Long gravity waves on a viscous fluid flowing down an inclined plane

1972 ◽  
Vol 6 (1) ◽  
pp. 15-21 ◽  
Author(s):  
P. Smith
Keyword(s):  
Viscous Fluid ◽  
Gravity Waves ◽  
Inclined Plane

Surface Waves of Viscous Fluid Down an Inclined Plane

1992 ◽  
pp. 105-114 ◽  
Author(s):  
Hirokazu Ninomiya ◽  
Takaaki Nishida ◽  
Yoshiaki Teramoto ◽  
Htay Aung Win
Keyword(s):  
Viscous Fluid ◽  
Surface Waves ◽  
Inclined Plane

Instability of a liquid film flow over a vibrating inclined plane

1995 ◽  
Vol 294 ◽  
pp. 391-407 ◽  
Author(s):  
David R. Woods ◽  
S. P. Lin
Keyword(s):  
Gravity Waves ◽  
Film Flow ◽  
Shear Waves ◽  
Faraday Waves ◽  
Critical Amplitude ◽  
Inclined Plane ◽  
Flow Parameters ◽  
Chebychev Polynomials ◽  
Liquid Film Flow ◽  
Faraday Wave

The problem of the onset of instability in a liquid layer flowing down a vibrating inclined plane is formulated. For the solution of the problem, the Fourier components of the disturbance are expanded in Chebychev polynomials with time-dependent coefficients. The reduced system of ordinary differential equations is analysed with the aid of Floquet theory. The interaction of the long gravity waves, the relatively short shear waves and the parametrically resonated Faraday waves occurring in the film flow is studied. Numerical results show that the long gravity waves can be significantly suppressed, but cannot be completely eliminated by use of the externally imposed oscillation on the incline. At small angles of inclination, the short shear waves may be exploited to enhance the Faraday waves. For a given set of relevant flow parameters, there exists a critical amplitude of the plane vibration below which the Faraday wave cannot be generated. At a given amplitude above this critical one, there also exists a cutoff wavenumber above which the Faraday wave cannot be excited. In general the critical amplitude increases, but the cutoff wavenumber decreases, with increasing viscosity. The cutoff wavenumber also decreases with increasing surface tension. The application of the theory to a novel method of film atomization is discussed.

scholarly journals Viscous damping of gravity waves over a permeable bed

1978 ◽  
Vol 1 (4) ◽  
pp. 497-507
Author(s):  
K. K. Puri
Keyword(s):  
Viscous Fluid ◽  
Gravity Waves ◽  
Fixed Bed ◽  
Higher Order ◽  
Viscous Damping ◽  
Porous Bed ◽  
Damping Effects ◽  
Dominant Influence

The damping of gravity waves over the surface of a layer of viscous fluid which overlies a porous bed saturated with the same fluid is studied. It is shown that viscosity may not be the dominant influence in the damping mechanism; the damping effects due to percolation in the fixed bed may be of the same or even higher order than those due to viscosity.

The character of the equilibrium of an incompressible heavy viscous fluid of variable density

1955 ◽  
Vol 51 (1) ◽  
pp. 162-178 ◽  
Author(s):  
S. Chandrasekhar
Keyword(s):  
Viscous Fluid ◽  
Gravity Waves ◽  
Order Differential Equation ◽  
Mathematical Problem ◽  
Variable Density ◽  
Static State ◽  
Vertical Coordinate ◽  
Infinitesimal Disturbance ◽  
Lower Fluid ◽  
Characteristic Values

ABSTRACTThis paper is devoted to a consideration of the following problem: Given a static state in which an incompressible viscous fluid is arranged in horizontal strata and the density is a function of the vertical coordinate only, to determine the initial manner of development of an infinitesimal disturbance. The mathematical problem is reduced to one in characteristic values in a fourth-order differential equation and a variational principle characterizing the solution is enunciated. The particular case of two uniform fluids of different densities (but the same kinematic viscosity) separated by a horizontal boundary is considered in some detail. The mode of maximum instability in case the upper fluid is more dense and the manner of decay in case the lower fluid is more dense are determined; and the results of the calculations are illustrated graphically. Gravity waves (obtained in the limit when the density of the upper fluid is zero) are also treated.

Capillary-Gravity waves in a viscous fluid

1977 ◽  
Vol 28 (1-4) ◽  
pp. 313-319 ◽  
Author(s):  
L. Debnath ◽  
K. K. Bagchi ◽  
S. Mukherjee
Keyword(s):  
Viscous Fluid ◽  
Gravity Waves

Stability of a thin viscous fluid film flowing down a rotating non-uniformly heated inclined plane

2010 ◽  
Vol 216 (1-4) ◽  
pp. 225-242 ◽  
Author(s):  
Asim Mukhopadhyay ◽  
Anandamoy Mukhopadhyay
Keyword(s):  
Viscous Fluid ◽  
Fluid Film ◽  
Inclined Plane ◽  
Viscous Fluid Film

THE EFFECT OF AN EXPLOSION IN A COMPRESSIBLE FLUID UNDER GRAVITY

1961 ◽  
Vol 39 (9) ◽  
pp. 1330-1346 ◽  
Author(s):  
R. A. Ross
Keyword(s):  
Exact Solution ◽  
Viscous Fluid ◽  
Gravity Waves ◽  
Speed Of Sound ◽  
Compressible Fluid ◽  
Asymptotic Methods ◽  
Axially Symmetric ◽  
Linearized Theory ◽  
The Waves ◽  
Special Case

In this paper an investigation is made of the effect of an axially symmetric explosion at any depth in a semi-infinite, compressible, non-viscous fluid, acted upon by gravity. The explosion is represented by a line source of the form δ(x)δ(z – h)δ(t), where h is the depth of the source. An exact solution is given using the linearized theory. This solution is studied in detail by asymptotic methods, for the special case of a surface explosion. It is found that compressibility results in the gravity waves being propagated with a speed less than c, the speed of sound in the fluid. If x is the distance from the explosion and t the time that has elapsed after the explosion, then for [Formula: see text] only "precursor" waves are noticed at the point of observation. For [Formula: see text] large amplitude waves are present, similar to the waves predicted by the incompressible theory.

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