Short wave instability of core‐annular flow

1992 ◽  
Vol 4 (1) ◽  
pp. 186-188 ◽  
Author(s):  
Kang Ping Chen
Keyword(s):  
Annular Flow ◽  
Short Wave ◽  
Wave Instability

Side wall effects on the instability of thin gravity-driven films—From long-wave to short-wave instability

2011 ◽  
Vol 23 (9) ◽  
pp. 094110 ◽  
Author(s):  
Thilo Pollak ◽  
André Haas ◽  
Nuri Aksel
Keyword(s):  
Side Wall ◽  
Short Wave ◽  
Wall Effects ◽  
Wave Instability ◽  
Long Wave ◽  
Gravity Driven

Short Wave Instability on Vortex Filaments

1998 ◽  
Vol 80 (21) ◽  
pp. 4665-4668 ◽  
Author(s):  
Hongyun Wang
Keyword(s):  
Short Wave ◽  
Wave Instability ◽  
Vortex Filaments

Elastic short wave instability in extrusion flows of viscoelastic liquids

1992 ◽  
Vol 42 (1-2) ◽  
pp. 189-211 ◽  
Author(s):  
KangPing Chen ◽  
Daniel D. Joseph
Keyword(s):  
Short Wave ◽  
Wave Instability ◽  
Viscoelastic Liquids

scholarly journals On the porosity influence on stability of flow over porous medium

2020 ◽  
Vol 30 (1) ◽  
pp. 134-144
Author(s):  
K.B. Tsiberkin
Keyword(s):  
Porous Medium ◽  
Stability Analysis ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Short Wave ◽  
Wave Instability ◽  
Plane Parallel ◽  
Long Wave ◽  
The Stability ◽  
Critical Wavenumber

The stability of incompressible fluid plane-parallel flow over a layer of a saturated porous medium is studied. The results of a linear stability analysis are described at different porosity values. The considered system is bounded by solid wall from the porous layer bottom. Top fluid surface is free and rigid. A linear stability analysis of plane-parallel stationary flow is presented. It is realized for parameter area where the neutral stability curves are bimodal. The porosity variation effect on flow stability is considered. It is shown that there is a transition between two main instability modes: long-wave and short-wave. The long-wave instability mechanism is determined by inflection points within the velocity profile. The short-wave instability is due to the large transverse gradient of flow velocity near the interface between liquid and porous medium. Porosity decrease stabilizes the long wave perturbations without significant shift of the critical wavenumber. Simultaneously, the short-wave perturbations destabilize, and their critical wavenumber changes in wide range. When the porosity is less than 0.7, the inertial terms in filtration equation and magnitude of the viscous stress near the interface increase to such an extent that the Kelvin-Helmholtz analogue of instability becomes the dominant mechanism for instability development. The stability band realizes in narrow porosity area. It separates the two branches of the neutral curve.

scholarly journals Short wave instability of co-extruded elastic liquids with matched viscosities

1997 ◽  
Vol 72 (2-3) ◽  
pp. 237-251 ◽  
Author(s):  
H.J Wilson ◽  
J.M Rallison
Keyword(s):  
Short Wave ◽  
Wave Instability

Patterns produced by a short-wave instability in the presence of a zero mode

1992 ◽  
Vol 45 (2) ◽  
pp. 1009-1017 ◽  
Author(s):  
Boris A. Malomed
Keyword(s):  
Zero Mode ◽  
Short Wave ◽  
Wave Instability

Shear-flow instability due to a wall and a viscosity discontinuity at the interface

1987 ◽  
Vol 179 ◽  
pp. 201-225 ◽  
Author(s):  
A. P. Hooper ◽  
W. G. C. Boyd
Keyword(s):  
Reynolds Number ◽  
Kinematic Viscosity ◽  
Flow Instability ◽  
Short Wave ◽  
Linear Instability ◽  
Wave Instability ◽  
New Type ◽  
Lower Fluid ◽  
Superposed Fluids ◽  
Shear Flow Instability

Consider the Couette flow of two superposed fluids of different viscosity with the depth of the lower fluid bounded by a wall and the interface while the depth of the upper fluid is unbounded. The linear instability of this flow configuration is studied at all values of flow Reynolds number and disturbance wavelength using both asymptotic and numerical methods. Three distinct forms of instability are found which are dependent on the magnitude of two dimensionless parameters β and (α R)1/3, where β is a dimensionless wavenumber measured on a viscous lengthscale, α is a dimensionless wavenumber measured on the scale of the depth of the lower fluid and R is the Reynolds number of the lower fluid. At large β there is the short-wave instability found previously by Hooper & Boyd (1983). At small β and small (αR)1/3 there is the long-wave instability first discovered by Yih. At small β and large (αR)1/3 there is a new type of instability which arises only if the kinematic viscosity of the lower bounded fluid is less than the kinematic viscosity of the upper fluid.

The stability of a helical vortex filament

1972 ◽  
Vol 54 (4) ◽  
pp. 641-663 ◽  
Author(s):  
Sheila E. Widnall
Keyword(s):  
Short Wave ◽  
Mutual Inductance ◽  
The Self ◽  
Vortex Filament ◽  
Wave Instability ◽  
Long Wave ◽  
Amplification Rate ◽  
Helical Vortex ◽  
Induced Motion ◽  
The Stability

The stability of a helical vortex filament of finite core and infinite extent to small sinusoidal displacements of its centre-line is considered. The influence of the entire perturbed filament on the self-induced motion of each element is taken into account. The effect of the details of the vorticity distribution within the finite vortex core on the self-induced motion due to the bending of its axis is calculated using the results obtained previously by Widnall, Bliss & Zalay (1970). In this previous work, an application of the method of matched asymptotic expansions resulted in a general solution for the self-induced motion resulting from the bending of a slender vortex filament with an arbitrary distribution of vorticity and axial velocity within the core.The results of the stability calculations presented in this paper show that the helical vortex filament has three modes of instability: a very short-wave instability which probably exists on all curved filaments, a long-wave mode which is also found to be unstable by the local-induction model and a mutual-inductance mode which appears as the pitch of the helix decreases and the neighbouring turns of the filament begin to interact strongly. Increasing the vortex core size is found to reduce the amplification rate of the long-wave instability, to increase the amplification rate of the mutual-inductance instability and to decrease the wavenumber of the short-wave instability.

Short-Wave Instability in Extended Systems with Additional Symmetry

1997 ◽  
Vol 07 (05) ◽  
pp. 997-1006 ◽  
Author(s):  
Michael I. Tribelsky
Keyword(s):  
Seismic Waves ◽  
Short Wave ◽  
Continuous Group ◽  
Periodic Patterns ◽  
Wave Instability ◽  
Coupled Modes ◽  
Additional Symmetry ◽  
Pattern Stability ◽  
Spatially Periodic ◽  
The Stability

Stability of steady spatially periodic patterns in systems with an additional continuous group of symmetry is discussed. It is shown that different systems with the same dimensionality of the continuous group of symmetry display remarkable similarity in all qualitative features of the pattern stability problem. Attention is called to the fact that, beside an extra band of slowly varying modes, the additional symmetry may yield a mixture of different scales in the final dispersion equation for pattern's perturbations, so that the stability conditions become unusually sensitive to very fine details of the problem. A one-dimensional partial differential equation governing seismic waves in viscoelastic media is considered as a particular example. The equation exhibits short-wave instability and additional invariance under the transformation u → u + const. , where the order parameter u(x, t) is associated with the displacement velocity. The analytical study of the equation is supplemented by computer simulations. The simulations show that the system undergoes a bifurcation from the trivial state with u ≡ 0 to well-developed chaos directly and the transition to the chaos is smooth, without any discontinuity. The chaos is characterized by excitation of a big number (in a boundless system — continuum) of coupled modes localized generally in two narrow subbands, centered around the critical wavenumber for the short-wave instability and the wavenumber equals zero, respectively.

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