Influence of an underwater ridge on a nonlinear wave expanding from a point on the surface of a liquid

A study is made of the influence of an underwater ridge on a solitary wave that prior to the interaction with the ridge has the form of a circle situated outside the ridge. It is shown that the nonlinear effects lead to a concentration of the wave energy above the ridge. As they move away from the source, the waves propagating above the ridge are not damped in the considered approximation but are damped everywhere away from the ridge. An analogy is pointed out between the propagation of the wave and two-dimensional steady flows of a fluid, and this makes it possible to use hydrodynamic intuition for qualitative predictions about the nature of the wave propagation in various cases. All the results of the paper can be extended to the case of waves that are periodic in time.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 100–105, July–August, 1982.     

关于平动相对平衡问题的液面不动点

为了方便叙述,我们定义平动相对平衡问题变形前后两液面交线上的点为不动点． 一般《工程流体力学》教材均采用等加速度运动罐车或其它容器来作为典型例题,以说明平动相对平衡问题的求解方法．其中不少教材［１～６］既不说明容器的具体形状,也不说明是变形前还是变形后的液面中心,或者简单地给出‘腋面中心点不变化”［１］的结论后,将坐标原点取在液面中心点;另有一些教材则将坐标原点取在液面上的某一点,从而得出压强分布规律和等压面方程．这就引出了以下两个问题; （１）液面中心点是否一定是不动点？如果不是,则由该点的边界…     

Displacement of a liquid from a horizontal circular tube by another liquid

We consider the axisymmetric problem of expulsion of one liquid from a horizontal circular pipe by another for the laminar flow regime.Studies of Taylor [1], Cox [2, 3], and others have been devoted to the experimental investigation of the displacement of a liquid from a capillary. Experiments on the displacement of mutually immiscible liquids show that the length of the combined flow region and the amount of displaced liquid remaining in this region are determined primarily by the magnitude of the interphase tension forces at the leading edge of the interface. The equilibrium of these forces and the hydrodynamic differential, established some time after the beginning of displacement, give rise to the rigid bullet-shaped form of the interface leading edge. This portion of the interface, whose stiffness is achieved as a result of the force balance, is termed the head of the interface between the liquids. The radius of the head-the relatively small autonomous portion of the interface-defines the dimensions and deformations of the entire remaining interface.The existence of a rigid autonomous interface head is the basis of the physical displacement model used in this article.     

Calculation of flow near the critical point with liquid cooling

The problem of thermal protection is formulated exactly and solved for objects covered with a film of liquid coolant. The results of calculations are shown for an axially symmetrical object in a stream of oxygen.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 44–48, March–April, 1972.     

Dripping retardation with corrugated ceiling

The instabilities of a pendent viscous thin film underneath two corrugated ceilings are studied numerically and theoretically in comparison with the case of a flat wall. With the same initial interface perturbations, it is shown numerically that both the supercritical instability and the subcritical instability can be retarded by the in-phase corrugated ceilings. The lubrication approximation is used to explain the retardation effect of the corrugated ceiling on the supercritical instability of the pendant film, where the linear growth rate is revealed to be power three of the initial film thickness.     

Interaction of molecular flow from a point source with a continuous medium

Kutateladze Institute of Thermophysics, Siberian Division, Russian Academy of Sciences, Novosibirsk 630090. Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 36, No. 5, pp. 3–6, September–October, 1995.     

Explosive projection of liquid from a thick-walled cylindrical container

The process of projection of a layer of an ideal liquid enclosed into a cylindrical elastoplastic shell by products of instantaneous detonation of a high explosive charge is studied numerically in a two-dimensional plane formulation. The processes of shell fracture and liquid exhaustion through the resultant slots are considered. Numerical results are analyzed, and analytical relations for angular distributions of radial velocity and mass of the liquid escaping through the slots are derived. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 56–63, May–June, 2009.     

Conditions of simulation of stagnation point heat transfer from a high-enthalpy flow

The problem of local simulation of stagnation point heat transfer to a blunt body is solved within the framework of boundary layer theory on the assumption that the simulation subsonic high-enthalpy flow is in equilibrium outside the boundary layer on the model, while the parameters of the natural flow are in equilibrium at the outer edge of the boundary layer on the body. The parameters of the simulating subsonic flow are expressed in terms of the total enthalpyH ₀, the stagnation point pressurep _w and the velocityV ₁ for the natural free-stream flow in the form of universal functions of the dimensionless modeling coefficients=R _m ^* /R _b ^* ( .<1),=V ₁/2H ₀ ( .<1) whereR _m ^* and R _b ^* are the effective radii of the model and the body at their stagnation points. Approximate conditions for modeling the heat transfer from a high-enthalpy (including hypersonic) flow to the stagnation point on a blunt body by means of hyposonic (M1) flows, corresponding to the case ²1, are obtained. The possibilities of complete local simulation of hypersonic nonequilibrium heat transfer to the stagnation point on a blunt body in the hyposonic dissociated air jets of a VGU-2 100-kilowatt induction plasma generator [4, 5] are analyzed.Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No.1, pp. 172–180, January–February, 1993.     

Development of wedge-shaped disturbances originating from a point source in a three-dimensional boundary layer

A recent study predicted possibility of existence of a new instability due to the curvature of external streamlines in three-dimensional boundary layers, besides the familiar cross-flow instability, but no reliable evidence of this phenomenon has yet been obtained in experiments. In expectation of dispersive development of the two instabilities, the present study deals with small disturbances induced by continuous forcing from a point source in the boundary layer along a yawed circular cylinder, and attempts to describe their spatial development into wedge-shaped distribution with a linear stability theory, which is applicable to both of the above instabilities. Unlike plane-wave disturbances, the point-source disturbances have an important peculiarity that their propagation is governed by a complex group velocity, and a new method based on the complex property of the group velocity is presented to predict the paths of propagation along which growth rates of disturbances are integrated. Results of this stability calculation clarify important differences in development between the cross-flow disturbances and the streamline-curvature disturbances. These differences will make it possible to observe the new mode of disturbances separately from the other in experiments.     

Scattering of acoustic waves from a point source over an impedance wedge

In this work we study diffraction of a spherical acoustic wave due to a point source, by an impedance wedge In the exterior of the wedge the acoustic pressure satisfies the stationary wave (Helmholtz) equation and classical impedance boundary conditions on two faces of the wedge, as well as Meixner’s condition at the edge and the radiation conditions at infinity. Solution of the boundary value problem is represented by a Weyl type integral and its asymptotic behavior is discussed. On this way, we derive various components in the far field interpreting them accordingly and discussing their physical meaning.     

Numerical study of convection of a liquid heated from below

The equilibrium of a liquid heated from below is stable only for small values of the vertical temperature gradient. With increase of the temperature gradient a critical equilibrium situation occurs, as a result of which convection develops. If the liquid fills a closed cavity, then there is a discrete sequence of critical temperature gradients (Rayleigh numbers) for which the equilibrium loses stability with respect to small characteristic disturbances. This sequence of critical gradients and motions may be found from the solution of the linear problem of equilibrium stability relative to small disturbances. If the temperature gradient exceeds the lower critical value, then (for steady-state heating conditions) there is established in the liquid a steady convective motion of a definite amplitude which depends on the magnitude of the temperature gradient. Naturally, the amplitude of the steady convective motion cannot be determined from linear stability theory; to find this amplitude we must solve the problem of convection with heating from below in the nonlinear formulation. A nonlinear study of the steady motion of a liquid in a closed cavity with heating from below was made in [1]. In that study it was shown that for Rayleigh numbers R which are less than the lower critical value R_c steady-state motions of the liquid are not possible. With R>R_c a steady convection arises, whose amplitude near the threshold is small and proportional to (R–R_c)^1/2 (the so-called soft instability)-this is in complete agreement with the results of the phenom-enological theory of Landau [2, 3].Primarily, various versions of the method of expansion in powers of the amplitude [4–8] have been used, and, consequently, the results obtained in those studies are valid only for values of R which are close to R_c, i. e., near the convection threshold.It is apparent that the study of developed convective motion far from the threshold can be carried out only numerically, with the use of digital computers. In [9, 10] the numerical methods have been successfully used for the study of developed convection in an infinite plane horizontal liquid layer.The present paper undertakes the numerical study of plane convective motions of a liquid in a closed cavity of square section. The complete nonlinear system of convection equations is solved by the method of finite differences on a digital computer for various values of the Rayleigh number, the maximal value exceeding by a factor of 40 the minimal critical value R_c. The numerical solution permits following the development of the steady motion which arises with R>R_c in the course of increase of the Rayleigh number and permits study of the oscillatory motions which occur at some value of the parameter R. The heat transfer through the cavity is studied. The corresponding linear problem on equilibrium stability is solved approximately by the Galerkin method.     

The generation of a draining liquid film by the vertical withdrawal of a flat plate from an elastico-viscous liquid

The analysis of Waters and Keeley [1] for the start-up of the drainage of an elastico-viscous liquid from a vertical surface is extended to include the effect of the vertical surface moving vertically with an arbitrary velocity. This is used to examine the effect of elasticity on the interesting drainage problems associated with the sudden withdrawal of a vertical plate from an elastico-viscous liquid.     

Scalar transport from a point source in flows over wavy walls

Simultaneous measurements of the velocity and concentration field in fully developed turbulent flows over a wavy wall are described. The concentration field originates from a low-momentum plume of a passive tracer. PLIF and digital particle image velocimetry are used to make spatially resolved measurements of the structure of the scalar distribution and the velocity. The measurements are performed at three different Reynolds numbers of Re _b = 5,600, Re _b = 11,200 and Re _b = 22,400, respectively, based on the bulk velocity u _b and the total channel height 2h. The velocity field and the scalar field are investigated in a water channel with an aspect ratio of 12:1, where the bottom wall of the test section consists of a train of sinusoidal waves. The wavy wall is characterized by the amplitude to wavelength ratio α = 0.05 and the ratio β between the wave amplitude and the half channel height where β = 0.1. The scalar is released from a point source at the wave crest. For the concentration measurements, Rhodamine B is used as tracer dye. At low to moderate Reynolds number, the flow field is characterized through a recirculation zone which develops after the wave crest. The recirculation zone induces high intensities of the fluctuations of the streamwise velocity and wall-normal velocity. Furthermore, large-scale structures are apparent in the flow field. In previous investigations it has been shown that these large-scale structures meander laterally in flows over wavy bottom walls. The investigations show a strong effect of the wavy bottom wall on the scalar mixing. In the vicinity of the source, the scalar is transported by packets of fluid with a high scalar concentration. As they move downstream, these packets disintegrate into filament-like structures which are subject to strong gradients between the filaments and the surrounding fluid. The lateral scale of the turbulent plume is smaller than the lateral scale of the large-scale structures in the flow field and the plume dispersion is dominated by the structures in the flow field. Due to the lateral meandering of the large-scale structures of the flow field, also the scalar plume meanders laterally. Compared to turbulent plumes in plane channel flows, the wavy bottom wall enhances the mixing effect of the turbulent flow and the spreading rate of the scalar plume is increased.     

Heavy particle dispersion from a point source in turbulent pipe flow

Dispersion of heavy particles from a point source in high-Reynolds pipe flow was studied using large-eddy simulation, LES. A stochastic Langevin type Lagrangian model developed by Berrouk et al. was used to account for heavy particle transport by the sub-grid scale motion. In both the LES and in an experiment by Arnason, the larger particles dispersed more than the small ones. The change in diffusivity with particle size is interpreted in terms of the effect of inertia and cross-trajectory effects and qualitatively compared with the analysis of heavy particle dispersion in isotropic turbulence by Wang and Stock. Particle inertia has a much larger influence on the dispersion than the crossing-trajectories effects.     

Explosive discharge of a gas-saturated liquid from channels and tanks

A mathematical model for the discharge of a gas-saturated liquid from cylindrical channels is developed. Two limiting cases of linear and quadratic, relations between the flow friction force and the flow velocity are considered. It is established that the process of evacuation, from a semi-infinite channel consists of two stages. In the initial stage, the flow drag can be ignored, and the process of discharge is described by a Riemann wave solution. For the next stage, in which inertia is insignificant, nonlinear equations are obtained and self-similar solutions are constructed for them. The problem of flow through a slot in a tank of finite volume is solved. It is shown that the discharge proceeds either in a gas-dynamic choking regime or in a subsonic regime, depending on the conditions inside the tank and at the outlet. Examples of numerical calculations are given. Institute of Mechanics, Ufa Scientific Center, Russian Academy of Sciences, Ufa 450000 Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 40, No. 1, pp. 64–73, January–February, 1999.