scholarly journals Boussinesq convection in a gaseous spherical shell

2019 ◽  
Vol 82 ◽  
pp. 373-382
Author(s):  
L. Korre ◽  
N. Brummell ◽  
P. Garaud
Keyword(s):  
Temperature Gradient ◽  
Boundary Conditions ◽  
Spherical Shell ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Boussinesq Approximation ◽  
Fixed Temperature ◽  
Planetary Interiors ◽  
Adiabatic Temperature Gradient ◽  
Relevant Quantity

In this paper, we investigate the dynamics of convection in a spherical shell under the Boussinesq approximation but considering the compressibility which arises from a non zero adiabatic temperature gradient, a relevant quantity for gaseous objects such as stellar or planetary interiors. We find that depth-dependent superiadiabaticity, combined with the use of mixed boundary conditions (fixed flux/fixed temperature), gives rise to unexpected dynamics that were not previously reported.

scholarly journals Toroidal free oscillations of a viscous liquid spherical shell with mixed boundary conditions

2021 ◽  
Vol 2094 (2) ◽  
pp. 022035
Author(s):  
Gleb Vodinchar
Keyword(s):  
Numerical Simulation ◽  
Free Surface ◽  
Viscous Fluid ◽  
Boundary Conditions ◽  
Spherical Shell ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Solid Boundary ◽  
Free Oscillations ◽  
Surface Conditions

Abstract The problem of toroidal eigenmodes of free oscillations of a viscous fluid spherical shell is solved under mixed boundary conditions. These conditions are a combination of free surface conditions and solid boundary conditions. Such an artificial combination is used sometimes in the numerical simulation of geodynamo problem. The scheme for calculating the eigenmodes is described. It is shown that the use of mixed conditions leads to the disappearance of the first eigenmode with the smallest eigenvalue. A possible reason for this is the physical incorrectness of the mixed boundary conditions.

scholarly journals General solutions in Chern-Simons gravity and $$ T\overline{T} $$-deformations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Eva Llabrés
Keyword(s):  
Variational Principle ◽  
Boundary Conditions ◽  
Dirichlet Boundary ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Spin Connection ◽  
Departure Point ◽  
Boundary Stress ◽  
Chern Simons

Abstract We find the most general solution to Chern-Simons AdS3 gravity in Fefferman-Graham gauge. The connections are equivalent to geometries that have a non-trivial curved boundary, characterized by a 2-dimensional vielbein and a spin connection. We define a variational principle for Dirichlet boundary conditions and find the boundary stress tensor in the Chern-Simons formalism. Using this variational principle as the departure point, we show how to treat other choices of boundary conditions in this formalism, such as, including the mixed boundary conditions corresponding to a $$ T\overline{T} $$ T T ¯ -deformation.

scholarly journals Casimir effect for a massive scalar field under mixed boundary conditions

2003 ◽  
Vol 33 (4) ◽  
pp. 860-866 ◽  
Author(s):  
A.C. Aguiar Pinto ◽  
T.M. Britto ◽  
R. Bunchaft ◽  
F. Pascoal ◽  
F.S.S. da Rosa
Keyword(s):  
Scalar Field ◽  
Boundary Conditions ◽  
Mixed Boundary ◽  
Casimir Effect ◽  
Mixed Boundary Conditions ◽  
Massive Scalar ◽  
Massive Scalar Field
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