On equatorially trapped boundary inertial waves

Zhang, K.

doi:10.1017/s0022112093000746

Cited by 54 publications

(43 citation statements)

References 8 publications

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“…The left three columns correspond to the critical m c = 1 mode of convection. The right columns show the critical inertial m c = 50 equatorially-attached mode of convection, of the type described in Zhang (1993). The size of the equatorial waveguide agrees very well with that of the inertial solutions found in that paper: consequently, due to the high wave number the conduction state is stable in almost all of the body of the fluid.…”

Section: Taylor Number Dependencesupporting

confidence: 82%

“…In this context, some authors first looked for solutions of the Poincaré equation in rotating spherical geometry. In a paper by Zhang (1993) symmetric and antisymmetric equatorially-attached modes of convection (EA), which travelled azimuthally, in either in the prograde or the retrograde direction, were found. In any of the cases, the latitudinal and radial radii of the waves were r l = (2/m) 1/2 and r r = (1/m), respectively, m being the azimuthal wave number.…”

Section: Introductionmentioning

confidence: 99%

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Critical torsional modes of convection in rotating fluid spheres at high Taylor numbers

2016

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A numerical study of the onset of convection in rotating, internally heated, selfgravitating fluid spheres is presented. The exploration of the stability of the conduction state versus the Taylor and the Prandtl numbers supplies a detailed idea of the laws that fulfil the four types of solutions obtained at low Prandtl numbers. The main result found is that axisymmetric (torsional) modes of convection are preferred at high Taylor numbers in the zero-Prandtl-number limit. This instability appears at low Rayleigh numbers and gives rise to an oscillating single vortex of very high frequency.

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Section: Taylor Number Dependencesupporting

confidence: 82%

Section: Introductionmentioning

confidence: 99%

Critical torsional modes of convection in rotating fluid spheres at high Taylor numbers

2016

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“…Ogilvie & Lin 2004). There also exist geomagnetic variations of non-axisymmetric magnetic flux, dominated by a single wavenumber at the core surface in the equatorial region, that are likely to be indicative of a magnetically modified equatorially trapped inertial wave (Zhang 1993;Finlay & Jackson 2003).…”

Section: Introductionmentioning

confidence: 99%

A new integral property of inertial waves in rotating fluid spheres

Liao

Zhang

2008

Proc. R. Soc. A.

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The problem of fluid motion in the form of inertial waves in an incompressible inviscid fluid contained in a rotating sphere is governed by the Poincaré equation, a second-order hyperbolic partial differential equation. Its explicit general analytical solution in terms of a double Poincaré polynomial was found by Zhang et al. (Zhang et al. 2001 J. Fluid Mech. 437, 103 -119), describing the pressure p mnK and the velocity u mnK of spherical inertial waves, where the triple indices (mnK ) are indicative of the azimuthal, vertical and radial structures, respectively. On the basis of the general explicit solution, we reveal a new intriguing integral property of the spherical inertial waves ðfor all possible values of m, l and n, where M and K are related to the degree of the double Poincaré polynomial and u Ã mlM denotes the complex conjugate of u mlM . A mathematical proof of the vanishing of the integral involving the construction of two auxiliary recurrence relations is presented. Furthermore, a comparison with the corresponding integral for rotating cylinders is made, showing a fundamental difference between the two systems.

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“…According to Zhang (1993Zhang ( , 1994, the equatorially trapped modes are quasiinertial waves, i.e. at leading order they are solutions of the Poincaré equation.…”

Section: Introductionmentioning

confidence: 99%

On the onset of low-Prandtl-number convection in rotating spherical shells: non-slip boundary conditions

Net¹,

García²,

Sánchez³

2008

J. Fluid Mech.

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Accurate numerical computations of the onset of thermal convection in wide rotating spherical shells are presented. Low-Prandtl-number (σ ) fluids, and non-slip boundary conditions are considered. It is shown that at small Ekman numbers (E), and very low σ values, the well-known equatorially trapped patterns of convection are superseded by multicellular outer-equatorially-attached modes. As a result, the convection spreads to higher latitudes affecting the body of the fluid, and increasing the internal viscous dissipation. Then, from E < 10 −5 , the critical Rayleigh number (R c ) fulfils a power-law dependence R c ∼ E −4/3 , as happens for moderate and high Prandtl numbers. However, the critical precession frequency (|ω c |) and the critical azimuthal wavenumber (m c ) increase discontinuously, jumping when there is a change of the radial and latitudinal structure of the preferred eigenfunction. In addition, the transition between spiralling columnar (SC), and outer-equatorially-attached (OEA) modes in the (σ , E)-space is studied. The evolution of the instability mechanisms with the parameters prevents multicellular modes being selected from σ & 0.023. As a result, and in agreement with other authors, the spiralling columnar patterns of convection are already preferred at the Prandtl number of the liquid metals. It is also found that, out of the rapidly rotating limit, the prograde antisymmetric (with respect to the equator) modes of small m c can be preferred at the onset of the primary instability.

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On equatorially trapped boundary inertial waves

Cited by 54 publications

References 8 publications

Critical torsional modes of convection in rotating fluid spheres at high Taylor numbers

Critical torsional modes of convection in rotating fluid spheres at high Taylor numbers

A new integral property of inertial waves in rotating fluid spheres

On the onset of low-Prandtl-number convection in rotating spherical shells: non-slip boundary conditions

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