Wave formation on vertical falling liquid films

The method of integral relations is used to derive a nonlinear “two-wave” structure equation for long waves on the surface of vertical falling liquid films. This equation is valid in a wide range of Reynolds numbers and reduces to the known equations for high and low Re. Theoretical data for the fastest growing waves are compared with the experimental results on velocities, wave numbers and growth rates of the waves in the inception region. The validity of theoretical assumptions is also confirmed by the direct measurements of the instantaneous velocity profiles in a wave liquid film.     

Wave influence on turbulence length scales in free surface channel flows

In order to predict sediment movements in coastal environments, the interaction between these particles and turbulence should be better understood. Although previous studies have particularly shown the importance of the turbulence length scales on sediment transport for current flows, few measurements have been made on wave/current flows. The purpose of our experiments is to get a better knowledge on wave action on these characteristic length scales. For this study, in the context of a grid-generated turbulence, we aimed to describe evolution of turbulence macro and micro scales in two kinds of free surface flow. Indeed, current and wave/current flows are studied. Two data analysis techniques are used to estimate these characteristic length scales depending on flow conditions. Whereas a well-known energetic method is used for current flow, a specific analysis based on correlation measurements is lead to describe temporal evolution of turbulence length scale over the wave period. As a main result, we show that the free surface causes a vortex stretching for current flow and that turbulence length scales follow a periodic evolution with a frequency which is twice as the swell period. The turbulence length scales also depend on wave period and amplitude.     

Dynamics of free liquid films

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 2, pp. 81–86, March–April, 1989.     

On the effect of drainage on free surface oscillations

Summary There are two conflicting results for the effect of small uniform drainage of an inviscid fluid from a tank on free surface oscillations. Miles [1] found the effect of drainage to be one of positive damping while Saad and Oliver [2] found a negative damping effect. When the viscosity is set equal to zero in this paper the results found using a multiple time method agree with those of Miles.Since there seems need of further experimental work in this area and in view of the small damping effects due to drainage, the effect of viscosity cannot be excluded. Thus in this paper both effects are included and the first terms in a uniformly valid (for all time) asymptotic solution for small viscosity and drainage (or filling) are found. To first order (but not in higher orders, which can be found) the two effects are uncoupled.     

Wave motion in a gravity field on the free surface and stratification interface of a fluid with stratified inhomogeneity. Nonlinear analysis

Regularities of the nonlinear gravitational wave motion in a two-layer density-stratified fluid are investigated for a finite thickness of the upper, lighter, layer. The characteristics of the nonlinear internal resonant interaction of the gravity waves generated by the free surface of the upper layer and the medium interface are considered. It is shown that in second-order calculations both degenerate (two-wave) and secondary combined (three-wave) resonant interactions may be realized.     

Wave formation in explosive welding

A hypothetical analogy between wave formation in explosive welding and the Karman vortex street is analyzed, and the physical laws of the wave formation process are investigated.Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 63–72, May–June, 1971.     

An experimental study on the free surface vertical vortex

An experimental investigation of the three-dimensional configuration of a vertical vortex flow, showing the importance of separating the radial and axial components of the total outflow, is presented. The relative magnitudes of the axial and radial flow components are measured and the depth of the air core is shown to be highly sensitive to the axial flow component. A representation of the flow in the core zone is also presented which may indicate internal boundary conditions that may be of interest to those developing theoretical models.     

Modeling the spread of an oil slick on the sea surface

The spread of an oil slick in the sea is considered. A mathematical model of the process is proposed and a formulas for determining the oil slick sizes in explicit form are obtained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 50, No. 3, pp. 127–130, May–June, 2009.     

The boundary layer on the free surface of a hollow vortex

Several problems are known which are associated with the circular motion of a viscous incompressible fluid with a rotating cylinder[l, 2]. In the present paper we consider the case of unsteady circular motion of a viscous fluid with a cavity in the fluid.     

Nonlinear waves on the free surface of an electrically conducting liquid

Gravity waves of small but finite amplitude on the free surface of an electrically conducting liquid are examined. For the waves whose propagation is described by the Korteweg-de Vries equation (in the absence of a magnetic field), equations are derived. In addition to nonlinearity and dispersion, these equations include the influence of applied magnetic fields. As an example, the effect of magnetic damping on a solitary wave is presented.     

An experimental study on free surface vortex dynamics

In the present research, hydrodynamic behavior of free surface vortices including surface displacement of the vortex core as a function of the vortex stability, relationship between the intake hydraulic parameters and vortex strength and characteristics of the vortex vertical stretching as a function of the intake hydraulic parameters were experimentally investigated in a horizontal intake. Relationship between the vortex-induced air and vortex strength was also evaluated and compared with the previous researches. In this regard, by defining a non-dimensional parameter as intake number, relationships between intake hydraulic parameters and other investigated dynamic aspects of free-surface vortices were discussed.     

Viscosity effect on free surface waves in fluids

The frequencies and damping coefficients of gravitational-capillary waves are found for a wide range of controlling dimensionless parameters. The transition to the limiting cases of deep water and an ideal fluid is analyzed. In the parameter plane, the boundary between the regions of oscillatory and aperiodic perturbations is determined and the region of weak damping is indicated. The equilibrium state of thin liquid films with account for the Van der Waals forces is considered and the dispersion equation for the capillary-Van der Waals surface waves is obtained. For a suitably chosen frequency scale, this equation is the same as that for gravitational-capillary waves. The physical conditions making it possible to observe capillary and Van der Waals waves in thin fluid layers are estimated. Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 4, pp. 156–164, July–August, 2000.     

Theory of thinning of free viscous fluid films

Thin viscous fluid films with free surfaces in the presence of surfactants are considered.