Modified Tietjens Function for Asymptotic Analysis of Shear Flow Stability

1977 ◽  
Vol 99 (1) ◽  
pp. 256-258
Author(s):  
A. K. M. F. Hussain ◽  
W. C. Reynolds
Keyword(s):  
Shear Flow ◽  
Velocity Profile ◽  
Asymptotic Analysis ◽  
Shear Flows ◽  
Present Note ◽  
Normal Modes ◽  
Viscous Effects ◽  
Stability Of Shear Flows ◽  
Arbitrary Velocity

In asymptotic analysis of the hydrodynamic stability of shear flows, the viscous effects enter through the modified Tietjens Function, which is used in the graphical determination of the eigenvalues. For neutral normal modes the argument of this function is real, and values of the function have been calculated previously. For non-neutral normal modes the argument is complex; the present note gives the modified Tietjens Function for complex arguments. This function is particularly useful in investigating the behavior of lightly damped eigenmodes for shear flows of arbitrary velocity profile.

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.

Some mathematical problems in the theory of the stability of parallel flows

1961 ◽  
Vol 10 (3) ◽  
pp. 430-438 ◽  
Author(s):  
C. C. Lin
Keyword(s):  
Shear Flows ◽  
Normal Modes ◽  
Initial Values ◽  
Parallel Flows ◽  
Mathematical Problems ◽  
Stability Of Shear Flows ◽  
The Stability ◽  
Apparent Conflict

By applying the method of initial values to the theory of stability of shear flows, Case has recently found certain results which are in apparent conflict with those obtained by the theory of normal modes. It is shown how these differences may be reconciled. Some new features in the theory of normal modes are also brought out. The relative merits of the two theories are compared.

scholarly journals Combined electrokinetic and shear flows control colloidal particle distribution across microchannel cross-sections

Soft Matter ◽  
2021 ◽  
Author(s):  
Varun Lochab ◽  
Shaurya Prakash
Keyword(s):  
Shear Flow ◽  
Cross Sections ◽  
Lift Force ◽  
Shear Flows ◽  
Colloidal Particle ◽  
Particle Distribution ◽  
Particle Migration ◽  
Flow Parameters

We quantify and investigate the effects of flow parameters on the extent of colloidal particle migration and the corresponding electrophoresis-induced lift force under combined electrokinetic and shear flow.

A note on the instabilities of a horizontal shear flow with a free surface

2000 ◽  
Vol 406 ◽  
pp. 337-346 ◽  
Author(s):  
L. ENGEVIK
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Shear Flow ◽  
Velocity Profile ◽  
Froude Number ◽  
The Other ◽  
Algebraic Equations ◽  
Horizontal Shear ◽  
Analytical Treatment ◽  
Unstable Region

The instabilities of a free surface shear flow are considered, with special emphasis on the shear flow with the velocity profile U* = U*0sech2 (by*). This velocity profile, which is found to model very well the shear flow in the wake of a hydrofoil, has been focused on in previous studies, for instance by Dimas & Triantyfallou who made a purely numerical investigation of this problem, and by Longuet-Higgins who simplified the problem by approximating the velocity profile with a piecewise-linear profile to make it amenable to an analytical treatment. However, none has so far recognized that this problem in fact has a very simple solution which can be found analytically; that is, the stability boundaries, i.e. the boundaries between the stable and the unstable regions in the wavenumber (k)–Froude number (F)-plane, are given by simple algebraic equations in k and F. This applies also when surface tension is included. With no surface tension present there exist two distinct regimes of unstable waves for all values of the Froude number F > 0. If 0 < F [Lt ] 1, then one of the regimes is given by 0 < k < (1 − F2/6), the other by F−2 < k < 9F−2, which is a very extended region on the k-axis. When F [Gt ] 1 there is one small unstable region close to k = 0, i.e. 0 < k < 9/(4F2), the other unstable region being (3/2)1/2F−1 < k < 2 + 27/(8F2). When surface tension is included there may be one, two or even three distinct regimes of unstable modes depending on the value of the Froude number. For small F there is only one instability region, for intermediate values of F there are two regimes of unstable modes, and when F is large enough there are three distinct instability regions.

Statistical determination of normal modes

1987 ◽  
Vol 64 (5) ◽  
pp. 425 ◽  
Author(s):  
John F. Geldard ◽  
Lawrence R. Pratt
Keyword(s):  
Normal Modes ◽  
Statistical Determination

Determination of the elastic component for polymeric melt under steady shear flow

1993 ◽  
Vol 48 (8) ◽  
pp. 1425-1432 ◽  
Author(s):  
H. T. Pham ◽  
C. P. Bosnyak ◽  
J. W. Wilchester ◽  
C. P. Christenson
Keyword(s):  
Shear Flow ◽  
Steady Shear ◽  
Elastic Component ◽  
Steady Shear Flow

Propagation of internal gravity waves in fluids with shear flow and rotation

1967 ◽  
Vol 30 (3) ◽  
pp. 439-448 ◽  
Author(s):  
Walter L. Jones
Keyword(s):  
Angular Momentum ◽  
Shear Flow ◽  
Gravity Waves ◽  
Shear Flows ◽  
Internal Gravity Waves ◽  
Vertical Transport ◽  
Wave Frequency ◽  
Slow Rotation ◽  
Critical Levels ◽  
Rotating System

In a rotating system, the vertical transport of angular momentum by internal gravity waves is independent of height, except at critical levels where the Doppler-shifted wave frequency is equal to plus or minus the Coriolis frequency. If slow rotation is ignored in studying the propagation of internal gravity waves through shear flows, the resulting solutions are in error only at levels where the Doppler-shifted and Coriolis frequencies are comparable.

Erratum: Plasma‐Filled Waveguide with Axial Magnetization. I. Variational Determination of Normal Modes

1969 ◽  
Vol 40 (12) ◽  
pp. 4999-4999
Author(s):  
K. S. Champlin ◽  
G. H. Glover ◽  
D. E. O'Connor
Keyword(s):  
Normal Modes
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