Linear stability of rotating convection in an 

imposed shear flow

Matthews, P. C.; Cox, Stephen M.

doi:10.1017/s0022112097006903

Cited by 15 publications

(15 citation statements)

References 22 publications

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“…They found that convective modes in the nonsheared problem become travelling when a weak shear is added. Some previous work found that this behaviour is possible either at low (Kropp and Busse, 1991) or if some form of symmetry breaking is present in the equations (Matthews and Cox, 1997). Since linear shear alone cannot do the job, it is likely that density stratification plays an important role in obtaining the result.…”

Section: Oscillatory Convection Rotation and Shearmentioning

confidence: 94%

The Sun’s Supergranulation

Rincon

Rieutord

2010

Living Rev. Solar Phys.

165

132

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The Sun's supergranulation refers to a physical pattern covering the surface of the quiet Sun with a typical horizontal scale of approximately 30,000 km and a lifetime of around 1.8 d. Its most noticeable observable signature is as a fluctuating velocity field of 360 m s -1 rms whose components are mostly horizontal. Supergranulation was discovered more than fifty years ago, however explaining why and how it originates still represents one of the main challenges of modern solar physics.A lot of work has been devoted to the subject over the years, but observational constraints, conceptual difficulties and numerical limitations have all concurred to prevent a detailed understanding of the supergranulation phenomenon so far. With the advent of 21st century supercomputing resources and the availability of unprecedented high-resolution observations of the Sun, a stage at which key progress can be made has now been reached. A unifying strategy between observations and modelling is more than ever required for this to be possible.The primary aim of this review is therefore to provide readers with a detailed interdisciplinary description of past and current research on the problem, from the most elaborate observational strategies to recent theoretical and numerical modelling efforts that have all taken up the challenge of uncovering the origins of supergranulation. Throughout the text, we attempt to pick up the most robust findings so far, but we also outline the difficulties, limitations and open questions that the community has been confronted with over the years.In the light of the current understanding of the multiscale dynamics of the quiet photosphere, we finally suggest a tentative picture of supergranulation as a dynamical feature of turbulent magnetohydrodynamic convection in an extended spatial domain, with the aim of stimulating future research and discussions.

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Section: Oscillatory Convection Rotation and Shearmentioning

confidence: 94%

The Sun’s Supergranulation

Rincon

Rieutord

2010

Living Rev. Solar Phys.

165

132

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“…These trivial results are well known. Matthews & Cox (1997) have shown that for the non-trivial extension when both horizontal rotation τ = 0 (µ = 0) at ϑ = π/2 and plane Couette shear (Re = 0) are present, the onset of convection continues to be characterized by either X-or Y -directed rolls.…”

Section: Locally Cartesian Formulationmentioning

confidence: 99%

“…Busse & Kropp (1992) considered the case of aligned horizontal rotation and shear, and found that, paradoxically, buoyantly driven oblique rolls are sometimes preferred. Matthews & Cox (1997) extended these studies by allowing an arbitrary angle between the horizontal rotation vector and the linear shear flow. They studied the roll orientation as a function of this angle and used arguments based on winding numbers to determine the dominant driving mechanism for the rolls, shear or convection, in certain parameter ranges.…”

Section: Introductionmentioning

confidence: 99%

The onset of thermal convection in EkmanCouette shear flow with oblique rotation

2003

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The onset of convection of a Boussinesq fluid in a horizontal plane layer is studied. The system rotates with constant angular velocity Ω Ω Ω, which is inclined at an angle ϑ to the vertical. The layer is sheared by keeping the upper boundary fixed, while the lower boundary moves parallel to itself with constant velocity U 0 normal to the plane containing the rotation vector and gravity g (i.e. U 0 g × Ω Ω Ω). The system is characterized by five dimensionless parameters: the Rayleigh number Ra, the Taylor number τ 2 , the Reynolds number Re (based on U 0 ), the Prandtl number Pr and the angle ϑ. The basic equilibrium state consists of a linear temperature profile and an Ekman-Couette flow, both dependent only on the vertical coordinate z. Our linear stability study involves determining the critical Rayleigh number Ra c as a function of τ and Re for representative values of ϑ and Pr.Our main results relate to the case of large Reynolds number, for which there is the possibility of hydrodynamic instability. When the rotation is vertical ϑ = 0 and τ 1, so-called type I and type II Ekman layer instabilities are possible. With the inclusion of buoyancy Ra = 0 mode competition occurs. On increasing τ from zero, with fixed large Re, we identify four types of mode: a convective mode stabilized by the strong shear for moderate τ , hydrodynamic type I and II modes either assisted (Ra > 0) or suppressed (Ra < 0) by buoyancy forces at numerically large τ , and a convective mode for very large τ that is largely uninfluenced by the thin Ekman shear layer, except in that it provides a selection mechanism for roll orientation which would otherwise be arbitrary. Significantly, in the case of oblique rotation ϑ = 0, the symmetry associated with U 0 ↔ −U 0 for the vertical rotation is broken and so the cases of positive and negative Re exhibit distinct stability characteristics, which we consider separately. Detailed numerical results were obtained for the representative case ϑ = π/4. Though the overall features of the stability results are broadly similar to the case of vertical rotation, their detailed structure possesses a surprising variety of subtle differences.

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“…The majority of work has focused on the case of a shear flow dependent on the vertical direction, arising from relative motion of the horizontal boundaries or, alternatively, from a fictitious force (see e.g. Hathaway, Toomre & Gilman 1980;Hathaway & Somerville 1983, 1986Kropp & Busse 1991;Matthews & Cox 1997;Cox 1998). The hydrodynamical problem of a horizontally dependent shear flow, the case we consider here, may also be of relevance in planetary atmospheres, and has been examined in the nonlinear regime by Hathaway & Somerville (1987).…”

Section: Flows and Fields In Rotating Sheared Convectionmentioning

confidence: 99%

The effect of velocity shear on dynamo action due to rotating convection

Hughes

Proctor

2013

J. Fluid Mech.

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Recent numerical simulations of dynamo action resulting from rotating convection have revealed some serious problems in applying the standard picture of mean field electrodynamics at high values of the magnetic Reynolds number, and have thereby underlined the difficulties in large-scale magnetic field generation in this regime.Here we consider kinematic dynamo processes in a rotating convective layer of Boussinesq fluid with the additional influence of a large-scale horizontal velocity shear. Incorporating the shear flow enhances the dynamo growth rate and also leads to the generation of significant magnetic fields on large scales. By the technique of spectral filtering, we analyse the modes in the velocity that are principally responsible for dynamo action, and show that the magnetic field resulting from the full flow relies crucially on a range of scales in the velocity field. Filtering the flow to provide a true separation of scales between the shear and the convective flow also leads to dynamo action; however, the magnetic field in this case has a very different structure from that generated by the full velocity field. We also show that the nature of the dynamo action is broadly similar irrespective of whether the flow in the absence of shear can support dynamo action.

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Linear stability of rotating convection in an imposed shear flow

Cited by 15 publications

References 22 publications

The Sun’s Supergranulation

The Sun’s Supergranulation

The onset of thermal convection in EkmanCouette shear flow with oblique rotation

The effect of velocity shear on dynamo action due to rotating convection

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