Short-wave Perturbations Research Articles

Bifurcation of finger-like structures in traveling waves of epithelial tissues spreading

We consider a continuous active polar fluid model for the spreading of epithelial monolayers introduced by R. Alert, C. Blanch-Mercader, and J. Casademunt, 2019. The corresponding free boundary problem possesses flat front traveling wave solutions. Linear stability of these solutions under periodic perturbations is considered. It is shown that the solutions are stable for short-wave perturbations while exhibiting long-wave instability under certain conditions on the model parameters (if the traction force is sufficiently strong). Then, considering the prescribed period as the bifurcation parameter, we establish the emergence of nontrivial traveling wave solutions with a finger-like periodic structure (pattern). We also construct asymptotic expansions of the solutions in the vicinity of the bifurcation point and study their stability. We show that, depending on the value of the contractility coefficient, the bifurcation can be a subcritical or a supercritical pitchfork.

To simple waves and small-amplitude perturbations in radiation gasodynamics

The paper analyzes one-dimensional simple waves and small-amplitude perturbations in radiating and scattering gray gas. The governing equation of radiation acoustics describing the dynamics of simple waves is derived. The conditions of radiation-thermal dissipation and radiation resistance force are introduced into this equation to describe the propagation with dissipation and attenuation of various radiation perturbation waves. The phenomenological approximate Whitham method is used to investigate non-equilibrium wave phenomena in radiative medium. This method is an effective way to analyze fundamental modes when more than one velocity appears in the governing equation. The use of this method is demonstrated in this paper by considering the evolution of one-dimensional harmonic waves caused by a short-wave initial perturbation of the equilibrium state of the radiating and scattering medium. Analytical solutions are obtained for all wave modes, which allow us to interpret their physical meaning. These solutions can be, in particular, an additional test for radiative hydrodynamic codes operating in the radiative acoustics regime. The presented approach may be useful in detailing higher-order numerical Godunov schemes for radiation acoustics problems.

Two-Field Model of Gravitational-Scalar Instability and Formation of Supermassive Black Holes in the Early Universe

Based on the previously formulated mathematical model of a statistical system with scalar interaction of fermions and the theory of gravitational-scalar instability of a cosmological model based on a two-component statistical system of scalarly charged degenerate fermions, a numerical model of the cosmological evolution of gravitational-scalar perturbations in the presence of classical and phantom scalar fields is constructed and studied. The gravitational-scalar instability at early stages of expansion arises in the model under study at sufficiently large scalar charges, and the instability develops near unstable points of the vacuum doublet. Short-wave perturbations of the free phantom field turn out to be stable at stable singular points of the vacuum doublet. It is shown that for sufficiently large scalar charges, mass perturbations can grow to the values of masses black hole seeds (BHS).

Простые волны и малоамплитудные возмущения в радиационной газодинамике

The paper analyses one-dimensional simple waves and small-amplitude disturbances in radiating and scattering grey gas. The governing equation of radiation acoustics describing the dynamics of simple waves is derived. Radiation-thermal dissipation conditions and radiation resistance force are introduced into this equation to describe the propagation and attenuation of various radiation perturbation waves. To study non-equilibrium wave phenomena in a radiating medium, the phenomenological Whitham method is used. This method is an effective way to analyse fundamental modes when more than one velocity appears in the governing equation. The use of this method is demonstrated in the paper by considering the evolution of one-dimensional harmonic waves caused by a short-wave initial perturbation of the equilibrium state of the radiating and scattering medium. For all wave modes, analytical solutions have been obtained, which allow us to understand their physical significance. These solutions can be, in particular, an additional test for radiative hydrodynamic codes operating in the radiative acoustics regime. The general approach can be useful in the development of higher-order Godunov numerical schemes for radiation hydrodynamics problems.

On the Short Wave Instability of the Liquid/Gas Contact Surface in Porous Media

We consider a problem of hydrodynamic stability of the liquid displacement by gas in a porous medium in the case when a light gas is located above the liquid. The onset of instability and the evolution of the small shortwave perturbations are investigated. We show that when using the Darcy filtration law, the onset of instability may take place at an infinitely large wavenumber when the normal modes method is inapplicable. The results of numerical simulation of the nonlinear problem indicate that the anomalous growth of the amplitude of shortwave small perturbations persists, but the growth rate of amplitude decreases significantly compared to the results of linear analysis. An analysis of the stability of the gas/liquid interface is also carried out using a network model of a porous medium. It is shown that the results of surface evolution calculations obtained using the network model are in qualitative agreement with the results of the continual approach, but the continual model predicts a higher velocity of the interfacial surfaces in the capillaries. The growth rate of perturbations in the network model also increases with decreasing perturbation wavelength at a constant amplitude.

LINEAR STABILITY OF A FILTRATION FLOW WITH GAS–OIL INTERFACE WITHIN THE BRINKMAN APPROACH

Abstract—The problem of vertical flow stability in an oil reservoir with a gas cap is considered, when the oil flow obeys the Brinkman equation. Boundary conditions at the moving boundary of the gas-oil interface are derived and a basic solution is obtained. The normal mode method is used to study the stability of the gas–oil interface. The obtained dispersion equation is investigated. Conditions for flow stability are found for all values of the parameters, and it is shown that, in the linear approximation, the growth rate of short-wave perturbations tends to zero with increasing wave number.

Forcing Convection to Aggregate Using Diabatic Heating Perturbations.

Tropical deep convection can aggregate into large clusters, which can have impacts on the local humidity and precipitation. Sea surface temperature (SST) gradients have been shown to organize convection, yet there has been little work done to investigate the impact of diabatic heating perturbations in the atmosphere on the aggregation of convection. Here we investigate how anomalous diabatic heating of the atmospheric column, through an idealized aerosol plume, affects the existence and mechanisms of convective aggregation in non‐rotating, global radiative‐convective equilibrium simulations. We show that the aerosol forcing has the ability to increase the degree of aggregation, especially at lower SSTs. Detailed investigation shows that the diabatic heating source incites a thermally driven circulation, forced by the shortwave perturbation. The increase in aggregation is caused in part by this circulation, and in part by the longwave heating anomalies occurring due to the surface convergence of moisture and convection. At higher SSTs, longwave feedbacks are crucial for the aggregation of convection, even with the shortwave heating perturbation. At lower SSTs, convection is able to aggregate with the shortwave perturbation in the absence of longwave feedbacks. These perturbations provide a link to studying the effects of absorbing aerosol plumes on convection, for example during the Indian monsoon season. We argue that, as there is aggregation for plumes with realistic aerosol absorption optical depths, this could be an analogue for real‐world organization in regions with high pollution.

On Linear Instability of Atmospheric Quasi-hydrostatic Equations in Response to Small Shortwave Perturbations

A set of 3-dimensional atmospheric-dynamics equations with quasi-hydrostatic approximation is proposed and justified with the practical goal to optimize atmospheric modelling at scales ranging from meso meteorology to global climate. Sound waves are filtered by applying the quasi-hydrostatic approximation. In the closed system of hydro/thermodynamic equations, the inertial forces are negligibly small compared to gravity forces, and the asymptotically exact equation for vertical velocity is obtained. Investigation of the stability of solutions to this system in response to small shortwave perturbations has shown that solutions have the property of shortwave instability. There are situations when the increment of the perturbation amplitude tends to infinity, corresponding to absolute instability. It means that the Cauchy problem for such equations may be ill-posed. Its formulation can become conditionally correct if solutions are sought in a limited class of sufficiently smooth functions whose Fourier harmonics tend to zero reasonably quickly when the wavelengths of the perturbations approach zero. Thus, the numerical scheme for the quasi-hydrostatic equations using the finite-difference method requires an adequately selected pseudo-viscosity to eliminate the instability caused by perturbations with wavelengths of the order of the grid size. The result is useful for choosing appropriate vertical and horizontal grid sizes for modelling to avoid shortwave instability associated with the property of the system of equations. Implementation of pseudo-viscosities helps to smoothen or suppress the perturbations that occur during modelling.

Marangoni instability in a viscoelastic binary film with cross-diffusive effect

Abstract

Stability of the Cosmological System of Degenerate Scalarly Charged Fermions and Higgs Scalar Fields. II. Evolution of Short-wave Perturbations

A mathematical model of the evolution of plane perturbations in the cosmological statistical system of completely degenerate scalar-charged fermions with Higgs scalar interaction for short-wave perturbations is formulated. These disturbance modes have been found and investigated. It is shown that in such a model an additional oscillation mode arises, which is associated directly with degenerate fermions, in which monotonically decreasing and increasing perturbations of the metric exist. In this case, there is such a time instant in the system that the potential of the scalar field, together with the energy density, tends to infinity. In this regard, an assumption is made about a possible mechanism for the formation of dark matter condensates.

How an uncertain short-wave perturbation on the North Atlantic wave guide affects the forecast of an intense Mediterranean cyclone (Medicane Zorbas)

Abstract. Mediterranean cyclogenesis is known to be frequently linked to ridge building over the North Atlantic and subsequent anticyclonic Rossby wave breaking over Europe. But understanding of how this linkage affects the medium-range forecast uncertainty of Mediterranean cyclones is limited, as previous predictability studies have mainly focused on the relatively rare cases of Mediterranean cyclogenesis preceded by upstream extratropical transition of tropical cyclones. This study exploits a European Centre for Medium-Range Weather Forecasts (ECMWF) operational ensemble forecast with an uncertain potential vorticity (PV) streamer position over the Mediterranean that, 3 d after initialization, resulted in an uncertain development of the Mediterranean tropical-like cyclone (Medicane) Zorbas in September 2018. Later initializations showed substantially lower forecast uncertainties over the Mediterranean. An ad hoc clustering of the ensemble members according to the PV streamer position in the Mediterranean is used to study the upstream evolution of the synoptic to mesoscale forecast uncertainties. Cluster differences show that forecast uncertainties were amplified on the stratospheric side of a jet streak over the North Atlantic during the first day of the ensemble prediction. Subsequently, they propagated downstream and were further amplified within a short-wave perturbation along the wave guide, superimposed onto the large-scale Rossby wave pattern. After 3 d, the uncertainties reached the Mediterranean, where they resulted in a large spread in the position of the PV streamer. These uncertainties further translated into uncertainties in the position and thermal structure of the Mediterranean cyclone. In particular, the eastward displacement of the PV streamer in more than a third of the ensemble members resulted in a very different cyclone scenario. In this scenario, cyclogenesis occurred earlier than in the other members in connection to a pre-existing surface trough over the Levantine Sea. These cyclones did not develop the deep warm core typical of medicanes. It is proposed that the eastward-shifted cyclogenesis resulted in reduced values of low-level equivalent potential temperature in the cyclogenesis area. As a result, latent heating was not intense and deep enough to erode the upper-level PV anomaly and allow the formation of a deep warm core. The westward displacement led to surface cyclones that were too weak, and a medicane formed in only half of the members. The central, i.e. correct, PV streamer position resulted in the most accurate forecasts with a strong medicane in most members. This study is the first that explicitly investigates the impact of PV streamer position uncertainty for medicane development. Overall, results extend current knowledge of the role of upstream uncertainties in the medium-range predictability and unsteady forecast behavior of Mediterranean cyclones including medicanes.

Spectral Features of Systems With Chaotic Dynamics

Using the Lorentz model and Hamiltonian systems without dissipation as an example, spectral methods for analyzing the dynamics of systems with chaotic behavior are considered. The insufficiency of the traditional approach to the study of perturbation dynamics based on an analysis of the roots of the classical spectral equation is discussed. It is proposed to study nonlinear systems using the method of constructing spectral equations with different eigenvalues, which allows one to take into account the randomness and multiplicity of states. The spectral features of instability and chaos for systems without dissipation are shown by the example of short-wave perturbations of a flow of a weakly ionized plasma gas.

On the porosity influence on stability of flow over porous medium

The stability of incompressible fluid plane-parallel flow over a layer of a saturated porous medium is studied. The results of a linear stability analysis are described at different porosity values. The considered system is bounded by solid wall from the porous layer bottom. Top fluid surface is free and rigid. A linear stability analysis of plane-parallel stationary flow is presented. It is realized for parameter area where the neutral stability curves are bimodal. The porosity variation effect on flow stability is considered. It is shown that there is a transition between two main instability modes: long-wave and short-wave. The long-wave instability mechanism is determined by inflection points within the velocity profile. The short-wave instability is due to the large transverse gradient of flow velocity near the interface between liquid and porous medium. Porosity decrease stabilizes the long wave perturbations without significant shift of the critical wavenumber. Simultaneously, the short-wave perturbations destabilize, and their critical wavenumber changes in wide range. When the porosity is less than 0.7, the inertial terms in filtration equation and magnitude of the viscous stress near the interface increase to such an extent that the Kelvin-Helmholtz analogue of instability becomes the dominant mechanism for instability development. The stability band realizes in narrow porosity area. It separates the two branches of the neutral curve.

Marangoni instability in a heated viscoelastic liquid film: Long-wave versus short-wave perturbations.

We investigate the Marangoni instability in a thin layer of viscoelastic fluid, confined between its deformable free surface and a substrate of low thermal conductivity. Following a theoretical analysis, we study the stability of the present system for the case when the fluid layer is subjected to heating from below. Here, we use the Maxwell model to depict the rheology of the viscoelastic fluid. Linear stability analysis of the quiescent base state reveals that, in addition to the conventional short-wave mode, a long-wave instability can also emerge in this system. We demonstrate the appearance of both the long-wave monotonic and oscillatory instabilities in such a system. We study this long-wave mode analytically using the scaling k∼sqrt[Bi] (k is the wave number and Bi is the Biot number), whereas the short-wave mode is examined numerically. The influential role of elasticity of the fluid and the other involved parameters on the stability of the system is aptly discussed, and their ranges are identified within which a particular instability mode gets critical.

Excitation of Convection in a System of Layers of a Binary Solution and an Inhomogeneous Porous Medium in a High-Frequency Vibration Field

The onset of convection in a system of horizontal layers of a binary solution and an inhomogeneous porous medium saturated with the solution is studied. The system is subjected to high-frequency transverse vibrations in the gravity field. It is assumed that the porosity of the medium depends linearly on the vertical coordinate. The permeability is estimated by the Karman–Kozeny formula for different values of the dimensionless gradient of the porosity, mz. The convection of the fluid under the action of high-frequency vibrations in the gravity field is described using the averaging method. The linear problem of the stability of the mechanical equilibrium of the fluid is solved numerically by the shooting method. The values of the critical parameters corresponding to the convection initiation threshold are determined for the system heated from below or from above. The heating from below is distinguished by a sharp change in the character of the instability with a variation in the porosity gradient or the vibration intensity. It is shown that, when the porosity increases with depth, at mz =–0.2, the instability is caused by the development of long-wave perturbations involving the fluid and the porous layers. When the porosity decreases with depth, at mz = 0.2, the most dangerous perturbations are short-wave perturbations localized in the fluid layer. For intermediate values of the porosity gradient,–0.2< mz < 0.2, the values of the minimum Rayleigh–Darcy critical numbers, which determine the equilibrium stability threshold with respect to short-wave and long-wave disturbances, approach one another. The neutral curves are bimodal. Upon heating from below, vertical vibrations effectively suppress convection in the fluid layer; therefore, with an increase in their intensity, the transition from short-wave vibrations, which are most dangerous, to long-wave perturbations is observed. A noticeable increase in the stability threshold is observed when the porosity decreases with depth. Upon heating from above, vibrations destabilize the equilibrium in the system and lead to a reduction in the wavelength of the critical perturbations. The wavelength decreases monotonically. Its maximum change is detected in layers whose porosity increases with depth.

Effect of Fluid Viscosity on the Faraday Surface Waves

The comprehensive experimental analysis of the fluid viscosity effect on the standing gravity waves excited at parametric resonance is carried out. The viscous effects on the frequency range of excitement of the second wave mode, its resonance dependences, and the processes of damping and approaching the steady-state regime are quantitatively estimated by varying the viscosity over a wide range. It is found that the waves are regularized without breaking when the kinematic viscosity of the workingmedium becomes higher than a threshold value. A mechanism of viscous regularization of wave motion is suggested. In accordance with this mechanism, the effects observed experimentally relate to the presence of the shortwave cutoff domain in which viscous dissipation becomes the dominant factor and the shortwave perturbations responsible for breaking the standing wave are suppressed.

Dust Impacts on the 2012 Hurricane Nadine Track during the NASA HS3 Field Campaign.

During the 2012 deployment of the NASA Hurricane and Severe Storm Sentinel (HS3) field campaign, several flights were dedicated to investigating Hurricane Nadine. Hurricane Nadine developed in close proximity to the dust-laden Saharan Air Layer, and is the fourth longest-lived Atlantic hurricane on record, experiencing two strengthening and weakening periods during its 22-day total lifecycle as a tropical cyclone. In this study, the NASA GEOS-5 atmospheric general circulation model and data assimilation system was used to simulate the impacts of dust during the first intensification and weakening phases of Hurricane Nadine using a series of GEOS-5 forecasts initialized during Nadine's intensification phase (12 September 2012). The forecasts explore a hierarchy of aerosol interactions within the model: no aerosol interaction, aerosol-radiation interactions, and aerosol-radiation and aerosol-cloud interactions simultaneously, as well as variations in assumed dust optical properties. When only aerosolradiation interactions are included, Nadine's track exhibits sensitivity to dust shortwave absorption, as a more absorbing dust introduces a shortwave temperature perturbation that impacts Nadine's structure and steering flow, leading to a northward track divergence after 5 days of simulation time. When aerosol-cloud interactions are added, the track exhibits little sensitivity to dust optical properties. This result is attributed to enhanced longwave atmospheric cooling from clouds that counters shortwave atmospheric warming by dust surrounding Nadine, suggesting that aerosol-cloud interactions are a more significant influence on Nadine's track than aerosol-radiation interactions. These findings demonstrate that tropical systems, specifically their track, can be impacted by dust interaction with the atmosphere.

Marangoni instability in a thin film heated from below: Effect of nonmonotonic dependence of surface tension on temperature.

We investigate Marangoni instability in a thin liquid film resting on a substrate of low thermal conductivity and separated from the surrounding gas phase by a deformable free surface. Considering a nonmonotonic variation of surface tension with temperature, here we analytically derive the neutral stability curve for the monotonic and oscillatory modes of instability (for both the long-wave and short-wave perturbations) under the framework of linear stability analysis. For the long-wave instability, we derive a set of amplitude equations using the scaling k∼(Bi)^{1/2}, where k is the wave number and Bi is the Biot number. Through this investigation, we demonstrate that for such a fluid layer upon heating from below, both monotonic and oscillatory instability can appear for a certain range of the dimensionless parameters, viz., Biot number (Bi), Galileo number (Ga), and inverse capillary number (Σ). Moreover, we unveil, through this study, the influential role of the above-mentioned parameters on the stability of the system and identify the critical values of these parameters above which instability initiates in the liquid layer.

Physical effects of magnetic fields on the Kelvin-Helmholtz instability in a free shear layer

The Kelvin-Helmholtz instability of a parallel shear flow with a hyperbolic-tangent velocity profile has been simulated numerically at a high Reynolds number. The fluid is perfectly conducting with low viscosity, and the strength of the applied magnetic field varies from weak to strong. We found that the magnetic field parallel to the mainstream direction has a stabilizing effect on the shear flow. The magnetic field mainly stabilizes short-wave perturbations. Small viscosity and/or slight compressibility could introduce some instability even in the presence of a strong magnetic field in a certain circumstance. The suppressing effect of the magnetic field on the instability is accomplished by two parts: the separating effect of the transverse magnetic pressure and the anti-bending effect of magnetic tension pointing to the center of curvature. The former shows prevailingly stronger effect on the fluid interface than the latter does, which is different from the conventional opinion that magnetic tension dominates. Essentially it is mainly the Maxwell stress that weakens and balances the momentum transport conducted by the Reynolds stress, reducing the mixing degree of the upper fluid and the lower fluid.

Dynamic evolution of Rayleigh-Taylor bubbles from sinusoidal, W-shaped, and random perturbations.

Implicit large eddy simulations of two-dimensional Rayleigh-Taylor instability at different density ratios (i.e., Atwood number A=0.05, 0.5, and 0.9) are conducted to investigate the late-time dynamics of bubbles. To produce a flow field full of bounded, semibounded, and chaotic bubbles, three problems with distinct perturbations are simulated: (I) periodic sinusoidal perturbation, (II) isolated W-shaped perturbation, and (III) random short-wave perturbations. The evolution of height h, velocity v, and diameter D of the (dominant) bubble with time t are formulated and analyzed. In problem I, during the quasisteady stage, the simulations confirm Goncharov's prediction of the terminal speed v_{∞}=Frsqrt[Agλ/(1+A)], where Fr=1/sqrt[3π]. Moreover, the diameter D at this stage is found to be proportional to the initial perturbation wavelength λ as D≈λ. This differed from Daly's simulation result of D=λ(1+A)/2. In problem II, a W-shaped perturbation is designed to produce a bubble environment similar to that of chaotic bubbles in problem III. We obtain a similar terminal speed relationship as above, but Fr is replaced by Fr_{w}≈0.63. In problem III, the simulations show that h grows quadratically with the bubble acceleration constant α≡h/(Agt^{2})≈0.05, and D expands self-similarly with a steady aspect ratio β≡D/h≈(1+A)/2, which differs from existing theories. Therefore, following the mechanism of self-similar growth, we derive a relationship of β=4α(1+A)/Fr_{w}^{2} to relate the evolution of chaotic bubbles in problem III to that of semibounded bubbles in problem II. The validity of this relationship highlights the fact that the dynamics of chaotic bubbles in problem III are similar to the semibounded isolated bubbles in problem II, but not to that of bounded periodic bubbles in problem I.