Wave Number Of Perturbation Research Articles

Stability of stratified two-phase flows in inclined channels

Linear stability of the stratified gas-liquid and liquid-liquid plane-parallel flows in the inclined channels is studied with respect to all wavenumber perturbations. The main objective is to predict the parameter regions in which the stable stratified configuration in inclined channels exists. Up to three distinct base states with different holdups exist in the inclined flows, so that the stability analysis has to be carried out for each branch separately. Special attention is paid to the multiple solution regions to reveal the feasibility of the non-unique stable stratified configurations in inclined channels. The stability boundaries of each branch of the steady state solutions are presented on the flow pattern map and are accompanied by the critical wavenumbers and the spatial profiles of the most unstable perturbations. Instabilities of different nature are visualized by the streamlines of the neutrally stable perturbed flows, consisting of the critical perturbation superimposed on the base flow. The present analysis confirms the existence of two stable stratified flow configurations in a region of low flow rates in the countercurrent liquid-liquid flows. These configurations become unstable with respect to the shear mode of instability. It was revealed that in slightly upward inclined flows the lower and middle solutions for the holdup are stable in the part of the triple solution region, while the upper solution is always unstable. In the case of downward flows, in the triple solution region, none of the solutions are stable with respect to the short-wave perturbations. These flows are stable only in the single solution region at low flow rates of the heavy phase, and the long-wave perturbations are the most unstable ones.

Stability of dust ion acoustic solitary waves in a collisionless unmagnetized nonthermal plasma in presence of isothermal positrons

A three-dimensional KP (Kadomtsev Petviashvili) equation is derived here describing the propagation of weakly nonlinear and weakly dispersive dust ion acoustic wave in a collisionless unmagnetized plasma consisting of warm adiabatic ions, static negatively charged dust grains, nonthermal electrons, and isothermal positrons. When the coefficient of the nonlinear term of the KP-equation vanishes an appropriate modified KP (MKP) equation describing the propagation of dust ion acoustic wave is derived. Again when the coefficient of the nonlinear term of this MKP equation vanishes, a further modified KP equation is derived. Finally, the stability of the solitary wave solutions of the KP and the different modified KP equations are investigated by the small-k perturbation expansion method of Rowlands and Infeld [J. Plasma Phys. 3, 567 (1969); 8, 105 (1972); 10, 293 (1973); 33, 171 (1985); 41, 139 (1989); Sov. Phys. - JETP 38, 494 (1974)] at the lowest order of k, where k is the wave number of a long-wavelength plane-wave perturbation. The solitary wave solutions of the different evolution equations are found to be stable at this order.

Predictability of Dry Convective Boundary Layers: An LES Study

Abstract The predictability horizon of convective boundary layers is investigated in this study. Large-eddy simulation (LES) and direct numerical simulation (DNS) techniques are employed to probe the evolution of perturbations in identical twin simulations of a growing dry convective boundary layer. Error growth typical of chaotic systems is observed, marked by two phases. The first comprises an exponential error growth as , with δ0 as the initial error, δ(t) as the error at time t, and Λ as the Lyapunov exponent. This phase is independent of the perturbation wavenumber, and the perturbation energy grows following a self-similar spectral shape dominated by higher wavenumbers. The nondimensional error growth rate in this phase shows a strong dependence on the Reynolds number (Re). The second phase involves saturation of the error. Here, the error growth follows Lorenz dynamics with a slower saturation of successively larger scales. An analysis of the spectral decorrelation times reveals two regimes: an Re-independent regime for scales larger than the boundary layer height and an Re-dependent regime for scales smaller than , which are found to decorrelate substantially faster for increasing Reynolds numbers.

BiGlobal linear stability analysis on low-Re flow past an airfoil at high angle of attack

We perform BiGlobal linear stability analysis on flow past a NACA0012 airfoil at 16° angle of attack and Reynolds number ranging from 400 to 1000. The steady-state two-dimensional base flows are computed using a well-tested finite difference code in combination with the selective frequency damping method. The base flow is characterized by two asymmetric recirculation bubbles downstream of the airfoil whose streamwise extent and the maximum reverse flow velocity increase with the Reynolds number. The stability analysis of the flow past the airfoil is carried out under very small spanwise wavenumber β = 10−4 to approximate the two-dimensional perturbation, and medium and large spanwise wavenumbers (β = 1–8) to account for the three-dimensional perturbation. Numerical results reveal that under small spanwise wavenumber, there are at most two oscillatory unstable modes corresponding to the near wake and far wake instabilities; the growth rate and frequency of the perturbation agree well with the two-dimensional direct numerical simulation results under all Reynolds numbers. For a larger spanwise wavenumber β = 1, there is only one oscillatory unstable mode associated with the wake instability at Re = 400 and 600, while at Re = 800 and 1000 there are two oscillatory unstable modes for the near wake and far wake instabilities, and one stationary unstable mode for the monotonically growing perturbation within the recirculation bubble via the centrifugal instability mechanism. All the unstable modes are weakened or even suppressed as the spanwise wavenumber further increases, among which the stationary mode persists until β = 4.

ON STABILITY OF THE OIL DISPLACEMENT FRONT UNDER CONDITIONS OF THERMOGAS IMPACT ON THE OIL BEARING LAYER

The method of thermogas impact on the oil bearing layer is a perspective one to improve oil recovery. It is now under experimental implementation in Belarus. Stability of the thermal front and that of the oil displacement is a point of principle for the given technology. The article offers solution based on the method of small perturbations for the problem of the oil-displacement front stability under thermogas impact on the oil layer. The perturbation growth increment is shown to be quite different from that of the gas filtration combustion. Being determined by the perturbation wave number (or wave length), by difference in speed of the blowing filtration and that of the heat development front, by the ratios of densities, filtration coefficients, compressibility of the displacement agent and the displaced oil mass, and by other parameters. The author analyses the main parameters influencing the stability of the front. Recommendations are given on possible methods and procedures improving stability of the displacement front (neutralizing perturbation growth). The mechanisms of suppression or compensation of the front perturbation growth are as follows: the crude oil viscosity reduction and increase of that of the displacement agent, the displacement agent compressibility increase, increase of the thermogas impact heat-front width in the first instance at the expense of the temperature growth and alteration in the chemism (low temperature catalysts utilization, etc.), reduction in speed of the front propagation and/or correspondingly of the displacement agent feed. Utilization of the gas or water-gas displacement agent as well as the agent impregnation with hydrophobic gases provides a relatively better stability of the front as compared to that employing water based compounds. Analytical data and derived recommendations are offered for utilization within the framework of general techniques and procedures of the thermogas impact process management in the context of developmental and experimental-industrial oil extraction. Further research into methods and mechanisms of the displacement front perturbation compensation, including the front dynamics at nonlinear stage, might be conducted via detailed 2D and 3D numerical simulation of the system.

ON THE PROPERTIES OF SLOW MHD SAUSAGE WAVES WITHIN SMALL-SCALE PHOTOSPHERIC MAGNETIC STRUCTURES

ABSTRACT The presence of magnetoacoustic waves in magnetic structures in the solar atmosphere is well-documented. Applying the technique of solar magneto-seismology (SMS) allows us to infer the background properties of these structures. Here, we aim to identify properties of the observed magnetoacoustic waves and study the background properties of magnetic structures within the lower solar atmosphere. Using the Dutch Open Telescope and Rapid Oscillations in the Solar Atmosphere instruments, we captured two series of high-resolution intensity images with short cadences of two isolated magnetic pores. Combining wavelet analysis and empirical mode decomposition (EMD), we determined characteristic periods within the cross-sectional (i.e., area) and intensity time series. Then, by applying the theory of linear magnetohydrodynamics (MHD), we identified the mode of these oscillations within the MHD framework. Several oscillations have been detected within these two magnetic pores. Their periods range from 3 to 20 minutes. Combining wavelet analysis and EMD enables us to confidently find the phase difference between the area and intensity oscillations. From these observed features, we concluded that the detected oscillations can be classified as slow sausage MHD waves. Furthermore, we determined several key properties of these oscillations such as the radial velocity perturbation, the magnetic field perturbation, and the vertical wavenumber using SMS. The estimated range of the related wavenumbers reveals that these oscillations are trapped within these magnetic structures. Our results suggest that the detected oscillations are standing harmonics, and this allows us to estimate the expansion factor of the waveguides by employing SMS. The calculated expansion factor ranges from 4 to 12.

Modulational instability of two crossing waves in the presence of wind flow

In this study, we investigate modulational instability in the presence of wind flow in a situation where sea states crossed over water with a finite depth. It is assumed that the wind flows in a specific direction to produce angles with two directions of propagation by two wave systems with the same carrier wave number and same frequency. The evolution equations considered in this study represent a balance among the effects of wind forcing, dispersion, and nonlinearity at the lowest order. These evolution equations are used to study the stability of the uniform wave solution in crossing seas. We show that in the presence of wind flow, the uniform waves grow super-exponentially. We also demonstrate that the region of asymptotic instability in the perturbed wave number plane is larger than that in the absence of wind flow.

Weakly nonlinear theory of secondary rippling instability in surfaces of stressed solids

Numerical simulations of the surface morphological evolution of uniaxially stressed elastic crystalline solids have demonstrated that in addition to Asaro-Tiller/Grinfeld (surface cracking) instabilities, long-wavelength perturbations from the planar surface morphology can trigger a tip-splitting instability that causes formation of a pattern of secondary ripples, which cannot be explained by linear stability theory. In this study, we develop a weakly nonlinear stability theory, which can explain the occurrence of such secondary rippling instabilities and predict the number of secondary ripples that form on the surface as a function of perturbation wavelength. The theory shows that this type of surface pattern formation arises entirely due to the competition between surface energy and elastic strain energy, regardless of surface diffusional anisotropy or the action of externally applied fields. The origin of secondary rippling is explained through nonlinear terms included in the analysis which generate sub-harmonic ripples in the surface morphology with wave numbers that are multiples of the original surface perturbation wave number. Based on the weakly nonlinear theory, we have developed simple analytical expressions that predict the critical wavelength for the onset of secondary rippling, the increase in the number of secondary ripples with increasing perturbation wavelength, and how the onset of the secondary rippling instability and the rippled surface pattern are affected by surface diffusional anisotropy and the action of an applied electric field. The conclusions of the theory are validated by systematic comparisons with results of self-consistent dynamical simulations of surface morphological evolution.

Phase diagrams of forced magnetic reconnection in Taylor’s model

Recent progress in the understanding of how externally driven magnetic reconnection evolves is organized in terms of parameter space diagrams. These diagrams are constructed using four pivotal dimensionless parameters: the Lundquist number $S$, the magnetic Prandtl number $P_{m}$, the amplitude of the boundary perturbation $\hat{{\it\Psi}}_{0}$, and the perturbation wave number $\hat{k}$. This new representation highlights the parameter regions of a given system in which the magnetic reconnection process is expected to be distinguished by a specific evolution. Contrary to previously proposed phase diagrams, the diagrams introduced here take into account the dynamical evolution of the reconnection process and are able to predict slow or fast reconnection regimes for the same values of $S$ and $P_{m}$, depending on the parameters that characterize the external drive, which have not been considered until now. These features are crucial to understanding the onset and evolution of magnetic reconnection in diverse physical systems.

Far-field scattering model for wave propagation in random media.

A simple approximate model is developed for ultrasonic wave propagation in a random elastic medium. The model includes second order multiple scattering and is applicable in all frequency ranges including geometric. It is based on the far field approximation of the reference medium Green's function and simplifications of the mass operator in addition to those of the first smooth approximation. In this approximation, the dispersion equation for the perturbed wave number is obtained; its solution yields the dispersive ultrasonic velocity and attenuation coefficients. The approximate solution is general and is suitable for nonequiaxed grains with arbitrary elastic symmetry. For equiaxed cubic grains, the solution is compared with the existing second order models and with the Born approximation. The comparison shows that the obtained solution has smaller error than the Born approximation and shows reasonably well the onset of multiple scattering and the applicability limit of the Born approximation at high frequency. The perturbed wave number in the developed model does not depend explicitly on the crystallite elastic properties even for arbitrary crystallographic symmetry; it depends on two nondimensional scattering elastic parameters and the macroscopic ultrasonic velocity (those are dependent on the crystallite moduli). This provides an advantage for potential schemes for inversion from attenuation to material microstructure.

Magnetic field generation and diffusion by a laser-produced blast wave propagating in non-homogenous plasma

In this paper we discuss the magnetic field self generation, via the so-called Biermann battery effect, and its diffusion for a blast wave (BW) expanding in a perturbed background medium. A series of simulations verify the bi-linear behavior of the Biermann battery source term both in amplitude and in wavenumber. Such a behavior is valid in the limit of no diffusivity. When diffusivity is also considered, we observe an inverse proportionality with the wavenumber: for large wavenumber perturbation magnetic diffusivity plays a key role. Writing the induction equation in a dimensionless form we discuss how, in terms of magnetic properties, the BW can be subdivided into three main regions: the remnant where the frozen-in-flow approximation holds, the thin shell where the magnetic field is in fact generated but at the same time begins to diffuse, and the shock front where the magnetic field diffuses away. A possible experimental scenario that could induce magnetic fields of about 100 gauss is finally investigated. Simulations have been performed with the code DUED.

Instability of a thin conducting foil accelerated by a finite wavelength intense laser

We derive a theoretical model for the Rayleigh–Taylor (RT)‐like instability for a thin foil accelerated by an intense laser, taking into account finite-wavelength effects in the laser wave field. These finite-wavelength effects lead to the diffraction of the electromagnetic wave off the periodic structures arising from the instability of the foil, which significantly modifies the growth rate of the RT-like instability when the perturbations on the foil have wavenumbers comparable to or larger than the laser wavenumber. In particular, the growth rate has a local maximum at a perturbation wavenumber approximately equal to the laser wavenumber. The standard RT instability, arising from a pressure difference between the two sides of a foil, is approximately recovered for perturbation wavenumbers smaller than the laser wavenumber. Differences in the results for circular and linear polarization of the laser light are pointed out. The model has significance for radiation pressure acceleration of thin foils, where RT-like instabilities are significant obstacles.

Two-phase viscous fingering of immiscible thixotropic fluids: A numerical study

The effects of a fluid’s thixotropic behavior is investigated on the viscous fingering phenomenon in a rectangular Hele-Shaw cell assuming that the displacing fluid is Newtonian while the displaced fluid obeys the Moore model for thixotropic fluids. Lubrication theory is used to simplify the gap-averaged governing equations in which the interfacial tension is treated as a body force. It is shown that the shapes of the fingers are dramatically affected by the displaced fluid’s thixotropic behavior. For highly thixotropic fluids, a chaotic behavior, accompanied by a blowup at prolonged times, is predicted to occur for certain set of parameter values. The viscosity ratio of the Moore fluid is also predicted to influence the shapes of the fingers provided that the zero-shear viscosity of the displaced fluid is higher than the viscosity of the displacing fluid. It is shown that the amplitude and wavenumber of the initial perturbation plays a crucial role on its time evolution. Also, a partial slip of the displaced and/or the displacing fluid is predicted to have a stabilizing effect on the viscous fingering phenomenon.

Numerical simulation to study the transient self focusing of laser beam in plasma

In this paper, we present the numerical simulation for the coupled system of equations governing the dynamics of laser and Ion Acoustic Wave (IAW) in a collisionless plasma, when the coupling between the waves is through ponderomotive non-linearity. The nonlinear evolution of the laser beam is studied when the pump laser is perturbed by a periodic perturbation. By changing the perturbation wave number, we have studied its effect on the nonlinear evolution pattern of laser beam. In order to have a physical insight into the nonlinear dynamics of laser beam evolution in time and space, we have studied the laser and IAW spectra containing spatial harmonics. The magnitude of these harmonics changes with time and leads to time dependent localization of laser beam in spatial domain. The nonlinear dynamics of this localization is investigated in detail by using simulation and a semi-analytical model.

Gravitational instability of thin gas layer between two thick liquid layers

We consider the problem of gravitational instability (Rayleigh-Taylor instability) of a horizontal thin gas layer between two liquid half-spaces (or thick layers), where the light liquid overlies the heavy one. This study is motivated by the phenomenon of boiling at the surface of direct contact between two immiscible liquids, where the rate of the “break-away” of the vapour layer growing at the contact interface due to development of the Rayleigh-Taylor instability on the upper liquid-gas interface is of interest. The problem is solved analytically under the assumptions of inviscid liquids and viscous weightless vapour. These assumptions correspond well to the processes in real systems, e.g., they are relevant for the case of interfacial boiling in the system water- n -heptane. In order to verify the results, the limiting cases of infinitely thin and infinitely thick gas layers were considered, for which the results can be obviously deduced from the classical problem of the Rayleigh-Taylor instability. These limiting cases are completely identical to the well-studied cases of gravity waves at the liquid-liquid and liquid-gas interfaces. When the horizontal extent of the system is long enough, the wavenumber of perturbations is not limited from below, and the system is always unstable.The wavelength of the most dangerous perturbations and the rate of their exponential growth are derived as a function of the layer thickness. The dependence of the exponential growth rate on the gas layer thickness is cubic.

Liquid Films Instability Analysis of Liquefying Hybrid Rocket Fuels Under Supercritical Conditions

Numerical analysis on the instability of liquid/dense fluid films under supercritical operating conditions is performed on methane fuel. A numerical code for compressible fluid flows, accommodated for the van der Waals equation of state, is developed in order to deal with supercritical fluid and dense fluid layers and has shown good convergence, even at a very low-Reynolds-number flow typically seen in actual hybrid rocket engines. A linear instability analysis is conducted and shows that an amplification rate has a peak at a certain wave number of initial perturbations. The perturbation becomes unstable as the Reynolds number and chamber pressure increase, and the instability region of the wave number is enlarged when an acceleration body force in the streamwise direction is imposed. A limit cycle of the amplitude of perturbations is observed at low-Reynolds-number flows, and the instability of dense fluid layers leads to the entrainment phenomena at high-Reynolds-number flows. It is deduced that the perturbation with the peak value of the amplification rate dominates in an actual hybrid rocket engine.

Richtmyer–Meshkov instability for elastic–plastic solids in converging geometries

We present a detailed study of the interface instability that develops at the boundary between a shell of elastic–plastic material and a cylindrical core of confined gas during the inbound implosive motion generated by a shock-wave. The main instability in this configuration is the so-called Richtmyer–Meshkov instability that arises when the shock wave crosses the material interface. Secondary instabilities, such as Rayleigh–Taylor, due to the acceleration of the interface, and Kelvin–Helmholtz, due to slip between solid and fluid, arise as the motion progresses. The reflection of the shock wave at the axis and its second interaction with the material interface as the shock moves outbound, commonly known as re-shock, results in a second Richtmyer–Meshkov instability that potentially increases the growth rate of interface perturbations, resulting in the formation of a mixing zone typical of fluid–fluid configurations and the loss of the initial perturbation length scales. The study of this problem is of interest for achieving stable inertial confinement fusion reactions but its complexity and the material conditions produced by the implosion close to the axis prove to be challenging for both experimental and numerical approaches. In this paper, we attempt to circumvent some of the difficulties associated with a classical numerical treatment of this problem, such as element inversion in Lagrangian methods or failure to maintain the relationship between the determinant of the deformation tensor and the density in Eulerian approaches, and to provide a description of the different events that occur during the motion of the interface. For this purpose, a multi-material numerical solver for evolving in time the equations of motion for solid and fluid media in an Eulerian formalism has been implemented in a Cartesian grid. Equations of state are derived using thermodynamically consistent hyperelastic relations between internal energy and stresses. The resolution required for capturing the state of solid and fluid materials close to the origin is achieved by making use of adaptive mesh refinement techniques. Rigid-body rotations contained in the deformation tensor have been shown to have a negative effect on the accuracy of the method in extreme compression conditions and are removed by transforming the deformation tensor into a stretch tensor at each time step. With this methodology, the evolution of the interface can be tracked up to a point at which numerical convergence cannot be achieved due to the inception of numerical Kelvin–Helmholtz instabilities caused by slip between materials. From that point, only qualitative conclusions can be extracted from this analysis. The influence of different geometrical parameters, initial conditions, and material properties on the motion of the interface are investigated. Some major differences are found with respect to the better understood fluid–fluid case. For example, increasing the wave number of the interface perturbations leads to a second phase reversal of the interface (i.e., the first phase reversal of the interface naturally occurs due to the initial negative growth-rate of the instability as the shock wave transitions from the high-density material to the low-density one). This phenomenon is caused by the compressive effect of the converging geometry and the low density of the gas with respect to the solid, which allows for the formation of an incipient spike in the center of an already existing bubble. Multiple solid–gas density ratios are also considered. Results show that the motion of the interface asymptotically converges to the solid–vacuum case. When a higher initial density for the gas is considered, the growth rate of interface perturbations decreases and, in some situations, its sign may reverse, as the fluid becomes more dense than the solid due to having higher compressibility. Finally, the influence of the Mach number of the driving shock and the yield stress on the mixing-zone is examined. We find that the width of the mixing zone produced after the re-shock increases in proportion to the strength of the incident shock. An increased yield stress in the solid material makes the interface less unstable due to vorticity being carried away from the interface by shear waves and limits the generation of smaller length scales after the re-shock.

INSTABILITY OF MAGNETIZED IONIZATION FRONTS SURROUNDING H II REGIONS

An ionization front (IF) surrounding an H II region is a sharp interface where a cold neutral gas makes transition to a warm ionized phase by absorbing UV photons from central stars. We investigate the instability of a plane-parallel D-type IF threaded by parallel magnetic fields, by neglecting the effects of recombination within the ionized gas. We find that weak D-type IFs always have the post-IF magnetosonic Mach number $\mathcal{M}_{\rm M2} \leq 1$. For such fronts, magnetic fields increase the maximum propagation speed of the IFs, while reducing the expansion factor $\alpha$ by a factor of $1+1/(2\beta_1)$ compared to the unmagnetized case, with $\beta_1$ denoting the plasma beta in the pre-IF region. IFs become unstable to distortional perturbations due to gas expansion across the fronts, exactly analogous to the Darrieus-Landau instability of ablation fronts in terrestrial flames. The growth rate of the IF instability is proportional linearly to the perturbation wavenumber as well as the upstream flow speed, and approximately to $\alpha^{1/2}$. The IF instability is stabilized by gas compressibility and becomes completely quenched when the front is D-critical. The instability is also stabilized by magnetic pressure when the perturbations propagate in the direction perpendicular to the fields. When the perturbations propagate in the direction parallel to the fields, on the other hand, it is magnetic tension that reduces the growth rate, completely suppressing the instability when $\mathcal{M}_{\rm M2}^2 < 2/(\beta_1 - 1)$. When the front experiences an acceleration, the IF instability cooperates with the Rayleigh-Taylor instability to make the front more unstable.

Ruga-formation instabilities of a graded stiffness boundary layer in a neo-Hookean solid

We present an analysis of ruga-formation instabilities arising in a graded stiffness boundary layer of a neo-Hookean half space, caused by lateral plane-strain compression. In this study, we represent the boundary layer by a stiffness distribution exponentially decaying from a surface value Q 0 to a bulk value Q B with a decay length of 1/ a . Then, the normalized perturbation wavenumber, k ¯ = k / a , and the compressive strain, ε , control formation of a wrinkle pattern and its evolution towards crease or fold patterns for every stiffness ratio η = Q B / Q 0 . Our first-order instability analysis reveals that the boundary layer exhibits self-selectivity of the critical wavenumber for nearly the entire range of 0&lt; η &lt;1, except for the slab ( η =0) and homogeneous half-space ( η =1) limits. Our second-order analysis supplemented by finite-element analysis further uncovers various instability-order-dependent bifurcations, from stable wrinkling of the first order to creasing of the infinite-order cascade instability, which construct diverse ruga phases in the three-dimensional parameter space of ( ε , k ¯ , η ) . Competition among film-buckling, local film-crease and global substrate-crease modes of energy release produces diverse ruga-phase domains. Our analysis also reveals the subcritical crease states of the homogeneous half space. Our results are, then, compared with the behaviour of equivalent bilayer systems for thin-film applications.

Combined Effect of Viscosity, Surface Tension and Compressibility on Rayleigh-Taylor Bubble Growth Between Two Fluids

The combined effect of viscosity, surface tension, and the compressibility on the nonlinear growth rate of Rayleigh-Taylor (RT) instability has been investigated. For the incompressible case, it is seen that both viscosity and surface tension have a retarding effect on RT bubble growth for the interface perturbation wave number having a value less than three times of a critical value (kc=(ρh-ρl)g/T, T is the surface tension). For the value of wave number greater than three times of the critical value, the RT induced unstable interface is stabilized through damped nonlinear oscillation. In the absence of surface tension and viscosity, the compressibility has both a stabilizing and destabilizing effect on RTI bubble growth. The presence of surface tension and viscosity reduces the growth rate. Above a certain wave number, the perturbed interface exhibits damped oscillation. The damping factor increases with increasing kinematic viscosity of the heavier fluid and the saturation value of the damped oscillation depends on the surface tension of the perturbed fluid interface and interface perturbation wave number. An approximate expression for asymptotic bubble velocity considering only the lighter fluid as a compressible one is presented here. The numerical results describing the dynamics of the bubble are represented in diagrams.