Kelvin-Helmholtz Instability Research Articles

Nonlinear interaction between double tearing mode and Kelvin–Helmholtz instability with different shear flows

The nonlinear interaction between the double tearing mode (DTM) and Kelvin–Helmholtz (KH) instabilities with different shear flow profiles has been numerically investigated via the use of a compressible magnetohydrodynamics (MHD) model. We focus on KH instabilities in weak and reversed magnetic shear plasmas with strong stabilizing effect of field line bending. Results show that KH instabilities coupled with DTMs occur in these plasmas and the KH mode dominates the instability dynamics, suggesting the crucial role of weak magnetic shear in the formation of high-mode harmonics. For symmetric flows, an asymmetric forced magnetic reconnection configuration is maintained during the growth phase, leading to interlocking of the modes. Additionally, this investigation of the DTM-KH instability interaction contributes to our understanding of the nonlinear reconnection mechanism in the regime of weak and reversed magnetic shear plasmas, which is relevant for astrophysical and fusion studies.

Development of multiphase solver for the modeling of turbidity currents (the case study of Dez Dam)

Dams in semi-arid regions, like Iran's Dez dam, are losing their capacity by sedimentation. Settling sediments reduces clear water, and hydropower plants' efficiency. Reservoir sedimentation relies on turbidity currents (TC). TC head velocity, and sediment content both affect particle tracking, and the removal from reservoirs. To comprehend the TC properties of Dez dam reservoir, large-scale TC modeling is required. To represent large-scale TC, a novel solver is developed. This solver couples a modified OpenFOAM® interFoam solver with the particle concentration transport equation. Two experimental tests, and Dez dam field data were verified and calibrated. The novel solution modeled these instances utilizing a two-dimensional vertical model (width averaged) with RANS turbulence closure, despite the fact that the Dez dam reservoir has a considerable size for numerical modeling. The solver simulated four Dez Dam reservoir scenarios with different water levels. Consequently, when the inlet water depth rose four times, the TC head velocity, and distance traveled by TC doubled. TC in Dez dam is a supercritical flow with the interface instabilities based on its local Richardson number, and gradient Richardson number. Furthermore, Kelvin-Helmholtz instabilities and recirculation vortex combine clear water with TC to reduce the particle concentration.

On the impact of dimensionally-consistent and physics-based inner products for POD-Galerkin and least-squares model reduction of compressible flows

Model reduction of the compressible Euler equations based on proper orthogonal decomposition (POD) and Galerkin orthogonality or least-squares residual minimization requires the selection of inner product spaces in which to perform projections and measure norms. The most popular choice is the vector-valued L2(Ω) inner product space. This choice, however, yields dimensionally-inconsistent reduced-order model (ROM) formulations which often lack robustness. In this work, we try to address this weakness by studying a set of dimensionally-consistent inner products with application to the compressible Euler equations. First, we demonstrate that non-dimensional inner products have a positive impact on both POD and Galerkin/least-squares ROMs. Second, we further demonstrate that physics-based inner products based on entropy principles result in drastically more accurate and robust ROM formulations than those based on non-dimensional L2(Ω) inner products. As test cases, we consider the following problems: the one-dimensional Sod shock tube, a two-dimensional Riemann problem, a two-dimensional Kelvin-Helmholtz instability, and two-dimensional homogeneous isotropic turbulence.

Magnetopause Dynamics at Saturn as Observed by Cassini

AbstractThe occurrence and impacts of magnetopause processes at outer planets, particularly magnetic reconnection and the Kelvin‐Helmholtz instability (KHI), remains unresolved. From a list of 2,114 magnetopause crossings at Saturn spanning the full duration of the Cassini mission, magnetic field and low‐energy plasma properties are analyzed for each crossing to determine the likelihood of particular dynamical processes at Saturn's magnetopause. Using Cassini magnetic field data, crossings are categorized as (a) those with signatures of possible magnetic reconnection, (b) those near/inside a magnetopause surface wave or vortex arising from KHI, and (c) those during quiescent conditions (i.e., lacking signatures indicative of magnetic reconnection or KH waves). Of magnetopause crossings with valid intervals on both sides of the boundary, nearly half of the crossings met criteria for signatures of reconnection, with little dependence on local time or latitude of the magnetopause crossing location. Crossings identified as associated with KHI are found to more likely occur toward the dawn sector as compared to other local times, but with both flanks likely being quasi‐unstable to the instability. Magnetopause properties for crossings with available low‐energy electron data from Cassini are further explored to provide insight into the local plasma conditions that may be conducive to magnetic reconnection and/or KH waves. This investigation reveals that certain dynamics along the magnetopause of Saturn may be more prevalent than previously considered, and provides a basis for a more comprehensive understanding of magnetopause dynamics and plasma transport at the outer planets.

Estimating the energy flux of transverse waves associated with Kelvin-Helmholtz instability in solar coronal loops

Context. The energy flux of kink waves in coronal loops has been estimated in previous studies. Recent numerical simulations have revealed that kink oscillations can induce a Kelvin-Helmholtz Instability (KHI) in magnetic flux tubes. This non-linear process breaks the assumptions that have typically been included in previous eigenmode analyses. Therefore, the current analytical expressions of energy flux need to be re-examined. Aims. In the present work, we aim to compare our numerical energy flux with previous analytical formulae and establish modifications to the estimation of the energy flux of kink waves in coronal loops. Methods. Working within the framework of ideal magnetohydrodynamics (MHD), we conducted three-dimensional (3D) simulations of kink oscillations in coronal cylinders. Forward models were also employed to translate our numerical results into observables using the FoMo code. Results. We find that the previous estimation of the energy flux of kink waves is reasonable up to the point before the KHI is fully developed. However, as small vortices develop, the energy flux derived from the analytical formula becomes smaller than the total Poynting flux calculated from our numerical results. Furthermore, when degrading the original numerical resolution to match a realistic instrumental resolution, for instance, the Extreme Ultraviolet Imager (EUI) on board the Solar Orbiter (SO), the energy flux becomes much smaller than the numerical value. Conclusions. The energy flux calculated from the analytical formula should be modified by multiplying it by a factor of about 2. When it comes to the energy flux estimation based on SO/EUI observations, this factor should be between about 3 and 4.

Damping of coronal oscillations in self-consistent 3D radiative magnetohydrodynamics simulations of the solar atmosphere

Context. Oscillations are abundant in the solar corona. Coronal loop oscillations are typically studied using highly idealised models of magnetic flux tubes. In order to improve our understanding of coronal oscillations, it is necessary to consider the effect of a realistic magnetic field topology and the density structuring. Aims. We analyse the damping of coronal oscillations using a self-consistent 3D radiation-magnetohydrodynamics simulation of the solar atmosphere spanning from the convection zone into the corona, the associated oscillation dissipation and heating, and finally, the physical processes that cause the damping and dissipation. The simulated corona that forms in this model does not depend on any prior assumptions about the shape of the coronal loops. Methods. We analysed the evolution of a bundle of magnetic loops by tracing the magnetic field. Results. We find that the bundle of magnetic loops shows damped transverse oscillations in response to perturbations in two separate instances, with oscillation periods of 177 s and 191 s, velocity amplitudes of 10 km s−1 and 16 km s−1, and damping times of 176 s and 198 s. The coronal oscillations lead to the development of velocity shear in the simulated corona, which results in the formation of vortices seen in the velocity field that are caused by the Kelvin-Helmholtz instability. This contributes to the damping and dissipation of the transverse oscillations. Conclusions. The oscillation parameters and evolution we observed are in line with the values that are typically seen in observations of coronal loop oscillations. The dynamic evolution of the coronal loop bundle suggests that the models of monolithic and static coronal loops with constant lengths might need to be re-evaluated by relaxing the assumption of highly idealised wave guides.

Jump penalty stabilization techniques for under-resolved turbulence in discontinuous Galerkin schemes

Jump penalty stabilization techniques for under-resolved turbulence have been recently proposed for continuous and discontinuous high order Galerkin schemes [1–3]. The stabilization relies on the gradient or solution discontinuity at element interfaces to incorporate localised numerical diffusion in the numerical scheme. This diffusion acts as an implicit subgrid model and stabilizes under-resolved turbulent simulations.This paper investigates the effect of jump penalty stabilization methods (penalising gradient or solution) for stabilization and improvement of high-order discontinuous Galerkin schemes in turbulent regime. We analyze these schemes using an eigensolution analysis, a 1D non-linear Burgers equation (mimicking a turbulent cascade) and 3D turbulent Navier-Stokes simulations (Taylor-Green Vortex and Kelvin-Helmholtz Instability problems).We show that the two jump penalty stabilization techniques can stabilize under-resolved simulations thanks to the improved dispersion-dissipation characteristics (when compared to non-penalized schemes) and provide accurate results for turbulent flows. The numerical results indicate that the proposed jump penalty methods stabilize under-resolved simulations and improve the simulations, when compared to the original unpenalized scheme and to classic explicit subgrid models (Smagorinsky and Vreman).

Estimation of the Kelvin–Helmholtz Unstable Boundary

AbstractThe Kelvin–Helmholtz (KH) instability is one of the most important mechanisms of the viscous‐like interaction between the solar wind and the magnetosphere (MSP), which transport the mass, energy, momentum, and magnetic flux. Thus, it is important to examine whether the magnetopause boundary is KH unstable or not. Based on the KH onset conditions, this report proposes to use a matrix to identify the most KH unstable direction based on the in situ measurements of the density, velocity, and magnetic field in the MSP and magnetosheath. The range of the KH unstable direction can be easily estimated based on the eigenvalues of the matrix. The eigenvectors of the matrix provide a new boundary normal coordinate system, which could be useful for 2‐D KH instability simulation.

Numerical study on coupled flow characteristics of a gas-solid two-phase jet in a supersonic crossflow

In this study, the Eulerian-Lagrangian scheme coupled with the gas-solid two-phase Reynolds-average Navier-Stokes (RANS) method was used to study the airflow and particles flow characteristics of particles of different diameters injected into a supersonic flow field by a sonic jet. The results show that introducing small particles has little effect on the flow field. When the particle diameter is 1e-6 m, most particles are mainly distributed in the shear layer, and some parts of the particles are sucked into the surface trailing counter-rotating vortex pairs (TCVP) and the wall boundary layers by the airflow. The introduction of large diameter particles hinders the jet's development, reduces the Mach disk's height, and makes the counter-rotating vortex pair (CVP) closer to the wall. This leads to a decrease in the streamwise velocity and an increase in the wall-normal velocity near the wall downstream of the jet. The streamwise velocity increases and the wall-normal velocity decreases at the far wall downstream of the jet. At the same time, it exacerbates the Kelvin-Helmholtz (K-H) instability in the shear layer on the windward side of the jet, forming a large-scale coherent structure between the shear layer and crossflow. The penetration depth and diffusion range of particles increase with particle diameter and density, and the velocity decreases with particle diameter increase by comparing the trajectories of particles with different diameters and densities.

Transient film outflow performances of laminated cooling configurations in leading edges of turbine vane

In this work, time-resolved quantitative light sheet technique is used to capture the transient outflow performances of the laminated cooling in turbine vane leading edges. A series of numerical simulations are performed to deeply understand the intrinsic flow and heat transfer mechanisms. Two laminated structures are compared, one is a traditional design with uniform hole-diameter (UD), and the other contains non-uniform hole-diameters (NUD) with locally-enlarged film and impingement holes on pressure side. Time-averaged results show that NUD can obtain a higher film effectiveness and a better film coverage due to the decreased momentum of cooling air-jet, and the relative improvement from UD can achieve 58.7%. The unsteadiness analysis of transient film is conducted by quantifying the standard deviation of instantaneous data, and it shows that the fluctuation of cooling air-jet mainly originates from Kelvin-Helmholtz instability at mainstream/coolant interfaces and separation vortex. The new design of NUD can also obtain a low near-wall unsteadiness level, because the separation vortex disappears on target surface, which implies a lower risk of thermal damage. Moreover, the mass flow rate of cooling air is an important factor on transient film performance, which can aggravate the separation of cooling air-jet and cause a higher unsteadiness level.

Legolas 2.0: Improvements and extensions to an MHD spectroscopic framework

We report on recent extensions and improvements to the Legolas code, which is an open-source, finite element-based numerical framework to solve the linearised (magneto)hydrodynamic equations for a three-dimensional force- and thermally balanced state with a nontrivial one-dimensional variation. The standard Fourier modes imposed give rise to a complex, generalised non-Hermitian eigenvalue problem which is solved to quantify all linear wave modes of the given system in either Cartesian or cylindrical geometries. The framework now supports subsystems of the eight linearised MHD equations, allowing for pure hydrodynamic setups, only one-dimensional density/temperature/velocity variations, or the option to treat specific closure relations. We discuss optimisations to the internal datastructure and eigenvalue solvers, showing a considerable performance increase in both execution time and memory usage. Additionally the code now has the capability to fully visualise eigenfunctions associated with given wave modes in multiple dimensions, which we apply to standard Kelvin-Helmholtz and Rayleigh-Taylor instabilities in hydrodynamics, thereby providing convincing links between linear stability analysis and the onset of non-linear phenomena.

Investigating the Occurrence of Kelvin‐Helmholtz Instabilities at Jupiter's Dawn Magnetopause

AbstractWe use the Kelvin‐Helmholtz instability (KHI) condition with particle and magnetic field observations from Jovian Auroral Distributions Experiment and MAG on Juno along the dawn flank of Jupiter's magnetosphere. We identify the occurrence of magnetopause crossings that show evidence of being KH (Kelvin‐Helmholtz) unstable. When estimating the k vector to be parallel to the velocity shear, we find that 25 of 62 (40%) magnetopause crossings satisfy the KHI condition. When considering the k vector of the maximum growth rate through a solid angle approach, we find that 60 of 62 (97%) events are KH unstable. This study shows evidence of KH waves at Jupiter's dawn flank, including primary drivers such as high velocity shears and changes in plasma pressure. Signatures of magnetic reconnection were also observed in ∼25% of the KH unstable crossings. We discuss these results and their implication for the prevalence of KHI at Juno's dawn magnetopause as measured by Juno.

Analysis of a multiple non-supercell tornado event in Mexico

Multiple tornado events frequently occur in different parts of the world. A region that seems favorable for recurring multiple tornado events due to its geographical location and topography is the eastern sector of the Trans-Mexican Volcanic Belt. A notable multiple tornado event that occurred in this region is investigated. It consisted of five simultaneous tornadoes during the convergence of three air masses: a cold air mass displaced from the north with moderately high relative humidity and specific humidity, a comparatively warm air mass with moderate relative humidity from the southeast, and a hotter air mass with low relative humidity from the southwest. This situation generated a line of intense horizontal wind shear through which the five tornadoes occurred. Numerical simulations revealed three cyclonic vortices and other minor disturbances along the shear line. Vertical cross-sections show rising air in these disturbances suggesting a cyclonic character. The results indicate that the relatively warm mass from the southeast moves over the one associated with a cold front coming from the north, generating multiple cyclonic rotation zones. Experiments with Lagrangian particles revealed vertical movements in the cyclonic rotation zones implying that the maximum heights of the tornadoes varied between 1000 and 1500 m. Moisture flux convergence calculations display structures resembling Kelvin-Helmholtz instabilities. This research proposes a conceptual model where the convergence of masses induced by topography can lead to multiple tornado generation.

Effect of the transverse magnetic field on the Kelvin–Helmholtz instability of the supersonic mixing layer

The Kelvin–Helmholtz instability (KHI) stems from the velocity shear in a single continuous fluid or a velocity difference across the interface between two distinct fluids. The effect of the transverse magnetic field on the KHI of the supersonic mixing layer is investigated by numerical method. An algorithm with corner-transport-upwind and constrained-transport is used to solve the equations of magnetohydrodynamic (MHD). The evolutions of vorticity, pressure, and shock-vortex structure of the supersonic mixing layer with and without the magnetic field are studied qualitatively and quantitively. The suppression mechanism of the transverse magnetic field on the KHI is analyzed from the aspects of magnetic pressure and magnetic tension, respectively. The results show that the transverse magnetic field has a significant influence on the evolution of shock-vortex structure in the supersonic mixing layer. The magnetic pressure makes the vorticity deposition at the shear layer, and the magnetic tension produces an anti-bending torque on the shear layer. Under these two kinds of effects, the instability of the shear layer is suppressed effectively, and a long-standing banded structure of the shear layer is formed and teared later, which results in a “fishhook-like” structure occurred. Moreover, the transverse magnetic field inhibits the formation of the high-convection Mach value (Mc) regions, which effectively inhibits the formation of shocklets. In addition, with the effect of the magnetic field, a premature laminar-turbulent transition is stimulated at the core region of the vortex structure.

On Monami modes and scales of a flexible vegetation array in a laminar boundary layer

Flexible aquatic vegetation exists widely in nature and serves multiple hydro-environmental functions mainly through fluid–structure interactions. The waving motion of vegetation arrays, known as Monami, is predominantly governed by Kelvin–Helmholtz (KH) instability, and its characteristic scales, such as wave height and wavelength, are still being explored. In this paper, the interactions between a large array of flexible vegetations and a laminar boundary-layer flow are investigated using direct numerical simulation. The parameters used are the Reynolds number Re = 400, mass ratio β = 1.0, bending rigidity γ = 0.04–0.22, and gap distance d = 0.4–1.6. A low frequency in Monami is found to be related to the fluctuation frequency of the onset position of the KH instability, which leads to the identification of four different Monami modes: regular Monami, quasi-regular Monami A, quasi-regular Monami B, and irregular Monami. The influences of the bending rigidity and gap distance on the Monami modes, KH instability onset position, and Monami characteristic scales are discussed. It was found that the causes of spatial and temporal variations in the characteristic scales of Monami vary depending on the mode. In the regular Monami mode, these variations result from the evolution of the KH vortex. In the quasi-regular Monami A mode, they are strongly affected by the shifting of the onset position of the KH instability. In the other two modes, these variations are caused by a combination of the fluctuation in the KH instability onset position and the complex interaction between vortices.

Analysis of turbulent mixing in a methane–oxygen recessed injector for space propulsion

Turbulent mixing in a methane–oxygen recessed injector is studied using direct numerical simulations. The operating point is chosen to be fuel-rich and at high pressure to recreate a representative environment for space propulsion applications. The results are used to investigate the transport of the turbulent mixture fraction statistics and the validity of conventional transport models. It is observed that molecular diffusion is only relevant near the boundary layer of the injection recess cavity and at the recirculation zone. Moreover, turbulent mixing in the axial direction is negligible as radial turbulent diffusion dominates. Radial turbulent diffusion near injection is driven by Kelvin–Helmholtz Instabilities (KHI) manifesting at large scales in the order of the injector geometry. The dominance of this process over microscale mixing originates negative turbulent diffusion, which produces a mixture resegregation and the appearance of lean pockets far from the oxidizer injection plane. Gradient models display poor capabilities for the prediction of this sort of phenomena. Closure models for the turbulent mixing transport terms are proposed and evaluated. An anisotropic gradient model is devised, providing performance improvements within the recess cavity and the recirculation region. In addition, a novel filtered Reynolds-averaged Navier Stokes approach based on the mixing state is proposed. This new methodology shows excellent prediction capabilities in the regions dominated by KHI, accurately predicting negative turbulent diffusivity. The challenges associated with this model are commented on, and strategies to enable its application are proposed.

Kelvin–Helmholtz instability at the interface of H ii region and molecular cloud under the influence of ambipolar diffusion: a discontinuous model of the interface

ABSTRACT For typical flow velocities in the interstellar medium (ISM), the Kelvin–Helmholtz instability (KHI) may result in the development of structures in molecular clouds near the interface between the clouds and H ii regions flowing past them (Berné et al. 2010). Ambipolar diffusion (AD) is one of the significant mechanisms considered frequently in the dynamics of molecular clouds. It may play a relevant role in the development of the KHI in the interface of the H ii region and the molecular clouds. Here, we examine the role of AD in the evolution of the KHI, using linear perturbation analysis. We model the interaction of two regions as a planar discontinuity separating two fluids in relative motion. Linear analysis, for a certain range of magnetosonic Mach number of flow ($\mathcal {M}_{sA1}\lt 1$), shows that AD has a destabilizing effect on the KHI and consequently decreases the e-fold time-scale of instability. The results indicate that AD is more effective on the KHI for large magnetosonic Mach numbers than for low magnetosonic Mach numbers. This may give rise to the development of larger numbers of KH structures in high-velocity flows. The results also indicate that AD is more effective for perturbation wavelengths $\lambda _{\rm KH} \ \lt \ 1\rm pc$ than for $\lambda _{\rm KH}\gt 1\rm pc$. This nominates a length-scale ($L=1 \rm \, pc$) above which AD is not important for the formation of KH structures. Conforming to the results, AD is proposed as a triggering factor in the development of the small-scale KH structures in the regions of high-velocity streams in ISM.

Nonlinear Kelvin-Helmholtz instability of a horizontal interface separating two electrified Walters' B liquids: A new approach

The present study scrutinizes the nonlinear stability of a plane interface concerning two fluids of Walters' B (WB) type. An unchanging tangential electric field (EF) impact upon the two dielectric fluids in the existence of a steady relative velocities. The two fluids have different density viscoelasticity, electrical properties, and in the existence of a surface tension at the interface. The growth implication in engineering and applied physics has motivated the attention of this concern. Due to the difficulty of the mathematical process, the viscoelastic contribution is established only at the interface, which is called the viscous potential flow (VPF). Therefore, the governing equations of motion are analyzed in a linear approach , instantaneously, the nonlinear boundary circumstances (BCs) are provided. This technique creates a nonlinear illustrative equation of the interface displacement. As well-known, the linear stability approach has intensively appeared in several literatures. Consequently, our study focuses only on the nonlinear sense. A new methodology based on the non-perturbative analysis (NPA) is employed to investigate the nonlinear stability and inspect the interface deflection in different situations. The latter equation represents a partial differential equation (PDE) with complex coefficients of the border displacement. Under some restrictions, this equation represents a nonlinear hybrid Rayleigh-Helmholtz oscillator. The considered NPA produces an equivalent linear equation. A numerical methodology is employed to confirm the solutions of the two equations. As well-known, the non-dimensional physical numbers are potential to analyze the structures of a fluid flow. Additionally, they reduce the number of variables that describe the system. These quantities frequently have physical meaning which help in some physical interpretations. Therefore, the investigation reveals several non-dimensional physical numerals. The instability benchmarks are theoretically inspected and computationally illustrated through a set of diagrams. The EF strength is strategized against the parameter of the traveling wave number, where the concern of stability/instability is portrayed. We think that the present analysis is easy, promising, and powerful, and may be applied in diverse contexts.

Clear Air Turbulence Resolved by Numerical Weather Prediction Model Validated by Onboard and Virtual Flight Data

AbstractA clear air turbulence (CAT) occurred on 30 December 2020 over Tokyo, Japan. The CAT was largely generated by breaking Kelvin‐Helmholtz (KH) instability waves in the free atmosphere. A regional numerical weather prediction model simulated the event with fine resolution (35 m). Onboard‐recorded flight data and a flight simulation were utilized to validate the meteorological simulation. The locations of the reproduced strong turbulence agree well with the regions where flights encountered turbulence on that day. In a simulation with the finest resolution, the KH waves and their breaking were resolved. When the resolution was finer, the turbulent eddies were stronger, causing meteorological effects on the airplanes. The response of a virtual airplane to the simulated turbulence was estimated using a flight simulation. By comparing onboard‐recorded data with virtual flight data, we confirm that turbulent eddies are reasonably reproduced.

Research on the Mesoscopic Characteristics of Kelvin–Helmholtz Instability in Polymer Fluids with Dissipative Particle Dynamics

In this paper, the two-dimensional Kelvin–Helmholtz (KH) instability occurring in the shear flow of polymer fluids is modeled by the dissipative particle dynamics (DPD) method at the coarse-grained molecular level. A revised FENE model is proposed to properly describe the polymer chains. In this revised model, the elastic repulsion and tension are both considered between the adjacent beads, the bond length of which is set as one segment’s equilibrium length. The entanglements between polymer chains are described with a bead repulsive potential. The characteristics of such a KH instability in polymer fluid shear flow can be successfully captured in the simulations by the use of the modified FENE model. The numerical results show that the waves and vortexes grow more slowly in the shear flow of the polymer fluids than in the Newtonian fluid case, these vortexes become flat, and the polymer impedes the mixing of fluids and inhibits the generation of turbulence. The effects of the polymer concentration, chain length, and extensibility are also investigated regarding the evolution of KH instability. It is shown that the mixing of two polymer fluids reduces, and the KH instability becomes more suppressed as the polymer concentration increases. The vortexes become much longer with the evolution of the elongated interface as the chain length turns longer. As the extensibility increases, the vortexes become more flattened. Moreover, the roll-up process is significantly suppressed if the polymer has sufficiently high extensibility. These observations show that the polymer and its properties significantly influence the formation and evolution of the coherent structures such as the waves and vortexes in the KH instability progress.