scholarly journals Nonlinear evolution of three-dimensional unstable disturbances in a sharply stratified shear flow with an inflection-free velocity profile

2009 ◽  
pp. 159-182
Author(s):  
S. M. Churilov ◽  
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Nonlinear Evolution ◽  
Three Dimensional ◽  
Stratified Shear Flow

The Effect of Boundaries on the Stability of Inviscid Stratified Shear Flows

1976 ◽  
Vol 43 (2) ◽  
pp. 243-248 ◽  
Author(s):  
F. Einaudi ◽  
D. P. Lalas
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Shear Flows ◽  
Infinite Domain ◽  
Hyperbolic Tangent ◽  
Stratified Shear Flow ◽  
The Stability ◽  
Exchange Of Stability

The influence of the presence and position of solid boundaries on the stability of an inviscid, stratified shear flow, is examined numerically for the case of a hyperbolic tangent velocity profile and an exponentially decreasing density. The presence of solid boundaries is shown to stabilize short wavelengths and destabilize large wavelengths. Furthermore, extra unstable modes, not present in an infinite domain, are found for large wavelengths, both for symmetric and asymmetric boundaries. Finally, the validity of the principle of exchange of stability is examined, and it is shown to be unreliable even for the case of symmetric boundaries.

scholarly journals The structure and origin of confined Holmboe waves

2018 ◽  
Vol 848 ◽  
pp. 508-544 ◽  
Author(s):  
Adrien Lefauve ◽  
J. L. Partridge ◽  
Qi Zhou ◽  
S. B. Dalziel ◽  
C. P. Caulfield ◽  
...  
Keyword(s):  
Shear Flow ◽  
Coherent Structure ◽  
Shear Flows ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Geophysical Flows ◽  
Two Dimensional ◽  
Lateral Confinement ◽  
Stratified Shear Flow ◽  
Spatio Temporal

Finite-amplitude manifestations of stratified shear flow instabilities and their spatio-temporal coherent structures are believed to play an important role in turbulent geophysical flows. Such shear flows commonly have layers separated by sharp density interfaces, and are therefore susceptible to the so-called Holmboe instability, and its finite-amplitude manifestation, the Holmboe wave. In this paper, we describe and elucidate the origin of an apparently previously unreported long-lived coherent structure in a sustained stratified shear flow generated in the laboratory by exchange flow through an inclined square duct connecting two reservoirs filled with fluids of different densities. Using a novel measurement technique allowing for time-resolved, near-instantaneous measurements of the three-component velocity and density fields simultaneously over a three-dimensional volume, we describe the three-dimensional geometry and spatio-temporal dynamics of this structure. We identify it as a finite-amplitude, nonlinear, asymmetric confined Holmboe wave (CHW), and highlight the importance of its spanwise (lateral) confinement by the duct boundaries. We pay particular attention to the spanwise vorticity, which exhibits a travelling, near-periodic structure of sheared, distorted, prolate spheroids with a wide ‘body’ and a narrower ‘head’. Using temporal linear stability analysis on the two-dimensional streamwise-averaged experimental flow, we solve for three-dimensional perturbations having two-dimensional, cross-sectionally confined eigenfunctions and a streamwise normal mode. We show that the dispersion relation and the three-dimensional spatial structure of the fastest-growing confined Holmboe instability are in good agreement with those of the observed confined Holmboe wave. We also compare those results with a classical linear analysis of two-dimensional perturbations (i.e. with no spanwise dependence) on a one-dimensional base flow. We conclude that the lateral confinement is an important ingredient of the confined Holmboe instability, which gives rise to the CHW, with implications for many inherently confined geophysical flows such as in valleys, estuaries, straits or deep ocean trenches. Our results suggest that the CHW is an example of an experimentally observed, inherently nonlinear, robust, long-lived coherent structure which has developed from a linear instability. We conjecture that the CHW is a promising candidate for a class of exact coherent states underpinning the dynamics of more disordered, yet continually forced stratified shear flows.

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