The Instability can therefore be interpreted as stability loss to r- and g-modes excitation. Regions of stellar parameters where r- or g-modes are preferentially excited are defined. Baroclinic Instability onsets at a very small differential rotation of below 1%. The characteristic time of Instability growth is about one thousand rotation periods. Growing disturbances possess kinetic helicity. Magnetic field generation by the turbulence resulting from Baroclinic Instability in differentially rotating radiation zones is, therefore, possible.

  • Baroclinic Instability in differentially rotating stars
    Astronomy Letters, 2013
    Co-Authors: Leonid L Kitchatinov

    Abstract:

    A linear analysis of Baroclinic Instability in a stellar radiation zone with radial differential rotation is performed. The Instability sets in at a very small rotation inhomogeneity, ΔΩ ∼ 10−3Ω. There are two families of unstable disturbances corresponding to Rossby waves and internal gravity waves. The Instability is dynamical: its growth time is several thousand rotation periods but is short compared to the stellar evolution time. A decrease in thermal conductivity amplifies the Instability. Unstable disturbances possess kinetic helicity. Magnetic field generation by the turbulence resulting from the Instability is possible.

Peter A Gilman – 2nd expert on this subject based on the ideXlab platform

  • effect of toroidal fields on Baroclinic Instability in the solar tachocline
    The Astrophysical Journal, 2015
    Co-Authors: Peter A Gilman

    Abstract:

    Using an MHD generalization of a two-layer hydrostatic but non-geostrophic model, we show that a toroidal field tends to stabilize Baroclinically unstable modes in the solar tachocline. In the hydrodynamic (HD) case, Baroclinic Instability occurs at almost all latitudes in both the radiative and overshoot tachoclines. The toroidal field creates stable bands of latitude near where the vertical rotation gradient changes sign, as well as near the equator and pole, which widen with increasing field until, by ?2.25 kG, all latitudes are stable. The stable bands center on where the local latitudinal entropy gradient is smallest. This result is independent of how subadiabatic the local stratification is, provided it is not so subadiabatic that Baroclinic Instability is absent in the HD case. Growth rates and most unstable longitudinal wavenumbers remain close to their HD values until the toroidal field gets within of the value that totally suppresses the Instability. The results are similar to those found in the 1960s from an MHD geostrophic model, but apply to a much wider range of latitudes and subadiabatic stratifications. Where tachocline toroidal fields are weak enough to allow Baroclinic Instability, magnetic patterns in longitude should be produced that could be transmitted through the convection zone to be seen in the photosphere. The results also show it should be possible to construct a Baroclinic wave dynamo for the solar tachocline.

  • Baroclinic Instability in the solar tachocline
    The Astrophysical Journal, 2014
    Co-Authors: Peter A Gilman, Mausumi Dikpati

    Abstract:

    The solar tachocline is likely to be close to a geostrophic ‘thermal wind’, for which the Coriolis force associated with differential rotation is closely balanced by a latitudinal pressure gradient, leading to a tight relation between the vertical gradient of rotation and the latitudinal entropy gradient. Using a hydrostatic but nongeostrophic spherical shell model, we examine Baroclinic Instability of the tachocline thermal wind. We find that both the overshoot and radiative parts of the tachocline should be Baroclinicly unstable at most latitudes. Growth rates are roughly five times higher in middle and high latitudes compared to low latitudes, and much higher in the overshoot than in the radiative tachocline. They range in e-folding amplification from 10 days in the high latitude overshoot tachocline, down to 20 yr for the low latitude radiative tachocline. In the radiative tachocline only, longitudinal wavenumbers m = 1, 2 are unstable, while in the overshoot tachocline a much broader range of m are unstable. At all latitudes and with all stratifications, the longitudinal scale of the most unstable mode is comparable to the Rossby deformation radius, while the growth rate is set by the local latitudinal entropy gradient. Baroclinic Instability in the tachocline competing withmore » Instability of the latitude rotation gradient established in earlier studies should be important for the workings of the solar dynamo and should be expected to be found in most stars that contain an interface between radiative and convective domains.« less

Kazunori Akitomo – 3rd expert on this subject based on the ideXlab platform

  • Baroclinic Instability and submesoscale eddy formation in weakly stratified oceans under cooling
    Journal of Geophysical Research, 2010
    Co-Authors: Kazunori Akitomo

    Abstract:

    [1] Numerical experiments with a three-dimensional nonhydrostatic model have been performed to investigate Baroclinic Instability and submesoscale eddy formation in weakly stratified oceans under cooling. Two types of Baroclinic Instability can exist in a two-layered ocean where the convectively formed deep mixed layer overlies the weakly stratified lower layer. One rapidly develops in the mixed layer with short wavelengths (shallow mode), and the other occupies the whole ocean depth with long wavelengths (deep mode). When a background flow is deep, the shallow mode develops first, but the deep mode replaces it in several days. In contrast, only the shallow mode is excited in the mixed layer overlying the strongly stratified layer. The linear stability analysis explains these results well. Despite active cooling, subsequently formed eddies restratify the mixed layer and modify water density over the whole depth. When a background flow is shallow, Baroclinic Instability is confined to the mixed layer and produces a dipole of surface-intensified cyclonic eddy and middepth-intensified anticyclonic eddy, both of which are of submesoscale (∼10 km). The anticyclonic eddy consisting of convectively formed but weakly stratified water moves across the front to ventilate the deep layer, where convection does not reach locally. In this way, density modification extends below the mixed layer. Surface cooling as well as Baroclinicity enhances restratification of the mixed layer and density modification at depths by activating submesoscale eddy formation. The results can explain the restratification of the deep mixed layer observed during a cooling season and the origins of submesoscale coherent vortices recently detected in polar oceans.

  • thermobaric deep convection Baroclinic Instability and their roles in vertical heat transport around maud rise in the weddell sea
    Journal of Geophysical Research, 2006
    Co-Authors: Kazunori Akitomo

    Abstract:

    [1] Numerical experiments with two- and three-dimensional nonhydrostatic models in a rotating frame have been executed to investigate thermobaric deep convection, subsequent Baroclinic Instability, and their roles in vertical heat transport, using hydrographic data around Maud Rise in the Weddell Sea, Antarctica. Overturning of the water column due to thermobaric convection is apt to occur on the southern and northern flanks of the rise, and induces upward heat transport. The depth of overturning is two times larger on the northern flank (∼1.5 km) than on the southern flank (∼0.7 km). To the contrary, no overturning occurs over the top of the rise in 90 days. Baroclinic Instability develops at a density front formed between the overturned and unoverturned regions since a density contrast at the front is enhanced by thermobaricity. Heat transport due to Baroclinic Instability is similarly upward, and at peak becomes comparable to that due to the overturning. Applicability of the results to the cooling events previously reported is also discussed.

  • Numerical study of Baroclinic Instability associated with thermobaric deep convection at high latitudes: Idealized cases
    Deep Sea Research Part I: Oceanographic Research Papers, 2005
    Co-Authors: Kazunori Akitomo

    Abstract:

    Abstract Numerical experiments with a three-dimensional nonhydrostatic model in a rotating frame have been executed to investigate Baroclinic Instability associated with thermobaric deep convection in weakly stratified polar oceans and its role in the transport processes. The model ocean has a two-layered structure with the cold, fresh mixed layer overlying the warm, saline deep water cell, as in the Weddell Sea. In contrast with a scenario based on the linear equation of state, thermobaric overturning of the water column enhances the horizontal density gradient (Baroclinicity) through nonlinearity of the equation of state. If temperature controls water density (TEM cases), Baroclinicity is intensified at the bottom of the overturned layer while at the surface if salinity does (SAL cases). Such intensification causes further development of Baroclinic Instability or Baroclinic destabilization and more effective vertical heat transport. In the post-overturning stage, on the other hand, surface cooling (convective motion) has two oppositely operating effects on Baroclinic Instability and the associated heat transport. One is that horizontal convergence due to convective motion enhances Baroclinic Instability in the surface layer, as in previous studies focusing on strongly stratified oceans. This is observed in SAL cases with weak cooling, but not in TEM cases. The other is that strong cooling suppresses Baroclinic Instability by homogenizing the overturned layer vertically. This effect has not been found in the strongly stratified oceans. As a result, the vertical heat transport is most effective at low cooling rates ( ∼ 125 W m – 2 ) in SAL cases while it monotonically decreases with cooling rate in TEM cases. When Baroclinicity is initially weak as in the Weddell Sea, the most effective transport occurs with the cooling rate of 25 W m – 2 which is a possible value under sea-ice cover in the actual situation.