Nonlinear dynamics of boussinesq convection in a deep rotating spherical shell III: Effects of velocity boundary conditions

1978 ◽  
Vol 11 (1) ◽  
pp. 181-203 ◽  
Author(s):  
Peter A. Gilman
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Spherical Shell

Boundaries and Geometries

2013 ◽  
Author(s):  
Gary A. Glatzmaier
Keyword(s):  
Fluid Flow ◽  
Boundary Conditions ◽  
Spherical Shell ◽  
Spherical Harmonic ◽  
Stable Stratification ◽  
Internal Gravity Waves ◽  
Box Model ◽  
Mean Flow ◽  
Flow Through ◽  
Nonzero Mean

This chapter examines how boundary and geometry affect convection. It begins with a discussion of how one can implement “absorbing” top and bottom boundaries, which reduce the large-amplitude convectively driven flows within shallow boundary layers or the reflection of internal gravity waves off these boundaries in a stable stratification. It then considers how to replace the impermeable side boundary conditions with permeable periodic side boundary conditions to allow fluid flow through these boundaries and nonzero mean flow. It also introduces “two and a half dimensional” geometry within a cartesian box geometry and describes how a fully 3D cartesian box model could be constructed. Finally, it presents a model of convection in a fully 3D spherical-shell and shows how it can be easily reduced to a 2.5D spherical-shell model. The horizontal structures are represented in terms of spherical harmonic expansions.

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.

Stresses in a Spherical Shell With a Nonradial Nozzle

1967 ◽  
Vol 34 (2) ◽  
pp. 299-307 ◽  
Author(s):  
D. E. Johnson
Keyword(s):  
Cylindrical Shell ◽  
Boundary Conditions ◽  
Spherical Shell ◽  
Shell Theory ◽  
Analytical Investigation ◽  
Type Method ◽  
Cylindrical Nozzle ◽  
Pass Through ◽  
External Forces ◽  
Radial Nozzle

An analytical investigation is made of the stresses due to external forces and moments acting on an elastic nonradial circular cylindrical nozzle attached to a spherical shell. The nozzle (a cylindrical shell) is nonradial in the sense that its axis is inclined and does not pass through the center of the sphere. Results are obtained by combining solutions from shell theory by a Galerkin-type method so as to satisfy boundary conditions at the intersection of the two shells. It is found that, as the nozzle inclination increases, the stresses change gradually from those previously given by Bijlaard for the radial nozzle.

Discontinuities in spherically symmetric gravitational fields and shells of radiation

1958 ◽  
Vol 248 (1254) ◽  
pp. 404-414 ◽  
Keyword(s):  
Boundary Conditions ◽  
Spherical Shell ◽  
Previous Treatment ◽  
Empty Space ◽  
Point Of View ◽  
Spherically Symmetric ◽  
Junction Conditions ◽  
Metric Tensor ◽  
Gravitational Fields

Boundary conditions at a 3-space of discontinuity ∑ are considered from the point of view of Lichnerowicz. The validity of the O’Brien—Synge junction conditions is established for co-ordinates derivable from Lichnerowicz’s ‘admissible co-ordinates’ by a transformation which is uniformly differentiable across ∑. The co-ordinates r , θ , ϕ , t , used by Schwarzschild and most later authors when dealing with spherically symmetric fields, are shown to be of this type. In Schwarzschild’s co-ordinates, the components of the metric tensor can always be made continuous across Ʃ, and simple relations are derived connecting the jumps in their first derivatives. A spherical shell of radiation expanding in empty space is examined in the light of the above ideas, and difficulties encountered by Raychaudhuri in a previous treatment of this problem are cleared up. A particular model is then discussed in some detail.

Nonlinear Dynamics Analysis of a Printed Wiring Board With Simple and Clamped Boundary Conditions

2001 ◽  
Author(s):  
Xiaoling He
Keyword(s):  
Nonlinear Dynamics ◽  
Boundary Conditions ◽  
Equations Of Motion ◽  
Nonlinear Resonance ◽  
Failure Criteria ◽  
Dynamics Analysis ◽  
Printed Wiring Board ◽  
Resonance Behavior ◽  
Condition Effect ◽  
Wiring Board

Abstract Dynamic response of a printed wiring board (PWB) is analyzed in nonlinear dynamics approach. Equations of motion for the simply supported PWB and the clamped PWB are obtained by the Galerkin’s method. A 2-layer plastic PWB made of isotropic laminates is studied for its boundary condition effect on the vibratory behavior in deflection and stresses. Failure due to plane stress interaction is estimated based on the composite failure criteria. It is found that nonlinear resonance occurs almost periodically in both frequency and temporal domain. Load frequency and magnitude affect the deflection response under different boundary conditions. Resonance behavior is critical in PWB failure prediction based on the stress analysis. The analytical results can be extended to the nonlinear dynamics analysis of the thin laminated plate.

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