scholarly journals Evolution of a vortex in a strongly stratified shear flow. Part 2. Numerical simulations

2020 ◽  
Vol 893 ◽  
Author(s):  
Paul Billant ◽  
Julien Bonnici
Keyword(s):  
Shear Flow ◽  
Numerical Simulations ◽  
Flow Part ◽  
Stratified Shear Flow ◽  
Image Position

scholarly journals Lee waves in a stratified flow Part 3. Semi-elliptical obstacle

1969 ◽  
Vol 35 (3) ◽  
pp. 481-496 ◽  
Author(s):  
Herbert E. Huppert ◽  
John W. Miles
Keyword(s):  
Shear Flow ◽  
Dynamic Pressure ◽  
Wave Functions ◽  
Reduced Frequency ◽  
Lee Waves ◽  
Lee Wave ◽  
Flow Part ◽  
Stratified Shear Flow ◽  
Static Instability ◽  
Stable Flow

The stratified shear flow over a two-dimensional obstacle of semi-elliptical crosssection is considered. The shear flow is assumed to be inviscid with constant upstream values of the density gradient and dynamic pressure (Long's model). Two complete sets of lee-wave functions, each of which satisfies the condition of no upstream reflexion, are determined in elliptic co-ordinates for ε ≤ 1 and ε ≥ 1, where ε is the ratio of height to half-width of the obstacle. These functions are used to determine the lee-wave field produced by, and the consequent drag on, a semi-elliptical obstacle as functions of ε and the reduced frequency (reciprocal Froude number) within the range of stable flow. The reduced frequency at which static instability first occurs is calculated as a function of ε.

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