Thermal instabilities in rapidly rotating systems

Busse, Friedrich H.

doi:10.1017/s0022112070001921

Cited by 677 publications

(604 citation statements)

References 3 publications

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“…Figure 2 demonstrates that the decrease of the Ekman number goes along with a smaller length scale. The reason becomes apparent when considering the linear onset of convection (Roberts 1968;Busse 1970): While the main part of the Coriolis force is balanced by pressure gradients, viscous forces must balance a remaining smaller part in order to facilitate convection (Zhang and Schubert 2000). As the Ekman number is lowered, the balance can only be maintained by further decreasing the length scale in order to keep viscous effects large enough.…”

Section: Convective Flow Dynamicsmentioning

confidence: 99%

Theory and Modeling of Planetary Dynamos

Wicht

Tilgner

2010

Space Sci Rev

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Numerical dynamo models are increasingly successful in modeling many features of the geomagnetic field. Moreover, they have proven to be a useful tool for understanding how the observations connect to the dynamo mechanism. More recently, dynamo simulations have also ventured to explain the surprising diversity of planetary fields found in our solar system. Here, we describe the underlying model equations, concentrating on the Boussinesq approximations, briefly discuss the numerical methods, and give an overview of existing model variations. We explain how the solutions depend on the model parameters and introduce the primary dynamo regimes. Of particular interest is the dependence on the Ekman number which is many orders of magnitude too large in the models for numerical reasons. We show that a minor change in the solution seems to happen at E = 3×10 −6 whose significance, however, needs to be explored in the future. We also review three topics that have been a focus of recent research: field reversal mechanisms, torsional oscillations, and the influence of Earth's thermal mantle structure on the dynamo. Finally we discuss the possibility of tidally or precession driven planetary dynamos.

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Section: Convective Flow Dynamicsmentioning

confidence: 99%

Theory and Modeling of Planetary Dynamos

Wicht

Tilgner

2010

Space Sci Rev

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“…Another possibility is the suggestion of Ioannou and Lindzen [1994] that tides raised in a slightly stable Jovian interior by Jupiter's moon Io force the zonal winds. Busse [1970Busse [ , 1976 first suggested that a multilayered structure of columnar convection rolls might produce the zonal jets in Jupiter's atmosphere through nonlinear interactions among the rolls. Convection in the rapidly rotating Jovian interior is assuredly more temporally and spatially complex than a simple set of quasi-steady columnar convection rolls.…”

Section: Static Stabilitymentioning

confidence: 99%

Thermal structure of Jupiter's atmosphere near the edge of a 5‐μm hot spot in the north equatorial belt

Seiff¹,

Kirk²,

Knight³

et al. 1998

J. Geophys. Res.

341

286

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Abstract. Thermal structure of the atmosphere of Jupiter was measured from 1029 km above to 133 km below the 1-bar level during entry and descent of the Galileo probe. The data confirm the hot exosphere observed by Voyager (---900 K at 1 nanobar). The deep atmosphere, which reached 429 K at 22 bars, was close to dry adiabatic from 6 to 16 bars within an uncertainty ---0.1 K/km. The upper atmosphere was dominated by gravity waves from the tropopause to the exosphere. Shorter waves were fully absorbed below 300 km, while longer wave amplitudes first grew, then were damped at the higher altitudes. A remarkably deep isothermal layer was found in the stratosphere from 90 to 290 km with T ---160 K. Just above the tropopause at 260 mbar, there was a second isothermal region ---25 km deep with T ---112 K. Between 10 and 1000 mbar, the data substantially agree with Voyager radio occultations. The Voyager 1 equatorial occultation was similar in detail to the present sounding through the tropopause region. The Voyager IRIS average thermal structure in the north equatorial belt (NEB) approximates a smoothed fit to the present data between 0.03 and 400 mbar. Differences are partly a result of large differences in vertical resolution but may also reflect differences between a hot spot and the average NEB. At 15 < p < 22 bars, where it was necessary to extrapolate the pressure calibration to sensor temperatures up to 118øC, the data indicate a stable layer in which stability increases with depth. Consistent with the indication of stability, regular fluctuations in probe vertical velocity imply gravity waves in this layer. At p > 4 bars, probe descent velocities derived from the data are consistently unsteady, suggesting the presence of large-scale turbulence or gravity waves. However, there was no evidence of turbulent temperature fluctuations >0.12 K. A conspicuous pause in the rate of decrease of descent velocity between 1.1 and 1.35 bars, where a disturbance was also detected by the two radio Doppler experiments, implies strong vertical flow in the cloud seen by the probe nephelometer. At p < 0.6 bar, measured temperatures were ---3 K warmer than the dry adiabat, possible evidence of radiative warming. This could be associated with a tenuous cloud detected by the probe nephelometer above the 0.51 bar level. For an ammonia cloud to form at this level, the required abundance is ---0.20 x solar. IntroductionThis paper reports principal results of the Galileo probe atmosphere structure experiment. The primary goal of the experiment was to define the thermal structure of Jupiter's atmosphere below the clouds, a region inaccessible to remote sensing, by direct sensing of atmospheric temperature and , 1996]. It was our intent to obtain measurements through and well below the clouds, to improve accuracy and resolution, and so to define the atmospheric stability against overturning, observe thermal effects of clouds, detect and quantify turbulence, and make other dynamical observations.Densities at a few levels in the upper atmosp...

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“…We shall focus on the second form of convection (Roberts 1968;Busse 1970; see also Jones et al . 2000), associated with large Prandtl number.…”

Section: Spatial Temporal and Amplitude Scales With A Weak¯eldmentioning

confidence: 99%

“…In (3.3), the coe¯cients of the asymptotic laws are functions of the Prandtl number Pr. It was shown by Busse (1970), based on a local asymptotic analysis, that convection with symmetry (u r ; u ; u )(r; ; ) = (u r ; u ; u )(r; ; ); (r; ; ) = (r; ; ); (3.4) (The critical Rayleigh number Rc , the corresponding azimuthal wavenumber mc and the frequency !c of convection in a rapidly rotating spherical shell with or without the e®ect of a magnetic¯eld for ri =ro = 0:4. The parameter P is related to the form of the basic magnetic eld in the magnetoconvection problem de¯ned by (4.1).…”

Section: Spatial Temporal and Amplitude Scales With A Weak¯eldmentioning

confidence: 99%

Scale disparities and magnetohydrodynamics in the Earth's core

Zhang

Gubbins

2000

Philosophical Transactions of the Royal Society of London. Seri

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Fluid motions driven by convection in the Earth's ®uid core sustain geomagnetic elds by magnetohydrodynamic dynamo processes. The dynamics of the core is critically in®uenced by the combined e¬ects of rotation and magnetic elds. This paper attempts to illustrate the scale-related di¯culties in modelling a convection-driven geodynamo by studying both linear and nonlinear convection in the presence of imposed toroidal and poloidal elds. We show that there exist three extremely large disparities, as a direct consequence of small viscosity and rapid rotation of the Earth's ®uid core, in the spatial, temporal and amplitude scales of a convection-driven geodynamo. We also show that the structure and strength of convective motions, and, hence, the relevant dynamo action, are extremely sensitive to the intricate dynamical balance between the viscous, Coriolis and Lorentz forces; similarly, the structure and strength of the magnetic eld generated by the dynamo process can depend very sensitively on the ®uid ®ow. We suggest, therefore, that the zero Ekman number limit is strongly singular and that a stable convection-driven strong-eld geodynamo satisfying Taylor's constraint may not exist. Instead, the geodynamo may vacillate between a strong eld state, as at present, and a weak eld state, which is also unstable because it fails to convect su¯cient heat.

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Thermal instabilities in rapidly rotating systems

Cited by 677 publications

References 3 publications

Theory and Modeling of Planetary Dynamos

Theory and Modeling of Planetary Dynamos

Thermal structure of Jupiter's atmosphere near the edge of a 5‐μm hot spot in the north equatorial belt

Scale disparities and magnetohydrodynamics in the Earth's core

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