Capillary-Gravity waves in a viscous fluid

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.

Download Full-text

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

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100030048 ◽

1955 ◽

Vol 51 (1) ◽

pp. 162-178 ◽

Cited By ~ 74

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.

Download Full-text

Nonlinear Gravity Waves in a Thin Sheet of Viscous Fluid

Journal of Mathematics and Physics ◽

10.1002/sapm1966451266 ◽

1966 ◽

Vol 45 (1-4) ◽

pp. 266-288 ◽

Cited By ~ 41

Author(s):

C. C. Mei

Keyword(s):

Viscous Fluid ◽

Gravity Waves ◽

Thin Sheet ◽

Nonlinear Gravity

Download Full-text

THE EFFECT OF AN EXPLOSION IN A COMPRESSIBLE FLUID UNDER GRAVITY

Canadian Journal of Physics ◽

10.1139/p61-157 ◽

1961 ◽

Vol 39 (9) ◽

pp. 1330-1346 ◽

Cited By ~ 1

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.

Download Full-text