A periodic boundary-layer flow in magnetohydrodynamics

1962 ◽  
Vol 13 (4) ◽  
pp. 519-528 ◽  
Author(s):  
D. L. Turcotte ◽  
J. M. Lyons
Keyword(s):  
Boundary Layer ◽  
Periodic Boundary ◽  
Viscous Effects ◽  
Expansion Technique ◽  
Type Flow ◽  
Upstream Direction ◽  
Periodic Boundary Layer ◽  
Overall Performance ◽  
Layer Flow ◽  
Incompressible Flow Problem

It is the purpose of this paper to solve a boundary-value problem posed by induction electromagnetic pumps and generators. Solutions are obtained by an expansion technique and a momentum method for the laminar, incompressible flow problem. For large values of the interaction parameter (μ2σH20λ/ρμe viscous effects are shown to be restricted to periodic boundary layers. In regions of high-field strength a local Hartmann solution is valid. Where the applied field is weak an inertial boundary layer is present which thickens in the upstream direction.A logical explanation of this phenomenon is given. The condition that a boundary-layer type flow exist is obtained and is shown to be in general satisfied. The results show that inviscid theory may be used to calculate the overall performance of electromagnetic pumps and generators while the boundary-layer theory developed here may be used to obtain the wall shear stress.

The instability of a stratified periodic boundary layer

1976 ◽  
Vol 75 (2) ◽  
pp. 287-303 ◽  
Author(s):  
Christian Von Kerczek ◽  
Stephen H. Davis
Keyword(s):  
Boundary Layer ◽  
Periodic Boundary ◽  
Vertical Plate ◽  
Neutral Curve ◽  
Time Dependent ◽  
Two Dimensional ◽  
Viscous Forces ◽  
Periodic Boundary Layer ◽  
Buoyancy Instability ◽  
Dependent State

A vertical plate oscillating vertically in a statically stably-stratified fluid induces an internal wave damped by viscous forces. A two-dimensional linear stability analysis of this time-dependent state shows that the wave is highly unstable when the buoyancy and forcing frequencies are comparable. This gravitational (buoyancy) instability is due to the presence of the background stratification. The neutral curve is calculated and the system energetics are explored. Excellent agreement is obtained with the recent experimental observations of Robinson & McEwan.

scholarly journals On the non-parallel instability of the rotating-sphere boundary layer

2017 ◽  
Vol 818 ◽  
pp. 288-318 ◽  
Author(s):  
Antonio Segalini ◽  
Stephen J. Garrett
Keyword(s):  
Boundary Layer ◽  
Type I ◽  
Type Ii ◽  
Local Surface ◽  
Viscous Effects ◽  
Rotating Sphere ◽  
Local Type ◽  
Instability Modes ◽  
Layer Flow ◽  
Remarkable Agreement

We present a new solution for the steady boundary-layer flow over the rotating sphere that also accounts for the eruption of the boundary layer at the equator and other higher-order viscous effects. Non-parallel corrections to the local type I and type II convective instability modes of this flow are also computed as a function of spin rate. Our instability results are associated with the previously observed spiral vortices and remarkable agreement between our predictions of the number of vortices and experimental observations is found. Vortices travelling at 70 %–80 % of the local surface speed are found to be the most amplified for sufficient spin rates, also consistent with prior experimental observations.

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