Evolution of three-dimensional gravitationally warped waves during the movement of a pressure zone of variable intensity

Three-dimensional, unestablished, gravitationally warped waves arising due to the motion of a harmonically time-varying pressure zone over a solid, thin plate floating on the surface of a homogeneous liquid of finite depth have been studied in the linear formulation. In the absence of a plate, three-dimensional waves are generated by the movement of a region of periodic perturbations, where established waves have been studied in [1, 2], and unestablished waves have been investigated in [3–5]. The evolution of three-dimensional, gravitationally warped waves formed during the motion of a constant load over a plate has been considered in [6].Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 54–60, September–October, 1986.     

Nonresonance parametric interactions of surface waves in isotropic solid bodies

A solution in parametric approximation is given of the nonlinear interaction problem of Rayleigh surface waves propagating in a solid body with given elastic fields. Shortened equations that govern the modulation effect of the surface waves, and also expressions for the modulation index in terms of the third-order elasticity constant, are obtained.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 163–172, July–August, 1973.     

Influence of rotation on the damping of surface waves in a cylindrical layer of viscous fluid

A study is made of the oscillations of the free surface of a cylindrical layer of viscous incompressible fluid attracted by gravity to a solid, uniformly rotating cylinder. Logarithmic decay rates are found for the damping of the surface gravitational waves when large Reynolds numbers are assumed. It is shown that rotation introduces an asymmetry into the damping of the waves traveling in and against the direction of rotation of the fluid.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6. pp. 171–173, November–December, 1984.     

Surface waves and stability of free surface of a magnetizable liquid

Linear theory of surface waves in a magnetizable liquid is examined. A stability criterion for a plane-free surface of a magnetizable liquid is studied for an arbitrary magnetization law.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 4, pp. 35–40, July–August, 1974.     

Instability of monochromatic waves on the surface of a liquid of arbitrary depth

A study is made of the stability, with respect to the spontaneous appearance of modulation, of steady periodic waves of small amplitude on the surface of an ideal liquid depth. The well-known instability of waves on the surface of a liquid of infinite depth disappears on making the transition to small depths.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 5, pp. 45–49, September–October, 1970.     

Nonstationary waves in the continuously stratified flow of a fluid of finite depth

A theoretical investigation is made of the development of linear two-dimensional waves in a continuously stratified flow of an ideal incompressible fluid. The waves are generated by pressures that are independent of time and that are applied at time t=0 to a bounded region on the free surface of an initially undisturbed flow. The stationary internal waves generated by such a disturbance have been investigated in [1–3]. The nonstationary waves in a continuously stratified fluid that are generated by initial disturbances or periodic surface pressures applied to the entire free surface have been studied in [4–7] in the absence of a slow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 87–93, November–December, 1976.     

Motion of deforming solid of revolution in a viscous incompressible liquid

In [1] a model of a wave generator, together with an experimental apparatus to determine the traditional forces generated by the model in water, is described. At the surface of the model six axisymmetric traveling waves are generated, giving rise to motion of the body and the surrounding liquid. The steady flow of liquid caused by oscillations of a cylindrical surface of infinite length was investigated in [2, 3]. The present work investigates the tractional forces of an elongated solid of revolution in a liquid produced by waves traveling over the flexible cylindrical part of the body. The hydrodynamic surface forces are determined by numerical integration of the Navier-Stokes equation. Graphs of the tractional force against the velocity and amplitude of the waves are given.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 145–149, May–June, 1977.In conclusion, thanks are due to M. A. Il'gamovfor his interest in the work and for useful advice.     

Stable equilibrium of the surface of a capillary liquid in contact with the edge of a solid

The equilibrium conditions which must be satisfied at the free surface of a capillary liquid and at the line of its contact with the smooth surface of a solid are well known [1]. These conditions are equivalent to the condition of steady-state conditions for the potential energy [2, 3], and the question of the stability of the equilibrium states reduces to a study of the sign of its second variation [2–4]. The case is discussed below where the surface of the solid has a break at the line of contact with the free surface. Stable equilibrium states are identified with the points of a local minimum of the potential energy. The necessary and sufficient conditions for a minimum are obtained.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 3–6, January–February, 1974.The authors thank A. D. Myshkis for his evaluation of the results obtained.     

Impingement of surface waves on the edge of compressed ice

The impingement of small-amplitude surface waves on the edge of a solid compressed ice sheet in a basin of finite constant depth is considered. The influence of the cylindrical rigidity and the value of the compressing force on the dependence of the amplitude coefficients of reflection and transmission on the incident wave period is analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, pp. 121–126, May–June, 1995.     

Nonsteady burning of a solid propellant in a gaseous oxidizer flow

The burning of a solid propellant is investigated for nonsteady heat propagation in the induction zone. The equation of heat conduction in the propellant is solved in finite form for the case of a sharp change in burning rate; the time dependence of the temperature gradient at the propellant surface is obtained and used to investigate the mechanism of collapse of the diffusion flame above the surface. The combustion stability of a propellant burning in a channel with a large free volume is analyzed. The perturbations of the gas-dynamic quantities are related with the perturbations of the burning rate and hence with the properties of the induction zone in the solid phase. An analysis of the dispersion relation for the limiting case of propagation of acoustic waves in a stationary gas shows that the longitudinal acoustic perturbations that develop in the channel may grow with time, interacting with the heated subsurface layer of propellant.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fizikt, No. 4, pp. 44–52, July–August, 1971.In conclusion the author thanks B. V. Librovich for formulating and discussing the problem and A. G. Istratov and V. G. Markov for their valuable comments.     

A spherical wave in a viscoelastic half-space

The propagation of spherical waves in an isotropie elastic medium has been studied sufficiently completely (see, e.g., [1–4]). it is proved [5, 6] that in imperfect solid media, the formation and propagation of waves similar to waves in elastic media are possible. With the use of asymptotic transform inversion methods in [7] a problem of an internal point source in a viscoelastic medium was investigated. The problem of an explosion in rocks in a half-space was considered in [8]. A numerical Laplace transform inversion, proposed by Bellman, is presented in [9] for the study of the action of an explosive pulse on the surface of a spherical cavity in a viscoelastic medium of Voigt type. In the present study we investigate the propagation of a spherical wave formed from the action of a pulsed load on the internal surface of a spherical cavity in a viscoelastic half-space. The potentials of the waves propagating in the medium are constructed in the form of series in special functions. In order to realize viscoelasticity we use a correspondence method [10]. The transform inversion is carried out by means of a representation of the potentials in integral form and subsequent use of asymptotic methods for their calculation. Thus, it becomes possible to investigate the behavior of a medium near the wave fronts. The radial stress is calculated on the surface of the cavity.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 139–146, March–April, 1976.     

Development of ship waves in a nonhomogeneous liquid

The article discusses the three-dimensional problem of unsteady-state waves arising on a free surface and at the interface between two liquids of different densities, with motion of the source. Analogous problems for steady-state waves in a two-layer liquid have been investigated in [1–6], and for unsteady-state waves in a homogeneous liquid in [7, 8].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 137–146, July–August, 1970.     

Parametric excitation of waves on the surface of an inviscid liquid

A study is made of the stability of the equilibrium of the free surface of an infinite layer of inviscid incompressible liquid executing oscillations along the vertical axis. The problem is solved in the nonlinear formulation by series expansion with respect to the amplitude of the excitation. Soft and hard excitation regimes of the surface waves are obtained. The stability of the regimes is investigated. It is shown that the plane wave formed on the surface of the liquid is unstable.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 68–75, September–October, 1982.I thank V. A. Briskman for suggesting the problem and for constant interest in the work and also A. A. Nepomnyashchii for discussing the results.     

Passage of shock waves through a curved boundary separating two media

We consider the interaction of shock waves with a mildly curved surface of separation, and also the motion of this surface due to the passage of shock waves.Moscow. Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 111–121, January–February, 1972.     

Nonlinear waves on the surface of a charged liquid. Instability,bifurcation, and nonequilibrium shapes of the charged surface

Plane nonlinear waves in shallow water are described by the Kortewegde Vries equation [1–3]. The present paper contains theoretical investigations of nonlinear waves and nonlinear equilibrium shapes on the surface of a charged liquid. The influence of the field on the velocity and shape of a hydrodynamic soliton is considered. The bifurcation of the equilibrium shapes is investigated. Problems of the equilibrium shapes of a charged liquid are solved in the nonlinear formulation of the dynamics of nonlinear solitary forms (lunes, trenches) on the surface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 94–102, May–June, 1984.     

Some results of a numerical analysis of transient waves in gas suspensions

Special aspects of the transmission of transient waves through gas mixtures carrying suspended solid particles of chemically inert substances are examined. The influence of the parameters of the gas suspension on the conditions governing the occurrence of transient processes is discussed. The interaction of shock waves with a dust-laden half-space is considered. The results of calculations relating to the decay of an arbitrary discontinuity during the reflection of a shock wave from a wall are presented.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 64–69, September–October, 1976.     

Swell wave propagation in an inhomogeneous ice sheet

The propagation of surface waves beneath a periodically inhomogeneous ice sheet is considered. Areas of broken ice and hummock ridges are considered as irregularities. It is shown that waves with frequencies corresponding to wind and swell waves are strongly scattered by the irregularities and are damped exponentially as they propagate beneath the ice.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 162–169, September–October, 1996.     

On the development of plane waves generated by a periodic pressure applied to the flow of a continuously stratified fluid

In the linear formulation, an investigation is made into the development of undamped (in time) plane waves generated by a. harmonically varying pressure applied to the free surface of an initially undisturbed flow of a continuously stratified fluid of finite depth. The cases of a homogeneous fluid and two-layer fluid are considered in [1–3]. Nonstationary waves in a continuously stratified flow generated by a time-independent pressure were investigated in [4].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 99–104, July–August, 1980.     

Unsteady gravity-elastic and gravity-capillary ship waves

The development of three-dimensional waves generated by a region of pressures moving uniformly and rectilinearly over the surface of a thin elastic isotropic plate covering an ideal fluid layer of finite depth is investigated. The pressures act starting at a certain instant. A qualitative similarity between the waves occurring and gravity-capillary waves is noted. The calculations are made for an ice cover. This model problem permits examining a number of properties of the oscillations of the ice cover occurring when hauling freight over ice roads, landing and takeoff of aircraft from ice fields, etc. [1]. The development of ship waves in a fluid of finite depth in the absence of a floating plate was investigated in [2, 3] and gravity-capillary waves were studied in [4–6]. Certain properties of steady three-dimensional waves occurring during movement of a load over the surface of a floating elastic plate were established in [1].Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 26–32, September–October, 1978.     

Free vibrations of two capillary liquids rotating in a cylindrical vessel

The problem of the small natural vibrations of two coaxially disposed ideal liquids rotating in a cylindrical vessel under conditions of complete weightlessness is considered. The set of normal vibrations of the system consists of internal wave motions and surface waves. Asymptotic formulas are derived for the vibration frequencies of the surface waves. The results of computer calculations are presented in the form of graphs and tables.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 97–104, September–October, 1976.