Turbulence in argon shock waves

Irregular density fluctuations with turbulent-like behaviors are found in ionizing shock fronts produced by our arc driven shock tube. We use electric probes as the primary diagnostic. Spectral analyses show statistical patterns which seem frozen-in and characterizable by a dominant mode and its harmonics.     

Hydrodynamics of nanoscopic capillary waves

The dynamics of nanoscopic capillary waves on simple liquid surfaces is analyzed using molecular dynamics simulations. Each Fourier mode of the surface is obtained from the molecular positions, and its time behavior compared with the hydrodynamic prediction. We trace the transition from propagating to overdamped modes, at short wavelengths. The damping rate is in very good agreement with the hydrodynamic theory up to surprisingly small wavelengths, of about four molecular diameters, but only if the wave number dependent surface tension is considered. At shorter scales, surface tension hydrodynamics break down and we find a transition to a molecular diffusion regime.     

Turbulence of near-inertial waves in the continuously stratified fluid

By using the normal form of continuously stratified “primitive” equations of geophysical fluid dynamics with density (in the ocean), or potential temperature (in the atmosphere) playing the role of the vertical coordinate, we decouple vortex and wave motions in the system, introduce normal variables, and derive the effective Hamiltonian for waves with frequencies close to the inertial frequency (near-inertial waves, NIW). We then apply the weak turbulence approach to the random-phase ensembles of these waves. We show how the anisotropic scale-invariance of NIW may be exploited in order to obtain the stationary power-law spectra. The non-decay anisotropic scale-invariant dispersion laws of the NIW-type were not studied previously in the weak-turbulence literature.     

Quantum capillary waves at the superfluid-Mott-insulator interface

We discuss quantum fluctuations of the interface between a superfluid and a Mott-insulating state of ultracold atoms in a trap. The fluctuations of the boundary are due to a new type of surface modes, whose spectrum is similar--but not identical--to classical capillary waves. The corresponding quantum capillary length sets the scale for the penetration of the superfluid into the Mott-insulating regime by the proximity effect and may be on the order of several lattice spacings. It determines the typical magnitude of the interface width due to quantum fluctuations, which may be inferred from single-site imaging of ultracold atoms in an optical lattice.     

Dynamics of roll domains of parametrically excited capillary waves

We study experimentally the dynamics of roll domains of the parametrically excited capillary waves. The domain rolls were perpendicular to one another and parallel to different boundaries of a rectangular cuvette. It is found that depending on the initial and boundary conditions, two-dimensional different-shape domains arise at the cuvette edges, and the dynamics of the domain is determined by the motion of their fronts. A model of the observed phenomenon is proposed, which is used for numerical calculations. Simulation results are in good agreement with the experimental evidence. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 51, No. 4, pp. 359–366, April 2008.     

Space-time chaos of capillary waves parametrically excited by noise

In experiments with parametrically excited capillary waves on the surface of a liquid with random pumping it was found that the transition to an irregular wave field starts to occur at a low supercriticality. Pulsations in the intensity of the ripples with almost complete preservation of the wave-field structure were noticed. The characteristic frequency of the pulsations calculated from experimental samples turned out to depend on the supercriticality. The results of numerical modeling were in good agreement with experiment.Institute of Applied Physics, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, No. 10, pp. 1281–1293, October, 1994.     

Suppression of thermally excited capillary waves by shear flow

We investigate the thermal fluctuations of the colloidal gas-liquid interface subjected to a shear flow parallel to the interface. Strikingly, we find that the shear strongly suppresses capillary waves, making the interface smoother. This phenomenon can be described by introducing an effective interfacial tension that increases with the shear rate. The increase of sigma(eff) is a direct consequence of the loss of interfacial entropy caused by the flow, which affects especially the slow fluctuations. This demonstrates that the interfacial tension of fluids results from an intrinsic as well as a fluctuation contribution.     

Bound states of topological defects in parametrically excited capillary waves

Bound states of topological defects arising in a tetragonal lattice formed by two orthogonal standing parametrically excited capillary surface waves are investigated. Such bound states are shown to consist either of two topological charges of one sign (type 1) or of topological charges having opposite signs (type 2). It was found that bound states of type 1 move primarily along wave fronts, and type 2 bound states move at an angle of 45^○ to the wave fronts forming a tetragonal lattice. A system of four coupled Ginzburg–Landau equations is proposed to model bound states. Numerical modeling of this system gave solutions corresponding to type 1 bound states observed in experiment.     

Nonlinear development of capillary waves in a viscous liquid jet

The one-dimensional approximate equations describing the dynamics of a Newtonian viscous fluid are used to analyze the nonlinear development of capillary waves in a jet. It is shown that the size of satellite droplets resulting from a nonuniform jet breakup decreases with the Reynolds number at a constant wavenumber. The satellite-droplet formation ceases at a certain value of the Reynolds number, which depends on the wavenumber and initial perturbation amplitude.     

The turbulence of capillary waves on the surface of liquid hydrogen

It is experimentally demonstrated that the surface excitation of liquid hydrogen at a low frequency results in the turbulent mode in a system of capillary waves. The experimental results are in good agreement with the theory of weak wave turbulence. The pair correlation function of the surface deviations is described by the exponential function ω^m. The exponent m decreases in magnitude from m=?3.7±0.3 to ?2.8±0.2 when the pumping at a single resonant frequency changes to broadband noise excitation. Measurements are made of the dependence of the boundary frequency ω_b of the upper edge of the inertial range in which the Kolmogorov spectrum is formed on the wave amplitude η_p at the pumping frequency. It is demonstrated that the obtained data are well described by a function of the form ω_b∝η _p ^4/3 ω _p ^23/9 .     

Instability of water jet: Aerodynamically induced acoustic and capillary waves

High-speed water jet cutting has important industrial applications. To further improve the cutting performance it is critical to understand the theory behind the onset of instability of the jet. In this paper, instability of a water jet flowing out from a nozzle into ambient air is studied. Capillary forces and compressibility of the liquid caused by gas bubbles are taken into account, since these factors have shown to be important in previous experimental studies. A new dispersion equation, generalizing the analogous Rayleigh equation, is derived. It is shown how instability develops because of aerodynamic forces that appear at the streamlining of an initial irregularity of the equilibrium shape of the cross-section of the jet and how instability increases with increased concentration of gas bubbles. It is also shown how resonance phenomena are responsible for strong instability. On the basis of the theoretical explanations given, conditions for stable operation are indicated.     

Polymer thin films and surfaces: Possible effects of capillary waves

It is discussed how the proximity of a free surface or mobile interface may affect the strain relaxation behavior in a viscoelastic material, such as a polymer melt. The eigenmodes of a viscoelastic film are thus derived, and applied in an attempt to explain the experimentally observed substantial shift of the glass transition temperature of sufficiently thin polymer films with respect to the bulk. Based on the idea that the polymer freezes due to memory effects in the material, and exploiting results from mode-coupling theory, the experimental findings of several independent groups can be accounted for quantitatively, with the elastic modulus at the glass transition temperature as the only fitting parameter. The model is finally applied discussing the possibility of polymer surface melting. A surface molten layer is predicted to exist, with a thickness diverging as the inverse of the reduced temperature. A simple model of thin polymer film freezing emerges which accounts for all features observed experimentally so far. Received 8 August 2001     

Frozen capillary waves on glass surfaces: an AFM study

Using atomic force microscopy on silica and float glass surfaces, we give evidence that the roughness of melted glass surfaces can be quantitatively accounted for by frozen capillary waves. In this framework the height spatial correlations are shown to obey a logarithmic scaling law; the identification of this behaviour allows to estimate the ratio kT_F/πγ where k is the Boltzmann constant, γ the interface tension and T_F the temperature corresponding to the “freezing” of the capillary waves. Variations of interface tension and (to a lesser extent) temperatures of annealing treatments are shown to be directly measurable from a statistical analysis of the roughness spectrum of the glass surfaces.     

Forced capillary waves in the pool covered with a thin film

Forced capillary waves are investigated in the pool of finite dimensions within the framework of linear dynamics of an incompressible liquid. Analytical expression for the velocity potential of the liquid in such waves is derived. It is demonstrated that amplitude poles of the forced capillary waves determine the frequency spectrum of free capillary waves. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 3–6, March, 2008.