scholarly journals Time-periodic boundary layer solutions to singularly perturbed parabolic problems

2017 ◽  
Vol 262 (9) ◽  
pp. 4823-4862 ◽  
Author(s):  
O.E. Omel'chenko ◽  
L. Recke ◽  
V.F. Butuzov ◽  
N.N. Nefedov
Keyword(s):  
Boundary Layer ◽  
Periodic Boundary ◽  
Singularly Perturbed ◽  
Parabolic Problems ◽  
Periodic Boundary Layer ◽  
Time Periodic ◽  
Singularly Perturbed Parabolic Problems

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.

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