Modeling collision of 3D moderately long disturbances of small but finite amplitude in viscous fluid layer

2019 ◽  
Author(s):  
Georgy A. Khabakhpashev ◽  
Dmitry G. Arkhipov
Keyword(s):  
Viscous Fluid ◽  
Fluid Layer ◽  
Finite Amplitude

On the Vibration Damping of a Plate by Means of a Viscous Fluid Layer

1987 ◽  
Vol 109 (2) ◽  
pp. 178-184 ◽  
Author(s):  
K. Uno Ingard ◽  
Adnan Akay
Keyword(s):  
Viscous Fluid ◽  
Frequency Response ◽  
Flow Resistance ◽  
Acoustic Radiation ◽  
Fluid Layer ◽  
Vibration Damping ◽  
Plate Motion ◽  
Flexible Plate ◽  
Dependent Flow ◽  
Rigid Plane

Vibration damping of a plate by means of a fluid layer is investigated. First, the frequency-dependent flow resistance of a fluid layer is explained with a simple illustration of the damping mechanism. Then, the vibration response of a plate is examined when it is backed by a rigid plane or another flexible plate with a fluid layer constricted in-between. Effects of the plate motion and acoustic radiation on the damping mechanism are also considered. The numerical results are presented in terms of frequency response of the plates.

Acoustic resonances in a viscous fluid layer

1980 ◽  
Vol 67 (S1) ◽  
pp. S24-S24
Author(s):  
Ralph Fiorito ◽  
Walter Madigosky ◽  
Herbert Überall
Keyword(s):  
Viscous Fluid ◽  
Fluid Layer ◽  
Acoustic Resonances

Nonlinear Thermal Instability in a Rotating Viscous Fluid Layer Under Temperature/Gravity Modulation

2012 ◽  
Vol 134 (10) ◽  
Author(s):  
B. S. Bhadauria ◽  
P. G. Siddheshwar ◽  
Om P. Suthar
Keyword(s):  
Viscous Fluid ◽  
Heat Transport ◽  
Thermal Instability ◽  
Fluid Layer ◽  
Landau Equation ◽  
Effect Of Temperature ◽  
Stationary Mode ◽  
Gravity Modulation ◽  
Nonlinear Stability Analysis ◽  
Weakly Nonlinear

In the present paper, the effect of time-periodic temperature/gravity modulation on the thermal instability in a rotating viscous fluid layer has been investigated by performing a weakly nonlinear stability analysis. The disturbances are expanded in terms of power series of amplitude of modulation, which has been assumed to be small. The amplitude equation, viz., the Ginzburg–Landau equation, for the stationary mode of convection is obtained and using the same, the effect of temperature/gravity modulation on heat transport has been investigated. The stability of the system is studied and the stream lines are plotted at different slow times as a function of the amplitude of modulation, Rossby number, and Prandtl number. It is found that the temperature/gravity modulation can be used as an external means to augment/diminish heat transport in a rotating system. Further, it is shown that rotation can be effectively used in regulating heat transport.

Nonlinear interaction of magnetic field and convection

1975 ◽  
Vol 71 (1) ◽  
pp. 193-206 ◽  
Author(s):  
F. H. Busse
Keyword(s):  
Magnetic Field ◽  
Magnetic Energy ◽  
Fluid Layer ◽  
Boussinesq Equations ◽  
Finite Amplitude ◽  
Magnetic Reynolds Number ◽  
Convection Rolls ◽  
Rayleigh Numbers ◽  
Horizontal Fluid Layer ◽  
Chandrasekhar Number

The interaction between convection in a horizontal fluid layer heated from below and an ambient vertical magnetic field is considered. The analysis is based on the Boussinesq equations for two-dimensional convection rolls and the assumption that the amplitude A of the convection and the Chandrasekhar number Q are small. It is found that the magnetic energy is amplified by a factor of order R½m, where Rm is the magnetic Reynolds number. The ratio between the magnetic and kinetic energies can reach values much larger than unity. Although the magnetic field always inhibits convection, this influence decreases with increasing amplitude of convection. Thus finite amplitude onset of steady convection becomes possible at Rayleigh numbers considerably below the values predicted by linear theory.

PROPERTIES OF A LORENZ MODEL FOR CONVECTION IN A ROTATING FLUID LAYER

1992 ◽  
Vol 06 (16n17) ◽  
pp. 1055-1061
Author(s):  
GOVINDAN RAJESH ◽  
SUPREETI DAS ◽  
JAYANTA K. BHATTACHARJEE
Keyword(s):  
Limit Cycle ◽  
Fluid Layer ◽  
Stable Limit Cycle ◽  
Period Doubling ◽  
Finite Amplitude ◽  
Stable Limit ◽  
Rotating Fluid ◽  
Onset Of Convection ◽  
Rayleigh Numbers ◽  
Period Doubling Bifurcations

A Lorenz-like model due to Veronis for onset of convection in a rotating fluid layer is analysed for Rayleigh numbers higher than the point at which stationary convection occurs. The most outstanding feature is that for Taylor numbers above a critical value, the Hopf bifurcation does lead to a finite amplitude stable limit cycle via a hysteretic transition. This limit cycle undergoes a sequence of period doubling bifurcations to form a Feigenbaum attractor which then makes a transition to the Lorenz-like attractor.

Finite Amplitude Longitudal Convection Rolls in an Inclined Layer

1973 ◽  
Vol 95 (3) ◽  
pp. 407-408 ◽  
Author(s):  
R. M. Clever
Keyword(s):  
Fluid Layer ◽  
Horizontal Layer ◽  
Finite Amplitude ◽  
Two Dimensional ◽  
Governing Equations ◽  
Inclined Layer ◽  
Experimental Heat ◽  
Inclined Fluid Layer ◽  
Longitudinal Coordinate ◽  
Convection Rolls

For the case of a large Prandtl number, buoyancy driven flow in an inclined fluid layer, it is shown that all longitudinal-coordinate-independent solutions of the governing equations are obtainable from a knowledge of the existing results for two-dimensional convection in a horizontal layer, heated from below. The rescaling here yields results which compare favorably with those of existing experimental heat transport values.

Distortion and necking of a viscous inclusion in Stokes flow

1989 ◽  
Vol 422 (1862) ◽  
pp. 173-192 ◽  
Keyword(s):  
Viscous Fluid ◽  
Stokes Flow ◽  
Numerical Solutions ◽  
Finite Amplitude ◽  
Elliptic Solution ◽  
Small Perturbations ◽  
All Solutions ◽  
Elliptic Profile ◽  
The Stability ◽  
Small Disturbances

Spence & Wilmott (1988) considered the deformation of a slender inclusion of highly-viscous fluid in a Stokes flow of less viscous fluid, and derived a coupled pair of equations to describe its evolution. The equations possess self-preserving solutions for elliptical inclusions, previously known from the work of Bilby et al . (1975, 1976) and Bilby & Kolbuszewski (1977). In the present paper numerical solutions are presented for non-elliptic shapes. These have been obtained on a CRAY XMP-22 by use of an eigenfunction expansion suggested by the elliptic solution, leading to an initial value problem for the coefficients. The solutions show that large deformations can develop in finite time from small perturbations of the ellipse, particularly at large viscosity ratios. Special attention is directed to the phenomenon of boudinage, whereby alternate swelling and necking develops as the inclusion is stretched by the Stokes flow. This appears to characterize all solutions that depart significantly from pure elliptic shape. In the Appendix the stability of the elliptic profile to small disturbances is examined. It is found that all subharmonics of a given disturbance are excited to a finite amplitude that increases with the viscosity ratio, but that higher harmonics are not excited in linear theory, although nonlinear coupling leads to the eventual excitation of all modes.

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