Localized rotating convection with no-slip boundary conditions

Beaume, Cédric; Kao, Hsuan-Yun; Knobloch, Edgar; Bergeon, Alain

doi:10.1063/1.4843155

Cited by 13 publications

(10 citation statements)

References 41 publications

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“…The solutions are represented as in figure 2 with multiples of 0.6 for the streamfunction contours except for the Re ≈ 264 and Re ≈ 500 solutions for which the contours are multiples of 0.9. for the splitting of the one-pulse state into two pulses. Similar splitting of a single-pulse localized structure occurs in rotating convection [4].…”

Section: Modulated Statesmentioning

confidence: 72%

Modulated patterns in a reduced model of a transitional shear flow

et al. 2016

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We use a reduced model of such flows constructed elsewhere to compute stationary exact coherent structures of Waleffe flow in periodic domains with a large spanwise period. The computations reveal the emergence of stationary states exhibiting strong amplitude and wavelength modulation in the spanwise direction. These modulated 1 states lie on branches exhibiting complex dependence on the Reynolds number but no homoclinic snaking.

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Section: Modulated Statesmentioning

confidence: 72%

Modulated patterns in a reduced model of a transitional shear flow

et al. 2016

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“…In the 2D planar geometry studied by Chandrasekhar [4], Veronis predicted a possible subcriticality in a window of low rotation rates [21], recently confirmed numerically [22]. The subcritical behavior is associated with the presence of large mean flows which reduce locally the effective rate of rotation and consequently, the rotational constraint on the flow and the critical Rayleigh number toward its non rotating value.…”

Section: Weak and Strong Branchesmentioning

confidence: 77%

Subcritical Thermal Convection of Liquid Metals in a Rapidly Rotating Sphere

et al. 2017

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Planetary cores consist of liquid metals (low Prandtl number Pr) that convect as the core cools. Here, we study nonlinear convection in a rotating (low Ekman number Ek) planetary core using a fully 3D direct numerical simulation. Near the critical thermal forcing (Rayleigh number Ra), convection onsets as thermal Rossby waves, but as Ra increases, this state is superseded by one dominated by advection. At moderate rotation, these states (here called the weak branch and strong branch, respectively) are smoothly connected. As the planetary core rotates faster, the smooth transition is replaced by hysteresis cycles and subcriticality until the weak branch disappears entirely and the strong branch onsets in a turbulent state at Ek<10^{-6}. Here, the strong branch persists even as the thermal forcing drops well below the linear onset of convection (Ra=0.7Ra_{crit} in this study). We highlight the importance of the Reynolds stress, which is required for convection to subsist below the linear onset. In addition, the Péclet number is consistently above 10 in the strong branch. We further note the presence of a strong zonal flow that is nonetheless unimportant to the convective state. Our study suggests that, in the asymptotic regime of rapid rotation relevant for planetary interiors, thermal convection of liquid metals in a sphere onsets through a subcritical bifurcation.

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“…Localized states remain, albeit at different values of the parameter, but snaking returns to its standard, nonslanted form (137). Related issues arise in studies of oscillons in granular media (or liquids), where the conservation of mass (or volume) also exerts a significant influence (138)(139)(140)(141).…”

Section: Fluid Systems With a Conserved Quantitymentioning

confidence: 97%

Spatial Localization in Dissipative Systems

Knobloch

2015

Annu. Rev. Condens. Matter Phys.

178

189

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Spatial localization is a common feature of physical systems, occurring in both conservative and dissipative systems. This article reviews the theoretical foundations of our understanding of spatial localization in forced dissipative systems, from both a mathematical point of view and a physics perspective. It explains the origin of the large multiplicity of simultaneously stable spatially localized states present in a parameter region called the pinning region and its relation to the notion of homoclinic snaking. The localized states are described as bound states of fronts, and the notions of front pinning, selfpinning, and depinning are emphasized. Both one-dimensional and two-dimensional systems are discussed, and the reasons behind the differences in behavior between dissipative systems with conserved and nonconserved dynamics are explained. The insights gained are specific to forced dissipative systems and are illustrated here using examples drawn from fluid mechanics (convection and shear flows) and a simple model of crystallization. 325 Annu. Rev. Condens. Matter Phys. 2015.6:325-359. Downloaded from www.annualreviews.org Access provided by Mahidol University on 03/10/15. For personal use only.

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Localized rotating convection with no-slip boundary conditions

Cited by 13 publications

References 41 publications

Modulated patterns in a reduced model of a transitional shear flow

Modulated patterns in a reduced model of a transitional shear flow

Subcritical Thermal Convection of Liquid Metals in a Rapidly Rotating Sphere

Spatial Localization in Dissipative Systems

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