Three-dimensional instability of viscoelastic elliptic vortices

1997 ◽  
Vol 353 ◽  
pp. 357-381 ◽  
Author(s):  
H. HAJ-HARIRI ◽  
G. M. HOMSY
Keyword(s):  
Plane Waves ◽  
Three Dimensional ◽  
Deborah Number ◽  
Base Flow ◽  
Necessary Condition ◽  
Inertial Instability ◽  
Viscoelastic Instability ◽  
Dimensional Instability ◽  
Model Oscillator ◽  
Vortex Axis

An analysis of the three-dimensional instability of two-dimensional viscoelastic elliptical flows is presented, extending the inviscid analysis of Bayly (1986) to include both viscous and elastic effects. The problem is governed by three parameters: E, a geometric parameter related to the ellipticity; Re, a wavenumber-based Reynolds number; and De, the Deborah number based on the period of the base flow. New modes and mechanisms of instability are discovered. The flow is generally susceptible to instabilities in the form of propagating plane waves with a rotating wavevector, the tip of which traces an ellipse of the same eccentricity as the flow, but with the major and minor axes interchanged. Whereas a necessary condition for purely inertial instability is that the wavevector has a non-vanishing component along the vortex axis, the viscoelastic modes of instability are most prominent when their wavevectors do vanish along this axis. Our analytical and numerical results delineate the region of parameter space of (E, ReDe) for which the new instability exists. A simple model oscillator equation of the Mathieu type is developed and shown to embody the essential qualitative and quantitative features of the secular viscoelastic instability. The cause of the instability is a buckling of the ‘compressed’ polymers as they are perturbed transversely during a particular phase of the passage of the rotating plane wave.

scholarly journals Latitudinal libration driven flows in triaxial ellipsoids

2015 ◽  
Vol 771 ◽  
pp. 193-228 ◽  
Author(s):  
S. Vantieghem ◽  
D. Cébron ◽  
J. Noir
Keyword(s):  
Numerical Simulations ◽  
Equations Of Motion ◽  
Liquid Core ◽  
Three Dimensional ◽  
Base Flow ◽  
Upper And Lower Bounds ◽  
Earth Planet ◽  
Ekman Layers ◽  
Core Dynamics ◽  
Inertial Instability

Motivated by understanding the liquid core dynamics of tidally deformed planets and moons, we present a study of incompressible flow driven by latitudinal libration within rigid triaxial ellipsoids. We first derive a laminar solution for the inviscid equations of motion under the assumption of uniform vorticity flow. This solution exhibits a resonance if the libration frequency matches the frequency of the spin-over inertial mode. Furthermore, we extend our model by introducing a reduced model of the effect of viscous Ekman layers in the limit of low Ekman number (Noir & Cébron, J. Fluid Mech., vol. 737, 2013, pp. 412–439). This theoretical approach is consistent with the results of Chan et al. (Phys. Earth Planet. Inter., vol. 187, 2011, pp. 404–415) and Zhang et al. (J. Fluid Mech., vol. 692, 2012, pp. 420–445) for spheroidal geometries. Our results are validated against systematic three-dimensional numerical simulations. In the second part of the paper, we present the first linear stability analysis of this uniform vorticity flow. To this end, we adopt different methods (Lifschitz & Hameiri, Phys. Fluids A, vol. 3, 1991, p. 2644; Gledzer & Ponomarev, Acad. Sci., USSR, Izv., Atmos. Ocean. Phys., vol. 13, 1977, pp. 565–569) that allow us to deduce upper and lower bounds for the growth rate of an instability. Our analysis shows that the uniform vorticity base flow is prone to inertial instabilities caused by a parametric resonance mechanism. This is confirmed by a set of direct numerical simulations. Applying our results to planetary settings, we find that neither a spin-over resonance nor an inertial instability can exist within the liquid core of the Moon, Io and Mercury.

Enhancement of three-dimensional instability of free shear layers

1999 ◽  
Vol 379 ◽  
pp. 23-38 ◽  
Author(s):  
VIVEK SAXENA ◽  
SIDNEY LEIBOVICH ◽  
GAL BERKOOZ
Keyword(s):  
Growth Rate ◽  
Growth Rates ◽  
Mixing Layer ◽  
Three Dimensional ◽  
Maximum Growth ◽  
Shear Layers ◽  
Base Flow ◽  
Two Dimensional ◽  
Free Shear Layers ◽  
Dimensional Instability

Enhancement of the temporal growth rate of inviscid three-dimensional instability waves in free shear layers by deformation of the basic flow is studied. The deformation of a two-dimensional mixing layer is assumed to yield a base flow that remains unidirectional, but has a steady spanwise speed variation in addition to the two- dimensional shear. The computed growth rates for hyperbolic tangent base flow, perturbed this way, show enhanced instability in the sense that the neutral waves of the unperturbed flow exhibit positive growth rates. For each imposed spanwise periodicity, an oblique mode is selected that shows maximum growth rate. The results are consistent with related theoretical studies and with qualitative observations in experiments.

Propagation and Reflection of Plane Waves in a Rotating Magneto-Elastic Fibre-Reinforced Semi Space with Surface Stress

2020 ◽  
Vol 22 (4) ◽  
pp. 939-958
Author(s):  
Indrajit Roy ◽  
D. P. Acharya ◽  
Sourav Acharya
Keyword(s):  
Surface Stress ◽  
Incident Angle ◽  
Plane Waves ◽  
Three Dimensional ◽  
Elastic Fibre ◽  
Amplitude Ratios ◽  
Governing Equations ◽  
Rotation Surface ◽  
Wave Velocities ◽  
Magnetic Field Rotation

AbstractThe present paper investigates the propagation of quasi longitudinal (qLD) and quasi transverse (qTD) waves in a magneto elastic fibre-reinforced rotating semi-infinite medium. Reflections of waves from the flat boundary with surface stress have been studied in details. The governing equations have been used to obtain the polynomial characteristic equation from which qLD and qTD wave velocities are found. It is observed that both the wave velocities depend upon the incident angle. After imposing the appropriate boundary conditions including surface stress the resultant amplitude ratios for the total displacements have been obtained. Numerically simulated results have been depicted graphically by displaying two and three dimensional graphs to highlight the influence of magnetic field, rotation, surface stress and fibre-reinforcing nature of the material medium on the propagation and reflection of plane waves.

Aspects of Shear Layer Unsteadiness in a Three-Dimensional Supersonic Wake

2005 ◽  
Vol 127 (6) ◽  
pp. 1085-1094 ◽  
Author(s):  
Alan L. Kastengren ◽  
J. Craig Dutton
Keyword(s):  
Shear Layer ◽  
Stream Flow ◽  
Free Stream ◽  
Angle Of Attack ◽  
Three Dimensional ◽  
Base Flow ◽  
Recirculation Region ◽  
Side View ◽  
Near Wake ◽  
Supersonic Wake

The near wake of a blunt-base cylinder at 10° angle-of-attack to a Mach 2.46 free-stream flow is visualized at several locations to study unsteady aspects of its structure. In both side-view and end-view images, the shear layer flapping grows monotonically as the shear layer develops, similar to the trends seen in a corresponding axisymmetric supersonic base flow. The interface convolution, a measure of the tortuousness of the shear layer, peaks for side-view and end-view images during recompression. The high convolution for a septum of fluid seen in the middle of the wake indicates that the septum actively entrains fluid from the recirculation region, which helps to explain the low base pressure for this wake compared to that for a corresponding axisymmetric wake.

Three-dimensional instability of an elliptic Kirchhoff vortex

1988 ◽  
Vol 23 (3) ◽  
pp. 356-360 ◽  
Author(s):  
V. A. Vladimirov ◽  
K. I. Il'in
Keyword(s):  
Three Dimensional ◽  
Dimensional Instability

scholarly journals Trapping of waves by a submerged elliptical torus

2002 ◽  
Vol 456 ◽  
pp. 277-293 ◽  
Author(s):  
M. McIVER ◽  
R. PORTER
Keyword(s):  
Fluid Velocity ◽  
Three Dimensional ◽  
Mode Frequency ◽  
The Body ◽  
Necessary Condition ◽  
Numerical Evidence ◽  
Side Condition ◽  
Trapped Mode ◽  
Specific Geometry ◽  
The Time Domain

An investigation is made into the trapping of surface gravity waves by totally submerged three-dimensional obstacles and strong numerical evidence of the existence of trapped modes is presented. The specific geometry considered is a submerged elliptical torus. The depth of submergence of the torus and the aspect ratio of its cross-section are held fixed and a search for a trapped mode is made in the parameter space formed by varying the radius of the torus and the frequency. A plane wave approximation to the location of the mode in this space is derived and an integral equation and a side condition for the exact trapped mode are obtained. Each of these conditions is satisfied on a different line in the plane and the point at which the lines cross corresponds to a trapped mode. Although it is not possible to locate this point exactly, because of numerical error, existence of the mode may be inferred with confidence as small changes in the numerical results do not alter the fact that the lines cross.If the torus makes small vertical oscillations, it is customary to try to express the fluid velocity as the gradient of the so-called heave potential, which is assumed to have the same time dependence as the body oscillations. A necessary condition for the existence of this potential at the trapped mode frequency is derived and numerical evidence is cited which shows that this condition is not satisfied for an elliptical torus. Calculations of the heave potential for such a torus are made over a range of frequencies, and it is shown that the force coefficients behave in a singular fashion in the vicinity of the trapped mode frequency. An analysis of the time domain problem for a torus which is forced to make small vertical oscillations at the trapped mode frequency shows that the potential contains a term which represents a growing oscillation.

Three-Dimensional Instability of Opposite Polarity Nonthermal Dusty Plasma

2019 ◽  
Vol 74 (2) ◽  
pp. 131-138
Author(s):  
E.K. El-Shewy ◽  
S.K. Zaghbeer ◽  
A.A. El-Rahman
Keyword(s):  
Growth Rate ◽  
Cyclotron Frequency ◽  
Three Dimensional ◽  
Dusty Plasmas ◽  
Opposite Polarity ◽  
Charge Ratio ◽  
Nonlinear Phenomena ◽  
Wave Instability ◽  
Direction Cosines ◽  
Dimensional Instability

AbstractNonlinearity properties of obliquely wave propagation and instability in collisionless magnetized nonthermal dusty plasmas containing fluid of negative-positive grains are investigated. Zakharov-Kuznetsov equation is obtained and the three-dimensional wave instability is studied. The parameters such as polarity charge ratio, cyclotron frequency and fast nonthermal effectiveness of the instability properties and growth rate are theoretically studied. It is found that both positive and negative soliton profiles are formed depending on the fraction ratio of electron-ion nonthermality. Also, the growth rate was dependent nonlinearly on the direction cosines, the cyclotron frequency and the positive (negative) grain charge ratio, but independent of the fractional ratio of electron-ion nonthermality. Present discussion may be very significant regarding the observations of nonlinear phenomena in space.

Sign in / Sign up

Export Citation Format

Share Document