Nonlinear Dynamics of Rayleigh Taylor Instabilities Studied with a Lattice Boltzmann Method

Multi-relaxation time lattice Boltzmann method is employed to study the later stages of Rayleigh Taylor instabilities. A heavy fluid is placed over an immiscible lighter fluid in an unstable equilibrium. Various initial disturbances are used to initiate the flow. The D2Q9 lattice arrangement is employed on the computational domain. The density distribution function is determined for both fluids, and a coloring function is used to highlight the two fluids. Interactive forces and body forces are modelled by using the Shah and Chert model. Three different initial disturbances are studied, and their late stages are examined. The classic mushroom structure can be seen on all three cases. Distortions of the mushroom structures are seen due to the effects of the boundary and the influence of the initial disturbance.

Rayleigh–Taylor instability of viscoelastic self-rewetting film flowing down a temperature-controlled inclined substrate

Rayleigh–Taylor(RT) instability of gravity-driven viscoelastic self-rewetting film flowing under an inclined substrate uniformly heated or cooled is considered. The surface tension of self-rewetting film is considered as a quadratic function of temperature. The long wave hypothesis is used to derive a nonlinear free surface evolution equation of the thin viscoelastic film. Linear stability analysis shows that for a prescribed the viscoelastic coefficient, substrate cooling products instability,while substrate heating remains stability. Furthermore, we analyze the influence of viscoelastic coefficient on RT instability. Results show that the viscoelastic coefficient reinforces the RT instability whether the substrate is heated or cooled.Moreover, we use the line method to numerically simulate the nonlinear evolution equation and systematically examine the space-time variation of the film free surface. The numerical results illustrate that increasing the viscoelastic coefficient can enhance the disturbance amplitude and wave frequency. This means that the viscoelastic coefficient makes the system unstable, which is consistent with result of the linear stability analysis. In addition, the oscillation tends to accumulate downstream of the inclined substrate when the evolution time is long enough. Finally, the variation of film thickness with related parameters for different viscoelastic coefficients is investigated.

Are cyclones in Jupiter's polar regions modulated by the radially directional Rayleigh–Taylor instability?

The persistence and symmetry of cyclones around the poles of Jupiter are unknown.In the present investigation,inspired by cyclones at the South Pole of the Earth,we propose a mechanism that provides an explanation for this problem.The negative temperature gradient with respect to latitude may play an important role here.This temperature gradient is induced by solar radiation because of the small axial inclination of Jupiter.Our numerical simulations suggest that cyclones in the polar regions of Jupiter may be modulated or controlled by the radially directional Rayleigh–Taylor instability,driven by centrifugal force and the negative temperature gradient along the latitude.

Cylindrical effects in weakly nonlinear Rayleigh Taylor instability

The classical Rayleigh–Taylor instability（RTI） at the interface between two variable density fluids in the cylindrical geometry is explicitly investigated by the formal perturbation method up to the second order. Two styles of RTI, convergent（i.e., gravity pointing inward） and divergent（i.e., gravity pointing outwards） configurations, compared with RTI in Cartesian geometry, are taken into account. Our explicit results show that the interface function in the cylindrical geometry consists of two parts： oscillatory part similar to the result of the Cartesian geometry, and non-oscillatory one contributing nothing to the result of the Cartesian geometry. The velocity resulting only from the non-oscillatory term is followed with interest in this paper. It is found that both the convergent and the divergent configurations have the same zeroth-order velocity, whose magnitude increases with the Atwood number, while decreases with the initial radius of the interface or mode number. The occurrence of non-oscillation terms is an essential character of the RTI in the cylindrical geometry different from Cartesian one.

Effect of initial phase on the Rayleigh–Taylor instability of a finite-thickness fluid shell

Rayleigh–Taylor instability(RTI) of finite-thickness shell plays an important role in deep understanding the characteristics of shell deformation and material mixing. The RTI of a finite-thickness fluid layer is studied analytically considering an arbitrary perturbation phase difference on the two interfaces of the shell. The third-order weakly nonlinear(WN) solutions for RTI are derived. It is found the main feature(bubble-spike structure) of the interface is not affected by phase difference. However, the positions of bubble and spike are sensitive to the initial phase difference, especially for a thin shell(kd < 1), which will be detrimental to the integrity of the shell. Furthermore, the larger phase difference results in much more serious RTI growth, significant shell deformation can be obtained in the WN stage for perturbations with large phase difference. Therefore, it should be considered in applications where the interface coupling and perturbation phase effects are important, such as inertial confinement fusion.

Rayleigh–Taylor instability at spherical interfaces of incompressible fluids

Rayleigh–Taylor instability（RTI） of three incompressible fluids with two interfaces in spherical geometry is derived analytically. The growth rate on the two interfaces and the perturbation feedthrough coefficients between two spherical interfaces are derived. For low-mode perturbation, the feedthrough effect from outer interface to inner interface is much more severe than the corresponding planar case, while the feedback from inner interface to the outer interface is smaller than that in planar geometry. The low-mode perturbations lead to the pronounced RTI growth on the inner interface of a spherical shell that are larger than the cylindrical and planar results. It is the low-mode perturbation that results in the difference between the RTI growth in spherical and cylindrical geometry. When the mode number of the perturbation is large enough, the results in cylindrical geometry are recovered.

Investigation of the Rayleigh–Taylor instability in charged fluids

The present study shows that the Rayleigh–Taylor(RT)instability and its growth rate are strongly dependent on the charge-mass ratio of charged particles in a charged fluid.A higher charge-mass ratio of the charged fluid appears to result in a stronger effect of the magnetic field to suppress the RT instability.We study the RT instabilities for both dusty plasma(small chargemass ratio of charged particles)and ion-electron plasma(large charge-mass ratio of charged particles).It is found that the impact of the external magnetic field to suppress the RT instability for ion-electron plasma is much greater than that for dusty plasma.It is also shown that,for a dusty plasma,in addition to region parameters such as the external magnetic field,region length,its gradient,as well as dust particle parameters such as number density,mass,and charge of dust particles,the growth rate of the RT instability in a dusty plasma also depends on parameters of both electrons and ions such as the number densities and temperatures of both electrons and ions.

Case study of an Equatorial Plasma Bubble Event investigated by multiple ground-based instruments at low latitudes over China

Observational evidence is insufficient to understand how equatorial plasma bubbles(EPBs)form over low latitudes.The mechanism of plasma-density enhancement(formation of"plasma blobs")at low latitudes is in dispute.In this paper,we use data from multiple ground-based instruments(one all-sky airglow imager,five digisondes,and one Fabry–Perot interferometer)to investigate the evolution of an EPB event that occurred at low latitudes over China on the night of 06 December 2015(06-Dec-2015).We provide observational evidence that an enhanced equatorward wind most likely induced by a substorm could have initiated the Rayleigh–Taylor instability(RTI)that destabilized several EPB depletions in an upwelling region of a large-scale wave-like structure(LSWS)in the bottomside ionosphere.Those EPB depletions were forced to surge poleward,from nearly 10°to 19°magnetic latitude,two hours before midnight.Smaller-scale bifurcations evolved rapidly from tips of airglow depletions by a secondary E×B instability when the aforementioned substorm-induced southwestward wind blew through.During the growth phase of the EPB depletions,a westward polarization electric field inside the LSWS is likely to have compressed plasma downward,inducing the two airglow-type blobs observed in the bottomside ionosphere,by a mechanism of LSWS-blob connection that we propose.We also provide observational evidence of brightness airglow depletions.We find that an enhanced poleward wind associated with a passing-by brightness wave(BW)is likely to have transported plasma to fill the airglow depletions,which finally evolved into brightness airglow structures.This study investigates the physical processes accompanied by the EPB event and those two-airglow blobs observed at low-latitudes over China.