Analysis of Nematic Liquid Crystals with Disclination Lines

We investigate the structure of nematic liquid crystal thin films described by the Landau–de Gennes tensor-valued order parameter model with Dirichlet boundary conditions on the sides of nonzero degree. We prove that as the elasticity constant goes to zero in the energy, a limiting uniaxial nematic texture forms with a finite number of defects, all of degree or all of degree , corresponding to vertical disclination lines at those locations. We also state a result on the limiting behavior of minimizers of the Chern–Simons–Higgs model without magnetic field that follows from a similar proof.     

Gyroscopic waves in a rotating liquid layer

The dispersion characteristics of gyroscopic waves in an incompressible liquid layer in a cavity of a rapidly rotating cylinder are studied. It is shown that in a viscous incompressible liquid layer, an inertial wave can be represented as the sum of six helical harmonics. The effects of the liquid viscosity and the ratio of the wave frequency to the angular velocity of rotation of the cylinder on the real and imaginary parts of the wavenumber are studied. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 15–20, March–April, 2008.     

Edge waves in a shallow fluid beneath a fractured elastic plate

It is shown that a fracture in an elastic plate floating on the surface of a shallow liquid layer is a waveguide along which wave energy can be transported. The edge wave velocity is less than the velocity of flexural-gravity waves. The existence of an antisymmetric edge wave mode depends on the Poisson's ratio of the elastic plate. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 185–189, July–August, 1994.     

Reflection of pressure waves of moderate intensity at a solid wall in a liquid with bubbles of a readily soluble gas

The present paper is concerned with an experimental study of the process of gas dissolution behind a shock wave in a liquid with bubbles of a readily soluble gas, the influence of gas dissolution on the wave evolution, and strengthening of the shock wave after reflection from a solid wall. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 39, No. 5, pp. 19–24, September–October, 1998.     

High-speed visualisation of primary break-up of an annular liquid sheet

In this experimental study, a thin annular moving water sheet is placed between two annular co-flowing air streams. The shear at the interface gives rise to Kelvin–Helmholtz type instabilities and promotes development of a sinuous surface wave at the gas–liquid interface. The amplitude of the surface wave is amplified as it travels downstream of the nozzle exit until it ruptures forming spanwise and streamwise ligaments. The liquid sheet is illuminated with high-powered halogen lamps. High-speed imaging is used in this study to qualitatively visualise the structure of the spray—of particular interest is the evolution of the spray into a ligament structure during the primary break-up and the role the outer air stream plays in this process. Sequences of images with high temporal resolution (∼2,000 fps) are recorded for image processing and analysis of the surface waves and ligament formation. A preliminary analysis of the waveform of the outer gas–liquid interface of the annular liquid sheet over a range of conditions shows the sheet Strouhal number to increase with increasing gas to liquid momentum ratio. Electronic supplementary material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Possibility of reaching higher contents of a gas in a liquid using shock waves

The effect of shock waves on gas absorption by liquid in bubbly media with different degrees of gas solubility is studied. It is shown that a shock wave acting on a gas-liquid medium can significantly enhance the mass transfer between the gas and the liquid. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 2, pp. 64–70, March–April, 2000.     

Mass minimization for a spherical screen with a specified level of transmitted wave energy

A layered spherical screen with minimum weight exposed to a spherical wave is synthesized from a finite set of elastic homogeneous isotropic materials under constraints imposed on the wave energy transferred through the screen and the screen thickness. The necessary optimality conditions are obtained and an example of calculation of the optimal structure is given. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 217–222, September–October, 2000.     

Shock structure in bubbly liquids: comparison of direct numerical simulations and model equations

Shock wave structure in a bubbly mixture composed of a cluster of gas bubbles in a quiescent liquid with initial void fractions around 10% inside a 3D rectangular domain excited by a sudden increase in the pressure at one boundary is investigated using the front tracking/finite volume method. The effects of bubble/bubble interactions and bubble deformations are, therefore, investigated for further modeling. The liquid is taken to be incompressible while the bubbles are assumed to be compressible. The gas pressure inside the bubbles is taken uniform and is assumed to vary isothermally. Results obtained for the pressure distribution at different locations along the direction of propagation show the characteristics of one-dimensional unsteady shock propagation evolving towards steady-state. The steady-state shock structures obtained by the present direct numerical simulations, which show a transition from A-type to C-type steady-state shock structures, are compared with those obtained by the classical Rayleigh–Plesset equation and by a modified Rayleigh–Plesset equation accounting for bubble/bubble interactions in the mean-field theory.      

Propagation of pressure waves in a gas-liquid medium with a cluster structure

Propagation of a stepwise shock wave in a liquid containing spherical gas-liquid clusters is experimentally studied. Measured results are compared with available theoretical models. It is shown that resonant interaction of gas-liquid clusters in the wave can increase the amplitude of oscillations in the shock wave. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 46, No. 3, pp. 50–60, May–June, 2005.     

Propagation of shock waves in a porous medium saturated by a liquid with bubbles of a soluble gas

The process of evolution and reflection of shock waves of moderate amplitude from a rigid boundary in a porous medium saturated by a liquid with bubbles of a soluble gas is studied experimentally. Experimental values of the amplitude and velocity of the reflected wave are compared with the calculated results obtained using mathematical models. The process of dissolution of gas bubbles in the liquid behind the shock wave is studied. Kutateladze Institute of Thermal Physics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 41, No. 5, pp. 91–102, September–October, 2000.     

Application of maximum entropy method for droplet size distribution prediction using instability analysis of liquid sheet

This paper describes the implementation of the instability analysis of wave growth on liquid jet surface, and maximum entropy principle (MEP) for prediction of droplet diameter distribution in primary breakup region. The early stage of the primary breakup, which contains the growth of wave on liquid–gas interface, is deterministic; whereas the droplet formation stage at the end of primary breakup is random and stochastic. The stage of droplet formation after the liquid bulk breakup can be modeled by statistical means based on the maximum entropy principle. The MEP provides a formulation that predicts the atomization process while satisfying constraint equations based on conservations of mass, momentum and energy. The deterministic aspect considers the instability of wave motion on jet surface before the liquid bulk breakup using the linear instability analysis, which provides information of the maximum growth rate and corresponding wavelength of instabilities in breakup zone. The two sub-models are coupled together using momentum source term and mean diameter of droplets. This model is also capable of considering drag force on droplets through gas–liquid interaction. The predicted results compared favorably with the experimentally measured droplet size distributions for hollow-cone sprays.     

Influence of a homogeneous axial magnetic field on Taylor–Couette flow of ferrofluids with low particle–particle interaction

Experimental results concerning the stability of Couette flow of ferrofluids under magnetic field influence are presented. The fluid cell of the Taylor–Couette system is subject to a homogeneous axial magnetic field and the axial flow profiles are measured by ultrasound Doppler velocimetry. It has been found that an axial magnetic field stabilizes the Couette flow. This effect decreases with a rotating outer cylinder. Moreover, it could be observed that lower axial wave numbers are more stable at a higher axial magnetic field strength. Since the used ferrofluid shows a negligible particle–particle interaction, the observed effects are considered to be solely based on the hindrance of free particle rotation.     

Direct Numerical Simulation of Turbulent Compression Ramp Flow

A numerical procedure for the direct numerical simulation of compressible turbulent flow and shock–turbulence interaction is detailed and analyzed. An upwind-biased finite-difference scheme with a compact centered stencil is used to discretize the convective part of the Navier–Stokes equations. The scheme has a uniformly high approximation order and allows for a spectral-like wave resolution while dissipating nonresolved wave numbers. When hybridized with an essentially nonoscillatory scheme near discontinuities, the scheme becomes shock–capturing and its resolution properties are preserved. Diffusive parts are discretized with symmetric compact finite differences and an explicit Runge–Kutta scheme is used for time-advancement. The peculiarities of efficient upwinding and coupling procedures are described and validation results are given. Using direct numerical simulation data, some aspects of turbulent supersonic compression ramp flow are studied to demonstrate the effectiveness of the simulation procedure. Received 13 November 1997 and accepted 14 May 1998     

Flow stability of a conducting liquid flowing down an inclined plane in the presence of a magnetic field

The stability of a steady flow of incompressible, conducting liquid down an inclined plane in the presence of longitudinal and transverse magnetic fields is studied. Solutions of the linearized magnetohydrodynamic equations with corresponding boundary conditions are found on the assumption that the Reynolds number R_g and the wave number are small. It is shown that the longitudinal magnetic field plays a stabilizing role. It is known [1] that the flow of a viscous liquid over a vertical wall is always unstable. In this article it is shown that the instability effect at small wave numbers may be eliminated if the longitudinal magnetic field satisfies the conditions found. The case when the Alfvén number and the wave number are small and the Reynolds number is finite is also examined.     

Structure of a turbulent bore in a homogeneous liquid

A mathematical model for the propagation of nonlinear long waves is constructed with allowance for nonhydrostatic pressure distribution and the development of a surface boundary layer due to wave breaking. The problem of the structure of a bore in a homogeneous liquid is solved. In particular, the transition of a wave bore to a turbulent bore as its amplitude increases is described within a single model. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 56–68, March–April, 1999.     

The Benjamin–Lighthill Conjecture for Steady Water Waves (revisited)

The two-dimensional nonlinear problem of steady gravity waves on water of finite depth is considered. The Benjamin–Lighthill conjecture is proved for these waves provided Bernoulli’s constant attains near-critical values. In fact this is a consequence of the following more general results. If Bernoulli’s constant is near-critical, then all corresponding waves have sufficiently small heights and slopes. Moreover, for every near-critical value of Bernoulli’s constant, there exist only the following waves: a solitary wave and the family of Stokes waves having their crests strictly below the crest of this solitary wave; this family is parametrised by wave heights which increase from zero to the height of the solitary wave. All these waves are unique up to horizontal translations. Most of these results were proved in our previous paper (Kozlov and Kuznetsov in Arch Rational Mech Anal 197, 433–488, 2010), in which it was supposed that wave slopes are bounded a priori. Here we show that the latter condition is superfluous by proving the following theorem. If any steady wave has the free-surface profile of a sufficiently small height, then the slope of this wave is also small.     

The vapour–liquid interface and stresses in dried bodies

The paper presents a contribution to modelling the problem of vapour–liquid interface receding into dried body and stresses induced by drying of capillary-porous bodies. A complex algorithm comprising the specific mechanisms of drying in the first and second periods of drying is constructed. It enables calculation and drawing of the body temperature and drying curves for the whole drying process and identification of the vapour–liquid interface receding into the body. The drying induced stresses caused by the receding vapour–liquid interface and the non-uniform distribution of moisture content and/or temperature are analyzed. Numerical calculations of the temperature and drying curves and the drying induced stresses are carried out for the example of a finite dimensional kaolin cylinder dried convectively.     

Dynamics and radiation of a single bubble under conditions of abnormal compressibility of a bubbly liquid

An equation is proposed for the pulsation of a single cavity in an abnormally compressible bubbly liquid which is in pressure equilibrium and whose state is described by the Lyakhov equation. In the equilibrium case, this equation is significantly simplified. Numerical analysis is performed of the bubble dynamics and acoustic losses (the profile and amplitude of the radiation wave generated on the bubble wall from the side of the liquid). It is shown that as the volumetric gas concentration k₀ in the equilibrium bubbly medium increases, the degree of compression of the cavity by stationary shock wave decreases and its pulsations decrease considerably and disappear already at k₀ = 3%. In the compression process, the cavity asymptotically reaches an equilibrium state that does not depend on the value of k₀ and is determined only by the shock-wave amplitude. The radiation wave takes the shape of a soliton whose amplitude is much smaller and whose width is considerably greater than the corresponding parameters in a single-phase liquid. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 3, pp. 51–57, May–June, 2007.     

Diffraction of internal waves by a circular cylinder near the pycnocline

Propagation of internal waves over a circular cylinder under the conditions of a continuous stratification characterized by the presence of a high-gradient density layer (the pycnocline) of finite thickness is studied. The dependences of the coefficent of wave propagation on the wavelength of the first-mode incident wave for various thicknesses of the pycnocline are obtained. In the diffraction of internal waves, substantial nonlinear effects are shown to occur, which result in the appearance of waves of double oscillation frequency compared to the frequency of the incident waves. The generation coefficient for these waves is found. Lavrent’ev Institute of Hydrodynamics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 2, pp. 79–85, March–April, 1999.     

Bottom effect on limiting Stokes waves

The problem of limiting progressive Stokes waves characterized by a crest angle of 120° propagating in an inviscid incompressible fluid of finite depth is solved numerically. The wave forms are obtained and the range of Froude numbers, calculated from the fluid depth and the phase velocity, on which solutions exist is determined. St. Petersburg. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 125–129, July–August, 1994.