Nonlinear Saturation of Baroclinic Instability in the Phillips Model: The Case of Energy

A conservation law for the Phillips model is derived. Using this law, the nonlinear saturation of purely baroclinic instability caused by the vertical velocity shear of the basic flow in the Phillips model—the case of energy—is studied within the context of Arnold’s second stability theorem. Analytic upper bounds on the energy of wavy disturbances are obtained. For one unstable region in the parameter plane, the result here is a second-order correction in ε to Shepherd’s; For another unstable region, the analytic upper bound on the energy of wavy disturbances offers an effective constraint on wavy (nonzonal) disturbances Φ′ i at any time.

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL(Ⅱ)- THE LOWER BOUND ON THE DISTURBANCE ENERGY AND POTENTIAL ENSTROPHY TO THE NONLINEARLY UNSTABLE BASIC FLOW

On the basis of the nonlinear stability theorem in the context of Arnol'd's second theorem for the generalized Phillips model,nonlinear saturation of baroclinic instability in the generalized Phillips model is investigatedThe lower bound on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model is presented,which indicates that there may exist an allocation between a nonlinearly unstable basic flow and a growing disturbance

Nonlinear saturation amplitude of cylindrical Rayleigh Taylor instability

The nonlinear saturation amplitude （NSA） of the fundamental mode in the classical Rayleigh-Taylor instability with a cylindrical geometry for an arbitrary Atwood number is analytically investigated by considering the nonlinear corrections up to the third order. The analytic results indicate that the effects of the initial radius of the interface （r0） and the Atwood number （A） play an important role in the NSA of the fundamental mode. The NSA of the fundamental mode first increases gently and then decreases quickly with increasing A. For a given A, the smaller the ro/λ（λ is the perturbation wavelength）, the larger the NSA of the fundamental mode. When ro/λ is large enough （r0 〉〉 λ）, the NSA of the fundamental mode is reduced to the prediction in the previous literatures within the framework of the third-order perturbation theory.

NONLINEAR SATURATION OF BAROCLINIC INSTABILITY IN THE GENERALIZED PHILLIPS MODEL (Ⅰ) -THE UPPER BOUND ON THE EVOLUTION OF DISTURBANCE TO THE NONLINEARLY UNSTABLE BASIC FLOW

On the basis of the nonlinear stability theorem in the context of Arnol's second theorem for the generalized Phillips model, nonlinear saturation of baroclinic instability in the generalized Phillips model is investigated. By choosing appropriate artificial stable basic flows, the upper bounds on the disturbance energy and potential enstrophy to the nonlinearly unstable basic flow in the generalized Phillips model are obtained, which are analytic completely and without the limitation of infinitesimal initial disturbance.

Numerical study on matching conditions of Langmuir parametric instability and the formation of Langmuir turbulence in ionospheric heating

Parametric decay instability(PDI)is an important process in ionospheric heating.This paper focuses on the frequency and wavevector matching condition in the initial PDI process,the subsequent cascade stage,and the generation of strong Langmuir turbulence.A more general numerical model is established based on Maxwell equations and plasma dynamic equations by coupling highfrequency electromagnetic waves to low-frequency waves via ponderomotive force.The primary PDI,cascade process,and strong Langmuir turbulence are excited in the simulation.The matching condition in the initial PDI stage and cascade process is verified.The result indicates that the cascade ion acoustic wave may induce or accelerate the formation of cavitons and lead to the wavenumber spectrum being more enhanced at 2k_(L)(where k_(L) is the primary Langmuir wavenumber).The wavenumber spectra develop from discrete to continuous spectra,which is attributed to the caviton collapse and strong Langmuir turbulence.

Large-Eddy Simulation of the Three-Dimensional Experiment on Richtmyer-Meshkov Instability Induced Turbulence

A program MVFT3D of large-eddy simulation is developed and performed to solve the multi compressible Navier- Stokes equations. The SGS dissipation and molecular viscosity dissipation have been analyzed, and the former is much larger than the later. Our test shows that the SGS dissipation of Vreman model is smaller than the Smagorinsky model. We mainly simulate the experiment of fluid instability of shock-accelerated interface by Poggi in this paper. The decay of the turbulent kinetic energy before the first reflected shock wave–mixing zone interaction and its strong enhancement by re-shocks are presented in our numerical simulations. The computational mixing zone width under double re-shock agreement well with the experiment, and the decaying law of the turbulent kinetic energy is consistent with Mohamed and Larue’s investigation. Also, by using MVFT3D we give some simulation results of the inverse Chevron model from AWE. The numerical simulations presented in this paper allow us to characterize and better understand the Richtmyer-Meshkov instability induced turbulence, and the code MVFT3D is validated.

Proton acceleration in plasma turbulence driven by high-energy lepton jets

The interaction of high energy lepton jets composed of electrons and positrons with background electron–proton plasma is investigated numerically based upon particle-in-cell simulation,focusing on the acceleration processes of background protons due to the development of electromagnetic turbulence.Such interaction may be found in the universe when energetic lepton jets propagate in the interstellar media.When such a jet is injected into the background plasma,theWeibel instability is excited quickly,which leads to the development of plasma turbulence into the nonlinear stage.The turbulent electric and magnetic fields accelerate plasma particles via the Fermi II type acceleration,where the maximum energy of both electrons and protons can be accelerated to much higher than that of the incident jet particles.Because of background plasma acceleration,a collisionless electrostatic shock wave is formed,where some pre-accelerated protons are further accelerated when passing through the shock wave front.Dependence of proton acceleration on the beam-plasma density ratio and beam energy is investigated.For a given background plasma density,the maximum proton energy generally increases both with the density and kinetic energy of the injected jet.Moreover,for a homogeneous background plasma,the proton acceleration via both turbulent fields and collisionless shocks is found to be significant.In the case of an inhomogeneous plasma,the proton acceleration in the plasma turbulence is dominant.Our studies illustrate a scenario where protons from background plasma can be accelerated successively by the turbulent fields and collisionless shocks.

Impedance Model for Instability Analysis of LCC-HVDCs Considering Transformer Saturation

In line commutated converter based high-voltage direct current(LCC-HVDC)transmission systems,the transformer saturation can induce harmonic instability,which poses a serious threat to the safe operation of the power system.However,the nonlinear characteristics of the power grids introduced by the transformer saturation considerably limit the application of the conventional analysis methods.To address the issue,this paper derives a linear model for the transformer saturation caused by the DC current due to the converter modulation.Afterwards,the nonlinear characteristics of power grids with the transformer saturation is described by a complex valued impedance matrix.Based on the derived impedance matrix,the system harmonic stability is analyzed and the mechanism of the transformer saturation induced harmonic instability is revealed.Finally,the sensitivity analysis is conducted to find the key factors that influence the system core saturation instability.The proposed impedance model is verified by the electromagnetic transient simulation,and the simulation results corroborate the effectiveness of the proposed impedance model.Index TermsLine commutated converter based high voltage direct current(LCC-HVDC),transformer saturation,harmonic instability,impedance model.

Experimental and numerical investigation of inclined air/SF_6 interface instability under shock wave

The shock tube experiments of inclined air/SF6 interface instability under the shock wave with the Mach numbers 1.23 and 1.41 are conducted. The numerical simulation is done with the parallel algorithm and the multi-viscous-fluid and turbulence （MVFT） code of the large-eddy simulation （LES）. The developing process of the interface accelerated by the shock wave is reproduced by the simulations. The complex wave structures, e.g., the propagation, refraction, and reflection of the shock wave, are clearly revealed in the flows. The simulated evolving images of the interface are consistent with the experimental ones. The simulated width of the turbulent mixing zone （TMZ） and the displacements of the bubble and the spike also agree well with the experimental data. Also, the reliability and effectiveness of the MVFT in simulating the problem of interface instability are validated. The more energies are injected into the TMZ when the shock wave has a larger Mach number. Therefore, the perturbed interface develops faster.

Zonal Jet Creation from Secondary Instability of Drift Waves for Plasma Edge Turbulence

A new strategy is presented to explain the creation and persistence of zonal flows widely observed in plasma edge turbulence.The core physics in the edge regime of the magnetic-fusion tokamaks can be described qualitatively by the one-state modified Hasegawa-Mima(MHM for short)model,which creates enhanced zonal flows and more physically relevant features in comparison with the familiar Charney-Hasegawa-Mima(CHM for short)model for both plasma and geophysical flows.The generation mechanism of zonal jets is displayed from the secondary instability analysis via nonlinear interactions with a background base state.Strong exponential growth in the zonal modes is induced due to a non-zonal drift wave base state in the MHM model,while stabilizing damping effect is shown with a zonal flow base state.Together with the selective decay effect from the dissipation,the secondary instability offers a complete characterization of the convergence process to the purely zonal structure.Direct numerical simulations with and without dissipation are carried out to confirm the instability theory.It shows clearly the emergence of a dominant zonal flow from pure non-zonal drift waves with small perturbation in the initial configuration.In comparison,the CHM model does not create instability in the zonal modes and usually converges to homogeneous turbulence.

Thermoelectromechanical instability of dielectric elastomer undergoes polarization saturation and temperature variation

When the electric field caused by voltage reaches a certain level,the charge on the compliant electrodes will not increase owing to the polarization saturation,which would limit the deformation of the dielectric elastomer.Some experiments show that temperature also has a significant effect on the deformation of dielectric elastomer.In this work,a free energy model coupling temperature and polarization saturation is developed to characterize the thermoelectromechanical instability of dielectric elastomer.The results reveal that both the polarization saturation parameters and electric field have a significant influence on the actuation ability of the dielectric elastomer,and the increase of temperature enhances thermoelectromechanical stability.It is hoped that this work could guide the development of dielectric elastomer materials and application devices operating in variable temperatures.

Electron acceleration by Langmuir turbulence in ionospheric heating

In this study,we investigate the generation of parametric decay instability,Langmuir turbulence formation,and electron acceleration in ionospheric heating via a two-fluid model using the Fokker-Planck equation and Vlasov-Poisson system simulations.The simulation results of both the magnetofluid model and the kinetic model demonstrate the dynamics of electron acceleration.Further,the results of the Vlasov-Poisson simulations suggest the formation of electron holes in phase space at the same spatial scale as the Langmuir wave,which are shown to be related to electron acceleration.In addition,electron acceleration is enhanced through the extension of the wavenumber spectrum caused by strong Langmuir turbulence,leading to more electron holes in phase space.

Nonlinear Saturation Amplitude in Classical Planar Richtmyer–Meshkov Instability

The classical planar Richtmyer–Meshkov instability(RMI) at a fluid interface supported by a constant pressure is investigated by a formal perturbation expansion up to the third order,and then according to definition of nonlinear saturation amplitude(NSA) in Rayleigh–Taylor instability(RTI),the NSA in planar RMI is obtained explicitly.It is found that the NSA in planar RMI is affected by the initial perturbation wavelength and the initial amplitude of the interface,while the effect of the initial amplitude of the interface on the NSA is less than that of the initial perturbation wavelength.Without marginal influence of the initial amplitude,the NSA increases linearly with wavelength.The NSA normalized by the wavelength in planar RMI is about 0.11,larger than that corresponding to RTI.

Large eddy simulation of a shocked gas cylinder instability induced turbulence

The Navier-Stokes equations for compressible fluid are solved with the operator splitting technique and LES (large eddy simulation) with the Smagorinsky model. A computational code MVFT (multi-viscosity-fluid and turbulence) is developed to study hydrodynamic instability and the induced turbulent mixing for multi compressible fluid. In order to validate the code MVFT,the LANL's shock tube experiment of shocked SF6 gas cylinder is simulated with the initial state of SF6 gas cylinder described by dissipative ITL (interface transition layer). It is shown that the width and height of gas cylinder calculated with MVFT are closer to the experimental results than RAGE,and that the velocities of upstream edge,downstream edge and vortex edge agree with the experimental results,and are appreciably smaller than the RAGE results. The code MVFT has been pre-liminarily validated.

Numerical Modelling for Dynamic Instability Process of Submarine Soft Clay Slopes Under Seismic Loading

Marine geological disasters occurred frequently in the deep-water slope area of the northern South China Sea,especially submarine landslides,which caused serious damage to marine facilities.The cyclic elastoplastic model that can describe the cyclic stress-strain response characteristic for soft clay,is embedded into the coupled Eulerian-Lagrangian(CEL)algorithm of ABAQUS by means of subroutine interface technology.On the basis of CEL technique and undrained cyclic elastoplastic model,a method for analyzing the dynamic instability process of marine slopes under the action of earthquake load is developed.The rationality for cyclic elastoplastic constitutive model is validated by comparing its calculated results with those of von Mises model built in Abaqus.The dynamic instability process of slopes under different conditions are analyzed.The results indicate that the deformation accumulation of soft clay have a significant effect on the dynamic instability process of submarine slopes under earthquake loading.The cumulative deformation is taken into our model and this makes the calculated final deformation of the slope under earthquake load larger than the results of conventional numerical method.When different contact conditions are used for analysis,the smaller the friction coefficient is,the larger the deformation of slopes will be.A numerical analysis method that can both reflect the dynamic properties of soft clay and display the dynamic instability process of submarine landslide is proposed,which could visually predict the topographies of the previous and post failure for submarine slope.

Cross-phase modulation instability in optical fibres with exponential saturable nonlinearity and high-order dispersion

Utilizing the linear-stability analysis, this paper analytically investigates and calculates the condition and gain spectra of cross-phase modulation instability in optical fibres in the ease of exponential saturable nonlinearity and high-order dispersion. The results show that, the modulation instability characteristics here are similar to those of conventional saturable nonlinearity and Kerr nonlinearity. That is to say, when the fourth-order dispersion has the same sign as that of the second-order one, a new gain spectral region called the second one which is far away from the zero point may appear. The existence of the exponential saturable nonlinearity will make the spectral width as well as the peak gain of every spectral region increase with the input powers before decrease. Namely, for every spectral regime, this may lead to a unique value of peak gain and spectral width for two different input powers. In comparison with the case of conventional saturable nonlinearity, however, when the other parameters are the same, the variations of the spectral width and the peak gain with the input powers will be faster in case of exponential saturable nonlinearity.

Impacts of higher-order dispersions and saturable nonlinearities on modulation instability in negative-refractive metamaterials

On the basis of the standard linear stability analysis and Drude electromagnetic model,the impacts of higher-order dispersions and three kinds of typical saturable nonlinearities on modulation instability（MI） have been analyzed and calculated for negative-refractive metamaterials（MMs）.Our results show that the MI gain spectra consist of only one spectral region instead of one or two regions in ordinary materials,which may be close to or far from the zero point.Particularly,the spectrum far from the zero point has a high cut-off frequency but a narrow spectral width,which is obviously beneficial to the generation of high-repetition-rate pulse trains.Moreover,MI characteristics here will vary with the normalized angular frequency which can be modified by adjusting the structures of negative-refractive MMs,signifying the controllability of bistable solitons and MI based applications.The effects of saturable nonlinearities are similar to those in ordinary materials.

A New Large Scale Instability in Rotating Stratified Fluids Driven by Small Scale Forces

In this paper, we find a new large scale instability displayed by a stratified rotating flow in forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. There is no other special constraint concerning the force. In previous papers, the force was either helical or violating parity invariance. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain a detailed study of the linear stage of the instability.

The Large Scale Instability in Rotating Fluid with Small Scale Force

In this paper, we find a new large scale instability in rotating flow forced turbulence. The turbulence is generated by a small scale external force at low Reynolds number. The theory is built on the rigorous asymptotic method of multi-scale development. The nonlinear equations for the instability are obtained at the third order of the perturbation theory. In this article, we explain the nonlinear stage of the instability and the generation vortex kinks.

Anomalous transport driven by ion temperature gradient instability in an anisotropic deuterium-tritium plasma

In this work,the anomalous transport driven by the ion temperature gradient instability is investigated in an anisotropic deuterium-tritium(D-T)plasma.The anisotropic factorα,defined as the ratio of perpendicular temperature to parallel temperature,is introduced to describe the temperature anisotropy in the equilibrium distribution function.The linear dispersion relation in local kinetic limit is derived,and then numerically evaluated to study the dependence of mode frequency on the anisotropic factorαof D and the fraction of T particleεTby choosing three sets of typical parameters,denoted as the cyclone base case,ITER and CFETR cases.Based on the linear results,the mixing length model approximation is adopted to analyze the quasi-linear particle and energy fluxes for D and T.It is found that choosing smallαand largeεTis beneficial for the confinement of particle and energy for D and T.This work may be helpful for the estimation of turbulent transport level in the ITER and CFETR devices.