Time dependent β-convection in rapidly rotating spherical shells

Morin, Vincent; Dormy, Emmanuel

doi:10.1063/1.1703530

Cited by 30 publications

(47 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With σ = 1 and for weak supercritical conditions the flow is strongly oscillatory, displaying an intermittent pattern [8]. The sequence of transitions observed in the full three-dimensional simulations of [36] was reproduced in [26] by using the quasi-geostrophic approximation. The authors found that, as the Ekman number is decreased, the transition to oscillatory convection occurs for marginally supercritical Rayleigh numbers.…”

mentioning

confidence: 80%

Oscillatory Convection in Rotating Spherical Shells: Low Prandtl Number and Non-Slip Boundary Conditions

García¹,

Sánchez²,

Dormy³

et al. 2015

SIAM J. Appl. Dyn. Syst.

Self Cite

View full text Add to dashboard Cite

Abstract.A five-degree model, which reproduces faithfully the sequence of bifurcations and the type of solutions found through numerical simulations of the three-dimensional Boussinesq thermal convection equations in rotating spherical shells with fixed azimuthal symmetry, is derived. A low Prandtl number fluid of σ = 0.1 subject to radial gravity, filling a shell of radius ratio η = 0.35, differentially heated, and with non-slip boundary conditions, is considered. Periodic, quasi-periodic, and temporal chaotic flows are obtained for a moderately small Ekman number, E = 10 −4 , and at supercritical Rayleigh numbers of order Ra ∼ O(2Rac). The solutions are classified by means of frequency analysis and Poincaré sections. Resonant phase locking on the quasi-periodic branches, as well as a sequence of period doubling bifurcations, are also detected.

show abstract

mentioning

confidence: 80%

Oscillatory Convection in Rotating Spherical Shells: Low Prandtl Number and Non-Slip Boundary Conditions

García¹,

Sánchez²,

Dormy³

et al. 2015

SIAM J. Appl. Dyn. Syst.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Morin & Dormy noted that the critical value of required to set the vacillation instability becomes quite small when E diminishes, and that the vacillation instability then transforms into a pulsed instability leading to relaxation oscillations (like the ones shown in the figure 8 of Morin & Dormy 2004). It would be interesting to run new simulations of this kind in a clearly subcritical case.…”

Section: Concluding Discussionmentioning

confidence: 99%

“…One should be aware that, at finite values of E, the thermal Rossby waves are typically subject to a secondary vacillation instability at rather small values of , as shown, for instance, by the numerical simulations of Tilgner & Busse (1997) with a three-dimensional model, and by Cole (2004), Morin & Dormy (2004) with cylindrical QG models. Morin & Dormy noted that the critical value of required to set the vacillation instability becomes quite small when E diminishes, and that the vacillation instability then transforms into a pulsed instability leading to relaxation oscillations (like the ones shown in the figure 8 of Morin & Dormy 2004).…”

Section: Concluding Discussionmentioning

confidence: 99%

See 1 more Smart Citation

Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell

et al. 2008

View full text Add to dashboard Cite

A general reformulation of the Reynolds stresses created by two-dimensional waves breaking a translational or a rotational invariance is described. This reformulation emphasizes the importance of a geometrical factor: the slope of the separatrices of the wave flow. Its physical relevance is illustrated by two model systems: waves destabilizing open shear flows; and thermal Rossby waves in spherical shell convection with rotation. In the case of shear-flow waves, a new expression of the Reynolds-Orr amplification mechanism is obtained, and a good understanding of the form of the mean pressure and velocity fields created by weakly nonlinear waves is gained. In the case of thermal Rossby waves, results of a three-dimensional code using no-slip boundary conditions are presented in the nonlinear regime, and compared with those of a two-dimensional quasi-geostrophic model. A semi-quantitative agreement is obtained on the flow amplitudes, but discrepancies are observed concerning the nonlinear frequency shifts. With the quasi-geostrophic model we also revisit a geometrical formula proposed by Zhang to interpret the form of the zonal flow created by the waves, and explore the very low Ekman-number regime. A change in the nature of the wave bifurcation, from supercritical to subcritical, is found. IntroductionIn hydrodynamic stability theory and turbulence modelling, it is natural and customary to separate the velocity field into a mean flow V and a fluctuating part v. In the Navier-Stokes equation for V , the nonlinear term expressing the feedback of the fluctuating flow onto the mean flow is usually written as the divergence of the Reynolds stress tensorwhere the angle brackets indicate a suitable averaging. A good understanding or modelling of τ is therefore required to explain the form of the mean flow, and other mean properties of the flow, such as the flow rate and head losses, in the case of an open system for instance. The tensor τ is also quite important for energy since in purely hydrodynamical systems its contraction with the mean strain rate tensor is the only possible source of growth of the fluctuating kinetic energy, as shown in a landmark paper by Reynolds (1895) Busse (1983) in the case of a fluctuating field corresponding to a columnar quasi-two-dimensional wave. He noted in his § 3 (see also his figure 3), a link between the variations of the 'phase function' of the wave and the relevant cross-diagonal Reynolds stress, which was revisited by Zhang (1992). The reformulation proposed by Zhang for the Reynolds stress, however, is limited to a special form of the streamfunction. In the somewhat more general case of a two-dimensional, x, y, fluctuating field, Pedlosky (1987) established ( § 7.3, p. 502) a link between the product v x v y that controls the most important Reynolds stress, i.e. the cross-diagonal stress τ xy , and the slope of the streamlines of v. Pedlosky offered no simple formula for the average v x v y , however.The primary aim of this paper is to complement these pioneering works by propo...

show abstract

“…With magnetic effects, we can imagine very complicated situations. Oscillation properties can drastically change, even disappear (Grote & Busse 2000;Morin & Dormy 2004).…”

Section: From Localized To Vacillating Convectionmentioning

confidence: 99%

Simulations of Turbulent Convection in Rotating Young Solarlike Stars: Differential Rotation and Meridional Circulation

Ballot

Brun

Turck‐Chièze

2007

ApJ

View full text Add to dashboard Cite

We present the results of three-dimensional simulations of the deep convective envelope of a young (10 Myr) 1 M star, obtained with the anelastic spherical harmonic code. Since young stars are known to be faster rotators than their main-sequence counterparts, we have systematically studied the impact of the stellar rotation speed, by considering stars spinning up to 5 times as fast as the Sun. The aim of these nonlinear models is to understand the complex interactions between convection and rotation. We discuss the influence of the turbulence level and of the rotation rate on the intensity and the topology of the mean flows. For all of the computed models, we find a solar-type superficial differential rotation, with an equatorial acceleration, and meridional circulation that exhibits a multicellular structure. Even if the differential rotation contrast Á decreases only marginally for high rotation rates, the meridional circulation intensity clearly weakens according to our simulations. We have also shown that, for Taylor numbers above a certain threshold (Ta k 10 9 ), the convection can develop a vacillating behavior. Since simulations with high turbulence levels and rotation rates exhibit strongly cylindrical internal rotation profiles, we have considered the influence of baroclinic effects at the base of the convective envelope of these young Suns to see whether such effects can modify the otherwise near-cylindrical profiles to produce more conical, solarlike profiles.

show abstract

Time dependent β-convection in rapidly rotating spherical shells

Cited by 30 publications

References 22 publications

Oscillatory Convection in Rotating Spherical Shells: Low Prandtl Number and Non-Slip Boundary Conditions

Oscillatory Convection in Rotating Spherical Shells: Low Prandtl Number and Non-Slip Boundary Conditions

Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell

Simulations of Turbulent Convection in Rotating Young Solarlike Stars: Differential Rotation and Meridional Circulation

Contact Info

Product

Resources

About