scholarly journals Convectons in a rotating fluid layer

2013 ◽  
Vol 717 ◽  
pp. 417-448 ◽  
Author(s):  
Cédric Beaume ◽  
Alain Bergeon ◽  
Hsien-Ching Kao ◽  
Edgar Knobloch
Keyword(s):  
Free Boundary ◽  
Shear Flow ◽  
Fluid Layer ◽  
Plane Layer ◽  
Two Dimensional ◽  
Rotating Fluid ◽  
Bifurcation Structure ◽  
Free Boundary Conditions ◽  
Localized Structures ◽  
Stress Free Boundary

AbstractTwo-dimensional convection in a plane layer bounded by stress-free perfectly conducting horizontal boundaries and rotating uniformly about the vertical is considered. Time-independent spatially localized structures, called convectons, of even and odd parity are computed. The convectons are embedded within a self-generated shear layer with a compensating shear flow outside the structure. These states are organized within a bifurcation structure called slanted snaking and may be present even when periodic convection sets in supercritically. These interesting properties are traced to the presence of a conserved quantity and hence to the use of stress-free boundary conditions.

scholarly journals Transition to geostrophic convection: the role of the boundary conditions

2016 ◽  
Vol 799 ◽  
pp. 413-432 ◽  
Author(s):  
Rudie P. J. Kunnen ◽  
Rodolfo Ostilla-Mónico ◽  
Erwin P. van der Poel ◽  
Roberto Verzicco ◽  
Detlef Lohse
Keyword(s):  
Boundary Layer ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Large Scale ◽  
Scaling Laws ◽  
Stokes Equations ◽  
Fluid Layer ◽  
Navier Stokes ◽  
Free Boundary Conditions ◽  
Stress Free Boundary

Rotating Rayleigh–Bénard convection, the flow in a rotating fluid layer heated from below and cooled from above, is used to analyse the transition to the geostrophic regime of thermal convection. In the geostrophic regime, which is of direct relevance to most geo- and astrophysical flows, the system is strongly rotating while maintaining a sufficiently large thermal driving to generate turbulence. We directly simulate the Navier–Stokes equations for two values of the thermal forcing, i.e. $Ra=10^{10}$ and $Ra=5\times 10^{10}$, at constant Prandtl number $Pr=1$, and vary the Ekman number in the range $Ek=1.3\times 10^{-7}$ to $Ek=2\times 10^{-6}$, which satisfies both requirements of supercriticality and strong rotation. We focus on the differences between the application of no-slip versus stress-free boundary conditions on the horizontal plates. The transition is found at roughly the same parameter values for both boundary conditions, i.e. at $Ek\approx 9\times 10^{-7}$ for $Ra=1\times 10^{10}$ and at $Ek\approx 3\times 10^{-7}$ for $Ra=5\times 10^{10}$. However, the transition is gradual and it does not exactly coincide in $Ek$ for different flow indicators. In particular, we report the characteristics of the transitions in the heat-transfer scaling laws, the boundary-layer thicknesses, the bulk/boundary-layer distribution of dissipations and the mean temperature gradient in the bulk. The flow phenomenology in the geostrophic regime evolves differently for no-slip and stress-free plates. For stress-free conditions, the formation of a large-scale barotropic vortex with associated inverse energy cascade is apparent. For no-slip plates, a turbulent state without large-scale coherent structures is found; the absence of large-scale structure formation is reflected in the energy transfer in the sense that the inverse cascade, present for stress-free boundary conditions, vanishes.

On Wave Reflection in an Elastic Plate

1974 ◽  
Vol 41 (4) ◽  
pp. 1031-1035
Author(s):  
R. Doby
Keyword(s):  
Free Boundary ◽  
Theoretical Analysis ◽  
Wave Reflection ◽  
Transverse Waves ◽  
Reflected Waves ◽  
Longitudinal Waves ◽  
Free Boundary Conditions ◽  
Transverse Modes ◽  
Parallel Surfaces ◽  
Stress Free Boundary

A precursor boundary concept is introduced which decouples the stress-free boundary conditions at the parallel surfaces of the plate. The resulting orthogonal eigenfunctions are longitudinal and transverse waves. This property is exploited so as to satisfy stress-free conditions at the edge. The theoretical analysis reveals that the reflected waves are reordered so that the longitudinal and transverse modes represent the gradients of the incident transverse and longitudinal waves.

scholarly journals Parallel Computing of Edwards—Anderson Model

Algorithms ◽  
2021 ◽  
Vol 15 (1) ◽  
pp. 13
Author(s):  
Mikhail Alexandrovich Padalko ◽  
Yuriy Andreevich Shevchenko ◽  
Vitalii Yurievich Kapitan ◽  
Konstantin Valentinovich Nefedev
Keyword(s):  
Parallel Computing ◽  
Free Boundary ◽  
Anderson Model ◽  
Spin Glasses ◽  
Quantum Computer ◽  
Two Dimensional ◽  
Matrix Approach ◽  
Free Boundary Conditions ◽  
Computer Simulator ◽  
Transfer Matrix Approach

A scheme for parallel computation of the two-dimensional Edwards—Anderson model based on the transfer matrix approach is proposed. Free boundary conditions are considered. The method may find application in calculations related to spin glasses and in quantum simulators. Performance data are given. The scheme of parallelisation for various numbers of threads is tested. Application to a quantum computer simulator is considered in detail. In particular, a parallelisation scheme of work of quantum computer simulator.

Diffraction by an elastic wedge with stress-free boundary: existence and uniqueness

2005 ◽  
Vol 462 (2065) ◽  
pp. 289-317 ◽  
Author(s):  
Vladimir V Kamotski ◽  
Gilles Lebeau
Keyword(s):  
Free Boundary ◽  
Absolute Continuity ◽  
Existence And Uniqueness ◽  
Existence Of Solutions ◽  
Elastic Wedge ◽  
Free Boundary Conditions ◽  
Cylindrical Waves ◽  
Radiation Conditions ◽  
Continuity Of The Spectrum ◽  
Stress Free Boundary

Applying the spectral function techniques, developed by Croisille and Lebeau, we prove the existence of solutions to problems of plane and cylindrical waves diffraction by an elastic wedge with stress-free boundary conditions. We also formulate radiation conditions, under which the uniqueness holds. The latter implies absolute continuity of the spectrum of the Lamé operator in a wedge domain with stress-free boundary.

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