We report on a new class of electromagnetically-driven fluid interface instability. Using the optical radiation pressure of a cw laser to bend a very soft near-critical liquid-liquid interface, we show that it becomes unstable for sufficiently large beam power P, leading to the formation of a stationary beam-centered liquid micro-jet. We explore the behavior of the instability onset by tuning the interface softness with temperature and varying the size of the exciting beam. The instability mechanism is experimentally demonstrated. It simply relies on total reflection of light at the deformed interface whose condition provides the universal scaling relation for the onset Ps of the instability.
In this work we consider the effect of a small-scale helical driving force on fluid with a stable temperature gradient with Reynolds number Re<<1. At first glance, this system does not appear to have any instability. However, we show that large-scale vortex instability appears in fluid despite its stable stratification. In the non-linear mode, this instability gets saturated and gives a large number of stationary spiral vortex structures. Among these structures there is a stationary helical soliton and a kink of a new type. The theory is built on the rigorous asymptotical method of multi-scale…
Stability criterion for the surface gravity capillary waves in a flowing two-layered fluid system with viscous dissipation is investigated. It is seen that the dissipative instability of negative energy waves is absent,- contrary to what earlier authors have concluded. Their error is identified to arise from an erroneous choice of the dissipation law, in which the wave profile velocity is wrongly equated to the particle velocity. Our corrected dissipation law is also shown to restore Galilean invariance to the stability condition of the system.
We derive a minimal continuum model to investigate the hydrodynamic mechanism behind the fingering instability recently discovered in a suspension of microrollers near a floor [Driscoll et al. Nature Physics, 2016]. Our model, consisting of two continuous lines of rotlets, exhibits a linear instability driven only by hydrodynamics interactions, and reproduces the lengthscale selection observed in large scale particle simulations and in experiments. By adjusting only one parameter, the distance between the two lines, our dispersion relation exhibits quantitative agreement with the simulations a…
Strong effects of the Faraday instability on suspensions of rodlike colloidal particles are reported through measurements of the critical acceleration and of the surface wave amplitude. We show that the transition to parametrically excited surface waves displays discontinuous and hysteretic features. This subcritical behaviour is attributed to the shear-thinning properties of our colloidal suspensions thanks to a phenomenological model based on rheological data under large amplitude oscillatory shear. Birefringence measurements provide direct evidence that Faraday waves induce local nematic or…
Starting from the Vlasov-Maxwell system, an exact relativistic hydrodynamic closure for a special type water bag distributions satisfying the Vlasov equation has been derived. It has been shown that the hydrodynamic equations are fully equivalent to the original Vlasov-Maxwell equations. The linear stability of the exact hydrodynamic closure has been studied as well. It has been shown that all basic features of the small signal gain can be derived from the fluid dynamic description developed here. Satisfactory agreement with previously reported results has been also found.
We investigate analytically the magnetic instability in a rotating and electrically conducting fluid induced by an imposed magnetic field with its associated electric current. The short-wavelength approximation is used in the linear stability analysis, i.e. the length scale of the imposed field is much larger than the wavelength of perturbations. The dispersion relationship is derived and then simplified to give the criteria for the onset of the magnetic instability in three cases of imposed field, namely the axial dependence, the radial dependence and the mixed case. The orientation of rotati…
We provide the possible resolution for the century old problem of hydrodynamic shear flows, which are apparently stable in linear analysis but shown to be turbulent in astrophysically observed data and experiments. This mismatch is noticed in a variety of systems, from laboratory to astrophysical flows. There are so many uncountable attempts made so far to resolve this mismatch, beginning with the early work of Kelvin, Rayleigh, and Reynolds towards the end of the nineteenth century. Here we show that the presence of stochastic noise, whose inevitable presence should not be neglected in the st…
We impose a linearized Eulerian perturbation on a steady, shallow, radial outflow of a liquid (water), whose local pressure function includes both the hydrostatic and the Laplace pressure terms. The resulting wave equation bears the form of a hydrodynamic metric. A dispersion relation, extracted from the wave equation, gives an instability due to surface tension and the cylindrical flow symmetry. Using the dispersion relation, we also derive three known relations that scale the radius of the circular hydraulic jump in the outflow. The first two relations are scaled by viscosity and gravity, wi…
A study was made of the instability that arises when acoustic and gravity waves propagate in an inhomogeneous medium which is characterized by oscillatory approach of the reaction coordinates to the steady state. It is shown that loss of stability can occur in two different ways: by bifurcation of the periodic solution and by Eckhaus bifurcation. It is considered how an introduced nonlinearity stabilizes the unstable modes when the controlling parameter passes through the bifurcation points.
The onset of monami ~-- the synchronous waving of sea grass beds driven by a steady flow -- is modeled as a linear instability of the flow. Unlike previous works, our model considers the drag exerted by the grass in establishing the steady flow profile, and in damping out perturbations to it. We find two distinct modes of instability, which we label Mode 1 and Mode 2. Mode 1 is closely related to Kelvin-Helmholtz instability modified by vegetation drag, whereas Mode 2 is unrelated to Kelvin-Helmholtz and arises from an interaction between the flow in the vegetated and unvegetated layers. The v…
Many hydrodynamic instability patterns can be put into correspondence with a subset of characteristic surfaces of tangential discontinuities. These topological limits sets to systems of hyperbolic PDE's are locally unstable, but a certain subset associated with minimal surfaces are globally stabilized, persistent and non-dissipative. Sections of these surfaces are the spiral scrolls so often observed in hydrodynamic wakes. This method of wake production does not depend explicitly upon viscosity.
We venture for the comparison between growth rates for magnetorotational instability (MRI) and hydrodynamics instability in the presence of an extra force in the local Keplerian accretion flow. The underlying model is described by the Orr-Sommerfeld and Squire equations in the presence of rotation, magnetic field and an extra force, plausibly noise with a nonzero mean. We obtain MRI using Wentzel-Kramers-Brillouin (WKB) approximation without extra force for purely vertical magnetic field and vertical wavevector of the perturbations. Expectedly, MRI is active within a range of magnetic field, w…
Origin of hydrodynamic turbulence in rotating shear flow, e.g. plane Couette flow including the Coriolis force, is a big puzzle. While the flow often exhibits turbulence in laboratory experiments, according to the linear perturbation theory it should always be stable. We demonstrate that the secondary disturbance to the primarily perturbed flow triggers the elliptical instability in such a system and hence an exponential growing eigenmode. This result has an immediate application to astrophysics and geophysics which often exhibit a turbulent flow with the Keplerian angular momentum profile. We…
Pulsating flows through tubular geometries are laminar provided that velocities are moderate. This in particular is also believed to apply to cardiovascular flows where inertial forces are typically too low to sustain turbulence. On the other hand flow instabilities and fluctuating shear stresses are held responsible for a variety of cardiovascular diseases. Here we report a nonlinear instability mechanism for pulsating pipe flow that gives rise to bursts of turbulence at low flow rates. Geometrical distortions of small, yet finite amplitude are found to excite a state consisting of helical vo…
A prototypical problem in the study of wetting phenomena is that of a solid plunging into or being withdrawn from a liquid bath. In the latter, de-wetting case, a critical speed exists above which a stationary contact line is no longer sustainable and a liquid film is being deposited on the solid. Demonstrating this behavior to be a hydrodynamic instability close to the contact line, we provide the first theoretical explanation of a classical prediction due to Derjaguin and Levi: instability occurs when the outer, static meniscus approaches the shape corresponding to a perfectly wetting fluid.
The stability and causality of the Landau-Lifshitz theory and the Israel-Stewart type causal dissipative hydrodynamics are discussed. We show that the problem of acausality and instability are correlated in relativistic dissipative hydrodynamics and instability is induced by acausality. We further discuss the stability of the scaling solution. The scaling solution of the causal dissipative hydrodynamics can be unstable against inhomogeneous perturbations.
Liquid-liquid phase separation occurs not only in bulk liquid, but also on surfaces. In physiology, the nature and function of condensates on cellular structures remain unexplored. Here, we study how the condensed protein TPX2 behaves on microtubules to initiate branching microtubule nucleation, which is critical for spindle assembly in eukaryotic cells. Using fluorescence, electron, and atomic force microscopies and hydrodynamic theory, we show that TPX2 on a microtubule reorganizes according to the Rayleigh-Plateau instability, like dew droplets patterning a spider web. After uniformly coati…
We report an experimental observation of an instability in gas of constant density (air) with an initial non-uniform seeding of small droplets that develops as a planar shock wave passes through the gas-droplet mix. The seeding non-uniformity is produced by vertical injection of a slow-moving jet of air pre-mixed with glycol droplets into the test section of a shock tube, with the plane of the shock parallel to the axis of the jet. After the shock passage, we observe development of two counter-rotating vortices in the plane normal to that axis. The physical mechanism of the instability we obse…
We numerically study water wave packets on a spatially varying counter-current in the presence of surface tension. Depending on the details of the velocity profile, we show that traversable and bi-directional analogue wormholes exist in fluid mechanics. The limitations on traversability of wormholes in general relativity are absent here because of the dispersion of water waves and the ability to form flow profiles that are not solutions of Einstein's equations. We observe that negative energy can be trapped between analogue horizons forming a LASER-like cavity. Six horizons are involved in the…
We show that, under Braginskii magneto-hydrodynamics, anti-parallel gradients in average ion charge state and electron temperature can be unstable to the growth of self-generated magnetic fields. The instability is analogous to the field-generating thermomagnetic instability, although it is driven by the collisional thermal force magnetic source term rather than the Biermann battery term. The gradient in ion charge state causes a gradient in collisionality, which couples with temperature perturbations to create a self-generated magnetic field. This magnetic field deflects the electron heat flu…
New condition Re>Re_th_min=124 of linear (exponential) instability of the Hagen-Poisseuille (HP) with respect to extremely small by magnitude axially-symmetric disturbances of the tangential component of the velocity field is obtained. For this, disturbances must necessarily have quasi-periodic longitude variability (not representable as a Fourier series or integral) along the pipe axis that complies with experimental data and differs from the usually considered idealized case of pure periodic disturbances for which HP flow is stable for arbitrary large Reynolds numbers Re. Obtained minimal th…
The numerical convergence of smoothed particle hydrodynamics (SPH) can be severely restricted by random force errors induced by particle disorder, especially in shear flows, which are ubiquitous in astrophysics. The increase in the number NH of neighbours when switching to more extended smoothing kernels at fixed resolution (using an appropriate definition for the SPH resolution scale) is insufficient to combat these errors. Consequently, trading resolution for better convergence is necessary, but for traditional smoothing kernels this option is limited by the pairing (or clumping) instability…
We present some new discoveries on the mathematical foundation of linear hydrodynamic stability theory. The new discoveries are: 1. Linearized Euler equations fail to provide a linear approximation on inviscid hydrodynamic stability. 2. Eigenvalue instability predicted by high Reynolds number linearized Navier-Stokes equations cannot capture the dominant instability of super fast growth. 3. As equations for directional differentials, Rayleigh equation and Orr-Sommerfeld equation cannot capture the nature of the full differentials.
The irradiation of an atomic cluster with a femtosecond x-ray free-electron laser pulse results in a nanoplasma formation. This typically occurs within a few hundreds femtoseconds. By this time the x-ray pulse is over, and the direct photoinduced processes no longer contributing. All created electrons within the nanoplasma are thermalized. The nanoplasma thus formed is a mixture of atoms, electrons and ions of various charges. While expanding, it is undergoing electron impact ionization and three-body recombination. Below we present a hydrodynamic model to describe the dynamics of such multi-c…
Transparent biological tissues can be precisely dissected with ultrafast lasers using optical breakdown in the tight focal zone. Typically, tissues are cut by sequential application of pulses, each of which produces a single cavitation bubble. We investigate the hydrodynamic interactions between simultaneous cavitation bubbles originating from multiple laser foci. Simultaneous expansion and collapse of cavitation bubbles can enhance the cutting efficiency by increasing the resulting deformations in tissue, and the associated rupture zone. An analytical model of the flow induced by the bubbles …
Eccentric Keplerian discs are believed to be unstable to three-dimensional hydrodynamical instabilities driven by the time-dependence of fluid properties around an orbit. These instabilities could lead to small-scale turbulence, and ultimately modify the global disc properties. We use a local model of an eccentric disc, derived in a companion paper, to compute the nonlinear vertical ("breathing mode") oscillations of the disc. We then analyse their linear stability to locally axisymmetric disturbances for any disc eccentricity and eccentricity gradient using a numerical Floquet method. In the …
