scholarly journals Understanding the destabilizing role for surface tension in planar shear flows in terms of wave interaction

2017 ◽  
Vol 2 (10) ◽  
Author(s):  
L. Biancofiore ◽  
E. Heifetz ◽  
J. Hoepffner ◽  
F. Gallaire
Keyword(s):  
Surface Tension ◽  
Shear Flows ◽  
Wave Interaction ◽  
Planar Shear

Instability in Stratified Shear Flow: Review of a Physical Interpretation Based on Interacting Waves

2011 ◽  
Vol 64 (6) ◽  
Author(s):  
Jeffrey R. Carpenter ◽  
Edmund W. Tedford ◽  
Eyal Heifetz ◽  
Gregory A. Lawrence
Keyword(s):  
Shear Flow ◽  
Physical Interpretation ◽  
Shear Flows ◽  
Flow Instability ◽  
Phase Locking ◽  
River Estuary ◽  
Wave Interaction ◽  
The Stability ◽  
Interaction Approach ◽  
The Waves

Instability in homogeneous and density stratified shear flows may be interpreted in terms of the interaction of two (or more) otherwise free waves in the velocity and density profiles. These waves exist on gradients of vorticity and density, and instability results when two fundamental conditions are satisfied: (I) the phase speeds of the waves are stationary with respect to each other (“phase-locking“), and (II) the relative phase of the waves is such that a mutual growth occurs. The advantage of the wave interaction approach is that it provides a physical interpretation to shear flow instability. This paper is largely intended to purvey the basics of this physical interpretation to the reader, while both reviewing and consolidating previous work on the topic. The interpretation is shown to provide a framework for understanding many classical and nonintuitive results from the stability of stratified shear flows, such as the Rayleigh and Fjørtoft theorems, and the destabilizing effect of an otherwise stable density stratification. Finally, we describe an application of the theory to a geophysical-scale flow in the Fraser River estuary.

An Experimental Study of a Free-Surface Shear Layer With and Without the Presence of Surfactants

2002 ◽  
Author(s):  
Amy Wamcke Lang ◽  
Carlos E. Manglano
Keyword(s):  
Experimental Study ◽  
Surface Tension ◽  
Free Surface ◽  
Shear Layer ◽  
Turbulence Intensity ◽  
Shear Flows ◽  
Surface Shear ◽  
Surface Deformations

A free-surface shear layer was studied to ascertain the effects due to the presence of surface tension gradients on the directional shift of the shear layer and turbulence intensities in the vicinity of the water free-surface. It was found that the presence of surfactants altered the direction of the shear layer in the vicinity of the free surface, with the shear layer being pulled to the higher surface tension side. In addition, the turbulence intensity in the plane of the free surface was dramatically reduced, also leading to damped surface deformations. These results show conclusively that the role surfactants play in turbulent free-surface shear flows needs to be considered.

scholarly journals A generalized action-angle representation of wave interaction in stratified shear flows

2017 ◽  
Vol 834 ◽  
pp. 220-236 ◽  
Author(s):  
Eyal Heifetz ◽  
Anirban Guha
Keyword(s):  
Shear Flows ◽  
Wave Interaction ◽  
Wave Action ◽  
Time Dependent ◽  
Compact Form ◽  
Instability Mechanism ◽  
Interfacial Waves ◽  
Action At A Distance ◽  
Hamilton's Equations ◽  
Hamilton’S Equations

In this paper we express the linearized dynamics of interacting interfacial waves in stratified shear flows in the compact form of action-angle Hamilton’s equations. The pseudo-energy serves as the Hamiltonian of the system, the action coordinates are the contribution of the interfacial waves to the wave action and the angles are the phases of the interfacial waves. The term ‘generalized action angle’ aims to emphasize that the action of each wave is generally time dependent and this allows for instability. An attempt is made to relate this formalism to the action at a distance resonance instability mechanism between counter-propagating vorticity waves via the global conservations of pseudo-energy and pseudo-momentum.

A vortex–wave interaction theory describing the effect of boundary forcing on shear flows

2021 ◽  
Vol 932 ◽  
Author(s):  
Philip Hall
Keyword(s):  
Reynolds Number ◽  
Shear Flows ◽  
Flow Direction ◽  
Wave Interaction ◽  
Propagation Speed ◽  
Instability Criterion ◽  
Stationary Waves ◽  
Critical Wavelength ◽  
High Reynolds ◽  
Forcing Mechanisms

A strongly nonlinear theory describing the effect of small amplitude boundary forcing in the form of waves on high Reynolds number shear flows is given. The interaction leads to an $O(1)$ change in the unperturbed flow and is relevant to a number of forcing mechanisms. The cases of the shear flow being bounded or unbounded are both considered and the results for the unbounded case apply to quite arbitrary flows. The instability criterion for unbounded flows is expressed in terms of the wall forcing and the friction Reynolds number. As particular examples we investigate wall transpiration or surface undulations as sources of the forcing and both propagating and stationary waves are considered. Results are given for propagating waves with crests perpendicular to the flow direction and for stationary waves with crests no longer perpendicular to the flow direction. In the first of those situations we find the instability induced by transpiration waves is independent of the propagation speed. For wavy walls downstream propagation completely stabilises the flow at a critical speed whereas upstream propagation greatly destabilises the flow. For stationary oblique waves we find that the instability is enhanced and a much wider range of unstable wavenumbers exists. For the bounded case with a wall of fixed wavelength we identify a critical wavelength where the most dangerous mode switches from the aligned to the oblique configuration. For the transpiration problem in the oblique configuration a strong resonance occurs when the vortex wavelength coincides with the spanwise wavelength of the forcing.

Streamwise vortices in shear flows: harbingers of transition and the skeleton of coherent structures

2010 ◽  
Vol 661 ◽  
pp. 178-205 ◽  
Author(s):  
PHILIP HALL ◽  
SPENCER SHERWIN
Keyword(s):  
Coherent Structures ◽  
Shear Flows ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Wave Interaction ◽  
Streamwise Vortex ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flows ◽  
External Flows

The relationship between asymptotic descriptions of vortex–wave interactions and more recent work on ‘exact coherent structures’ is investigated. In recent years immense interest has been focused on so-called self-sustained processes in turbulent shear flows where the importance of waves interacting with streamwise vortex flows has been elucidated in a number of papers. In this paper, it is shown that the so-called ‘lower branch’ state which has been shown to play a crucial role in these self-sustained processes is a finite Reynolds number analogue of a Rayleigh vortex–wave interaction with scales appropriately modified from those for external flows to Couette flow, the flow of interest here. Remarkable agreement between the asymptotic theory and numerical solutions of the Navier–Stokes equations is found even down to relatively small Reynolds numbers, thereby suggesting the possible importance of vortex–wave interaction theory in turbulent shear flows. The relevance of the work to more general shear flows is also discussed.

scholarly journals Spanwise-localized solutions of planar shear flows

2014 ◽  
Vol 745 ◽  
pp. 25-61 ◽  
Author(s):  
J. F. Gibson ◽  
E. Brand
Keyword(s):  
Channel Flow ◽  
Shear Flows ◽  
Travelling Wave ◽  
Wall Region ◽  
Travelling Wave Solutions ◽  
Simulation Data ◽  
Localized Solutions ◽  
Wave Solutions ◽  
Planar Shear ◽  
Near Wall

AbstractWe present several new spanwise-localized equilibrium and travelling-wave solutions of plane Couette and channel flows. The solutions exhibit concentrated regions of vorticity that are centred over low-speed streaks and flanked on either side by high-speed streaks. For several travelling-wave solutions of channel flow, the vortex structures are concentrated near the walls and form particularly isolated and elemental versions of coherent structures in the near-wall region of shear flows. One travelling wave appears to be the invariant solution corresponding to a near-wall coherent structure educed from simulation data by Jeong et al. (J. Fluid Mech., vol. 332, 1997, pp. 185–214) and analysed in terms of transient growth modes of streaky flow by Schoppa & Hussain (J. Fluid Mech., vol. 453, 2002, pp. 57–108). The solutions are constructed by a variety of methods: application of windowing functions to previously known spatially periodic solutions, continuation from plane Couette to channel flow conditions, and from initial guesses obtained from turbulent simulation data. We show how the symmetries of localized solutions derive from the symmetries of their periodic counterparts, analyse the exponential decay of their tails, examine the scale separation and scaling of their streamwise Fourier modes, and show that they develop critical layers for large Reynolds numbers.

Numerical simulations of asymmetric mixing in planar shear flows

1986 ◽  
Vol 165 (-1) ◽  
pp. 201 ◽  
Author(s):  
F. F. Grinstein ◽  
E. S. Oran ◽  
J. P. Boris
Keyword(s):  
Numerical Simulations ◽  
Shear Flows ◽  
Planar Shear
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