The generalized Kelvin-Helmholtz (KH) and Miles mechanisms of the water wave generation by wind are investigated for two-layer piece-wise linear model of the wind profile. It is shown by asymptotic expansions in small air-to-water density ratio that two mechanisms of the instability operate in quite different scales. Miles' short waves are generated by weak winds, in particular, Miles' regime is responsible for initiation of the instability at the minimum wind speed, while the generalized KH regime dominates at strong winds and raises moderately-short waves.
In this fluid dynamics video prepared for the APS-DFD Gallery of Fluid Motion we study the Kelvin-Helmholtz instability for both Newtonian and viscoelastic jets. The nonlinear dynamics of the jet motion are slowed down by orders of magnitude using a synchronized strobe effect coupled with precise timing control of perturbation frequencies. Our results show that at high wave-numbers the imposed perturbations initially grow linearly with time and the jet axis remains straight while the Kelvin-Helmholtz wave amplitude grows and rolls up into bags that encapsulate the central jet within themselves…
The Kelvin-Helmholtz instability in superfluids is discussed, based on the first experimental observation of such instability at the interface between superfluid 3He-A and superfluid 3He-B (cond-mat/0111343). We discuss why (i) the Kelvin-Helmholtz criterion, (ii) the Landau critical velocity for nucleation of ripplons, and (iii) the free energy consideration, all give different values for the instability treshold.
We demonstrate an experimentally feasible method for generating the classical Kelvin-Helmholtz instability in a single component atomic Bose-Einstein condensate. By progressively reducing a potential barrier between two counter-flowing channels we seed a line of quantised vortices, which precede to form progressively larger clusters, mimicking the classical roll-up behaviour of the Kelvin-Helmholtz instability. This cluster formation leads to an effective superfluid shear layer, formed through the collective motion of many quantised vortices. From this we demonstrate a straightforward method t…
We report experimental results for the Kelvin-Helmholtz instability between two immiscible fluids in parallel flow in a Hele-Shaw cell. We focus our interest on the influence of the gap size between the walls on the instability characteristics. Experimental results show that the instability threshold, the critical wavelength, the phase velocity and the spatial growth rate depend on this gap size. These results are compared to both the previous two-dimensional analysis of Gondret and Rabaud (1997) and the three-dimensional analysis recently derived by Plourabou=E9 and Hinch (2001), showing that…
Screech tones in supersonic jets are underpinned by resonance between downstream-travelling Kelvin-Helmholtz waves and upstream-travelling acoustic waves. Specifically, recent work suggests that the relevant acoustic waves are guided within the jet and are described by a discrete mode of the linearised Navier-Stokes equations. However, the reflection mechanism that converts downstream-travelling waves into upstream-travelling waves, and vice versa, has not been thoroughly addressed, leading to missing physics within most resonance models. In this work we investigate the reflection and transmis…
We derive boundary conditions at interfaces (contact discontinuities) for a class of Lagrangian models describing, in particular, bubbly flows. We use these conditions to study Kelvin-Helmholtz' instability which develops in the flow of two superposed layers of a pure incompressible fluid and a fluid containing gas bubbles, co-flowing with different velocities. We show that the presence of bubbles in one layer stabilizes the flow in some intervals of wave lengths.
We show that the dynamics, in particular the Kelvin-Helmholtz (KH) instability, of an inviscid fluid with velocity shear admits Parity-Time (PT) symmetry, which provides a physical explanation to the well-known observation that the spectrum of the perturbation eigenmodes of the system is symmetric with respect to the real axis. It is found that the KH instability is triggered when and only when the PT symmetry is spontaneously broken. The analysis of PT symmetry also reveals that the relative phase between parallel velocity and pressure perturbations needs to be locked at $π/2$ when the instab…
We theoretically study the Kelvin-Helmholtz instability in phase-separated two-component Bose-Einstein condensates using the Gross-Pitaevskii and Bogoliubov-de Gennes models. A flat interface between the two condensates is shown to deform into sawtooth or Stokes-like waves, leading to the formation of singly quantized vortices on the peaks and troughs of the waves. This scenario of interface instability in quantum fluids is quite different from that in classical fluids.
We analyze nonlinear dynamics of the Kelvin-Helmholtz quantum instability of the He-II free surface, which evolves during counterpropagation of the normal and superfluid components of liquid helium. It is shown that in the vicinity of the linear stability threshold, the evolution of the boundary is described by the $|ϕ|^4$ Klein-Gordon equation for the complex amplitude of the excited wave with cubic nonlinearity. It is important that for any ratio of the densities of the helium component, the nonlinearity plays a destabilizing role, accelerating the linear instability evolution of the boundar…
A relative motion of the normal and superfluid components of Helium II results in Kelvin-Helmholtz instability (KHI) at their common free surface. We found the exact solutions for the nonlinear stage of the development of that instability. Contrary to the usual KHI of the interface between two fluids, the dynamics of Helium II free surface allows decoupling of the governing equations with their reduction to the Laplace growth equation which has the infinite number of exact solutions including the formation of sharp cusps at free surface in a finite time.
We study the dynamical system of a forced stratified mixing layer at finite Reynolds number $Re$, and Prandtl number $Pr=1$. We consider a hyperbolic tangent background velocity profile in the two cases of hyperbolic tangent and uniform background buoyancy stratifications. The system is forced in such a way that these background profiles are a steady solution of the governing equations. As is well-known, if the minimum gradient Richardson number of the flow, $Ri_m$, is less than a certain critical value $Ri_c$, the flow is linearly unstable to Kelvin-Helmholtz instability in both cases. Using …
The nonlinear evolution of the Kelvin-Helmholtz instability is a popular test for code verification. To date, most Kelvin-Helmholtz problems discussed in the literature are ill-posed: they do not converge to any single solution with increasing resolution. This precludes comparisons among different codes and severely limits the utility of the Kelvin-Helmholtz instability as a test problem. The lack of a reference solution has led various authors to assert the accuracy of their simulations based on ad-hoc proxies, e.g., the existence of small-scale structures. This paper proposes well-posed Kelv…
When a fast-moving drop impacts onto a smooth substrate, splashing will be produced at the edge of the expanding liquid sheet. This ubiquitous phenomenon lacks a fundamental understanding. Combining experiment with model, we illustrate that the ultrathin air film trapped under the expanding liquid front triggers splashing. Because this film is thinner than the mean free path of air molecules, the interior airflow transfers momentum with an unusually high velocity comparable to the speed of sound and generates a stress 10 times stronger than the airflow in common situations. Such a large stress…
In the paper, the effects of initial perturbations on the Rayleigh-Taylor instability (RTI), Kelvin-Helmholtz instability (KHI), and the coupled Rayleigh-Taylor-Kelvin-Helmholtz instability (RTKHI) systems are investigated using a multiple-relaxation-time discrete Boltzmann model. Six different perturbation interfaces are designed to study the effects of the initial perturbations on the instability systems. Based on the mean heat flux strength $D_{3,1}$, the effects of initial interfaces on the coupled RTKHI are examined in detail. The research is focused on two aspects: (i) the main mechanism…
We provide numerical evidence that a Kelvin-Helmholtz instability occurs in the Dirac fluid of electrons in graphene and can be detected in current experiments. This instability appears for electrons in the viscous regime passing though a micrometer-scale obstacle and affects measurements on the time scale of nanoseconds. A possible realization with a needle-shaped obstacle is proposed to produce and detect this instability by measuring the electric potential difference between contact points located before and after the obstacle. We also show that, for our setup, the Kelvin-Helmholtz instabil…
We present a fluid dynamics video showing the results of a 9-billion atom molecular dynamics simulation of complex fluid flow in molten copper and aluminum. Starting with an atomically flat interface, a shear is imposed along the copper-aluminum interface and random atomic fluctuations seed the formation of vortices. These vortices grow due to the Kelvin-Helmholtz instability. The resulting vortical structures are beautifully intricate, decorated with secondary instabilities and complex mixing phenomena. This work performed under the auspices of the U.S. Department of Energy by Lawrence Liverm…
The effect of Prandtl number on the evolution of Kelvin-Helmholtz (KH) billows and the amount of mixing they generate is studied through direct numerical simulation (DNS). The results indicate that the time evolution of the rate of mixing through different stages of the life-cycle of KH flow is significantly influenced by the Prandtl number. As the Prandtl number increases, the final amount of mixing increases for Reynolds that are too low to support active three-dimensional motions. This trend is the opposite in sufficiently high Reynolds number KH flows that can overcome viscous effects, and…
The Kelvin-Helmholtz instability has been proposed as a mechanism to extract energy from magnetohydrodynamic (MHD) kink waves in flux tubes, and to drive dissipation of this wave energy through turbulence. It is therefore a potentially important process in heating the solar corona. However, it is unclear how the instability is influenced by the oscillatory shear flow associated with an MHD wave. We investigate the linear stability of a discontinuous oscillatory shear flow in the presence of a horizontal magnetic field within a Cartesian framework that captures the essential features of MHD osc…
Kelvin-Helmholtz {instability induced} turbulence is one promising mechanism by which loops in the solar corona can be heated by MHD waves. In this paper we present an analytical model of the dissipation rate of {Kelvin-Helmholtz instability induced} turbulence $\varepsilon_{\rm D}$, finding it scales as the wave amplitude ($d$) to the third power ($\varepsilon_{\rm D}\propto d^3$). Based on the concept of steady-state turbulence, we expect the turbulence heating throughout the volume of {the} loop to match the total energy injected through its footpoints. In situations where this holds, the w…
The first realization of instabilities in the shear flow between two superfluids is examined. The interface separating the A and B phases of superfluid He-3 is magnetically stabilized. With uniform rotation we create a state with discontinuous tangential velocities at the interface, supported by the difference in quantized vorticity in the two phases. This state remains stable and nondissipative to high relative velocities, but finally undergoes an instability when an interfacial mode is excited and some vortices cross the phase boundary. The measured properties of the instability are consiste…
The dynamics of singularity formation on the interface between two ideal fluids is studied for the Kelvin-Helmholtz instability development within the Hamiltonian formalism. It is shown that the equations of motion derived in the small interface angle approximation (gravity and capillary forces are neglected) admit exact solutions in the implicit form. The analysis of these solutions shows that, in the general case, weak root singularities are formed on the interface in a finite time for which the curvature becomes infinite, while the slope angles remain small. For Atwood numbers close to unit…
The macroscopic dynamics of a droplet impacting a solid is crucially determined by the intricate air dynamics occurring at the vanishingly small length scale between droplet and substrate prior to direct contact. Here we investigate the inverse problem, namely the role of air for the impact of a horizontal flat disk onto a liquid surface, and find an equally significant effect. Using an in-house experimental technique, we measure the free surface deflections just before impact, with a precision of a few micrometers. Whereas stagnation pressure pushes down the surface in the center, we observe …
On reference solutions and the sensitivity of the 2D Kelvin-Helmholtz instability problem
Georg-August-Universität Göttingen（哥廷根大学）；Weierstrass Institute for Applied Analysis and Stochastics（魏尔斯特拉斯应用分析与随机性研究所）；Freie Universität Berlin（柏林自由大学）；TU Wien（维也纳工业大学）
Prominences are incredibly dynamic across the whole range of their observable spatial scales, with observations revealing gravity-driven fluid instabilities, waves, and turbulence. With all these complex motions, it would be expected that instabilities driven by shear in the internal fluid motions would develop. However, evidence of these have been lacking. Here we present the discovery in a prominence, using observations from the Interface Region Imaging Spectrograph (IRIS), of a shear flow instability, the Kelvin-Helmholtz sinusoidal-mode of a fluid channel, driven by flows in the prominence…
Quantum turbulence (QT) generated by the Rayleigh-Taylor instability in binary immiscible ultracold 87Rb atoms at zero temperature is studied theoretically. We show that the quantum vortex tangle is qualitatively different from previously considered superfluids, which reveals deep relations between QT and classical turbulence. The present QT may be generated at arbitrarily small Mach numbers, which is a unique property not found in previously studied superfluids. By numerical solution of the coupled Gross-Pitaevskii equations we find that the Kolmogorov scaling law holds for the incompressible…
Kelvin-Helmholtz instability (KHI) is widely spread in nature on scales from micrometer up to Galactic one. This instability refers to the growth of perturbation of an interface between two parallel streams of Newtonian fluids with different velocities and densities, destabilized by shear strain and stabilized by density stratification with the heavier fluid at the bottom. Here, we report the discovery of the purely elastic KH-like instability in planar straight channel flow of viscoelastic fluid, which is theoretically considered to be stable. However, despite the remarkable similarity to the…
Kelvin-Helmholtz instabilities are common in astrophysical systems, ranging from jet black holes up to protoplanetary accretion disk. An astrophysical object with strong characteristics of the Kelvin-Helmholtz instability is Caraguejo Nebula, in which the material expansion was caused by the explosion of a supernova about 1000 years ago. This instability occurs at the boundary between two fluids of different densities when one of the fluids accelerated with respect to the other. In order to study this instability, we performed a simulation with the code ATHENA Eulerian mesh. For this simulatio…
Many dynamic pipe flow simulator tools are capable of predicting the onset of hydrodynamic flow instability through detailed simulation. These instabilities provide a natural mechanism for flow regime transition. The quality and reliability of flow predictions are however strongly dependent upon the numerics within these simulator tools, the scheme type and resolution in particular. A Kelvin-Helmholtz stability analysis for the differential two-fluid model is in the present work presented and extended to discrete representations of said model. This analysis provides algebraic expressions which…
Three amplification mechanisms present in turbulent jets, namely lift-up, Kelvin-Helmholtz, and Orr, are characterized via global resolvent analysis and spectral proper orthogonal decomposition (SPOD) over a range of Mach numbers. The lift-up mechanism was recently identified in turbulent jets via local analysis by Nogueira et al. (J. Fluid Mech., vol. 873, 2019, pp. 211-237) at low Strouhal number ($St$) and non-zero azimuthal wavenumbers ($m$). In these limits, a global SPOD analysis of data from high-fidelity simulations reveals streamwise vortices and streaks similar to those found in turb…
We investigate the various physical mechanisms that underlie the dynamical instability of a quantized vortex array at the interface between two counter-propagating superflows in a two-dimensional Bose--Einstein condensate. Instabilities of markedly different nature are found to dominate in different flow velocity regimes. For moderate velocities where the two flows are subsonic, the vortex lattice displays a quantized version of the hydrodynamic Kelvin--Helmholtz instability (KHI), with the vortices rolling up and co-rotating. For supersonic flow velocities, the oscillation involved in the KHI…
Recent observations show cool, oscillating prominence threads fading when observed in cool spectral lines and appearing in warm spectral lines. A proposed mechanism to explain this evolution is that the threads were heated by turbulence driven by the Kelvin--Helmholtz instability that developed as a result of wave-driven shear flows on the surface of the thread. As the Kelvin--Helmholtz instability is an instability that works to mix the fluids, in the solar corona it can be expected to work by mixing the cool prominence material with that of the hot corona to form a warm boundary layer. In th…
Viscous solitons are strongly non-linear surface deformations generated by blowing wind over a liquid beyond a critical viscosity. Their shape and dynamics result from a balance between wind drag, surface tension and viscous dissipation in the liquid. We investigate here the influence of the liquid viscosity in their generation and propagation. Experiments are carried out using silicon oils, covering a wide range of kinematic viscosities $ν_\ell$ between 20 and 5000~mm$^2$~s$^{-1}$. \modif{We show that, for $ν_\ell> 200$~mm$^2$~s$^{-1}$, viscous solitons are sub-critically generated from an un…
The nonlinear magnetic Kelvin-Helmholtz instability (KHi), and the turbulence it creates, appears in many astrophysical systems. This includes those systems where the local plasma conditions are such that the plasma is not fully ionised, for example in the lower solar atmosphere and molecular clouds. In a partially ionised system, the fluids couple via collisions which occur at characteristic frequencies, therefore neutral and plasma species become decoupled for sufficiently high-frequency dynamics. Here we present high-resolution 2D two-fluid simulations of the nonlinear KHi for a system that…
