The stability of steady shear flows of some viscoelastic fluids

We show how DDM measures microscopic dynamics in oscillatory or steady shear flows and use the technique to explore the yielding of a concentrated emulsion.

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Thermodynamically consistent modelling of abrasive granular materials. II. Thermodynamic equilibrium and applications to steady shear flows

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2002.1020 ◽

2002 ◽

Vol 458 (2028) ◽

pp. 3053-3077 ◽

Cited By ~ 18

Author(s):

Nina P. Kirchner ◽

Andreas Teufel

Keyword(s):

Granular Materials ◽

Thermodynamic Equilibrium ◽

Shear Flows ◽

Steady Shear

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Stability of linear shear flows in shallow water

Journal of Fluid Mechanics ◽

10.1017/s002211209500423x ◽

1995 ◽

Vol 303 ◽

pp. 203-214 ◽

Cited By ~ 5

Author(s):

Charles Knessl ◽

Joseph B. Keller

Keyword(s):

Shallow Water ◽

Shear Flows ◽

Special Functions ◽

Rigid Wall ◽

Eigenvalue Equation ◽

Reflection And Transmission ◽

Transmission Coefficients ◽

Linear Shear ◽

The Stability ◽

Rigid Walls

The stability or instability of various linear shear flows in shallow water is considered. The linearized equations for waves on the surface of each flow are solved exactly in terms of known special functions. For unbounded shear flows, the exact reflection and transmission coefficients R and T for waves incident on the flow, are found. They are shown to satisfy the relation |R|2= 1+ |T|2, which proves that over reflection occurs at all wavenumbers. For flow bounded by a rigid wall, R is found. The poles of R yield the eigenvalue equation from which the unstable mides can be found. For flow in a channel, with two rigid walls, the eigenvalue equation for the modes is obtained. The results are compared with previous numerical results.

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Non-normal origin of modal instabilities in rotating plane shear flows

Proceedings of The Royal Society A Mathematical Physical and Engineering Sciences ◽

10.1098/rspa.2019.0550 ◽

2020 ◽

Vol 476 (2233) ◽

pp. 20190550

Author(s):

Sharath Jose ◽

Rama Govindarajan

Keyword(s):

Reynolds Number ◽

Shear Flows ◽

Critical Reynolds Number ◽

Flow System ◽

Neutral Line ◽

Plane Couette Flow ◽

Plane Shear ◽

Perturbation Amplitude ◽

Fundamental Reason ◽

The Stability

Small variations introduced in shear flows are known to affect stability dramatically. Rotation of the flow system is one example, where the critical Reynolds number for exponential instabilities falls steeply with a small increase in rotation rate. We ask whether there is a fundamental reason for this sensitivity to rotation. We answer in the affirmative, showing that it is the non-normality of the stability operator in the absence of rotation which triggers this sensitivity. We treat the flow in the presence of rotation as a perturbation on the non-rotating case, and show that the rotating case is a special element of the pseudospectrum of the non-rotating case. Thus, while the non-rotating flow is always modally stable to streamwise-independent perturbations, rotating flows with the smallest rotation are unstable at zero streamwise wavenumber, with the spanwise wavenumbers close to that of disturbances with the highest transient growth in the non-rotating case. The instability critical rotation number scales inversely as the square of the Reynolds number, which we demonstrate is the same as the scaling obeyed by the minimum perturbation amplitude in non-rotating shear flow needed for the pseudospectrum to cross the neutral line. Plane Poiseuille flow and plane Couette flow are shown to behave similarly in this context.

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