This paper calls attention to some of the most important and easily recognizable forms of surface wave, pointing out that their essential common characteristic is the evanescent field structure over the wave front, as represented by equiphase planes. The problems of launching and supporting surface waves must, in general, be distinguished from one another and it does not necessarily follow that because a particular surface is capable of supporting a surface wave that a given aperture distribution of radiation, e.g. a vertical dipole, can excite such a wave. The paper concludes with a discussion of the behavior of surface waves and their applications.

http://ieeexplore.ieee.org/iel5/10933/4065481/04065500.pdf

Surface Waves

Highly resolved three-dimensional and two-dimensional simulations of gravity currents in planar and cylindrical configurations are presented. The volume of release of the heavy fluid is varied and the different phases of spreading, namely acceleration, slumping, inertial and viscous phases, are studied. The incompressible Navier–Stokes equations are solved assuming that the Boussinesq approximation is valid for small density difference. The simulations are performed for three different Reynolds numbers (Re): 895, 3450 and 8950 (this particular choice corresponds to values of Grashof number: 10 5 ,1 .5×10 6 and 10 7 , respectively). Following their sudden release, the gravity currents are observed to go through an acceleration phase in which the maximum front velocity is reached. As the interface of the current rolls up, the front velocity slightly decreases from the maximum and levels off to a nearly constant value. At higher Re, three-dimensional disturbances grow rapidly and the currents become strongly turbulent. In contrast, in two-dimensional simulations, the rolled-up vortices remain coherent and very strong. Depending on the initial Re of the flow and on the size of the release, the current may transition from the slumping to the inertial phase, or directly to the viscous phase without an inertial phase. New criteria for the critical Re are introduced for the development of the inertial phase. Once the flow transitions to the inertial or viscous phase, it becomes fully three-dimensional. During these phases of spreading, two-dimensional approximations underpredict the front location and velocity. The enhanced vortex coherence of the two-dimensional simulations leads to strong vortex interaction and results in spurious strong time variations of the front velocity. The structure and dynamics of the three-dimensional currents are in good agreement with previously reported numerical and experimental observations.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0022112007005769

On the front velocity of gravity currents

The approach to self-similarity of the solutions of the shallow-water equations representing gravity-current releases

A phase-plane method is used to study the existence of similarity solutions of the two-dimensional and axisymmetric shallow-water equations representing gravity currents with volumes proportional to tα, where α ≥ 0 and t is the time after the flow is initiated. Only currents for which there is a balance between the inertia of the current and the driving buoyancy force are considered. It is found that similarity solutions exist for the two-dimensional problem for all α ≥ 0, with some restrictions on the condition at the current front. It is shown that no similarity solutions satisfying the boundary conditions on the axis of symmetry exist for the axisymmetric problem except when α = 0.

Self-similar solutions of the shallow-water equations representing gravity currents with variable inflow

The dispersive motion of a fluid column, collapsing under its own weight whilst immersed in a lighter fluid, both fluids resting on a rigid horizontal bottom, is idealized as a symmetric problem of incompressible potential flow. The velocity potentials in the two fluids are functions of two space-variables and time, and satisfy Laplace’s equation in the two space-variables; and the principal boundary conditions are that, at every point of the fluid interface, the two fluid pressures are equal, and the two normal fluid velocities are both equal to the normal velocity of the interface itself. The initial accelerations of the boundary of a column of semicircular cross-section are derived analytically. An approximate numerical method of solution for the early stages of such a motion is obtained by satisfying these boundary conditions at only a finite number of angular positions instead of everywhere on the fluid interface. Some calculations by this method are shown for certain fluid columns in vacuo . Alternatively, by neglecting vertical accelerations in the motion, the problem is reduced to one of hyperbolic type in one space-variable and time, and this approximation may be solved by the numerical method of characteristics. Some calculations of this type are also shown, in which vertical accelerations have been neglected ab initio , and which are therefore appropriate to initially squat columns. The hydrodynamical problem of the collapse of a fluid column surrounded by a second lighter fluid, both resting on a rigid horizontal plane, was suggested by the ‘base surge’ observed at the Atomic Weapon Trials at Bikini.

Part III. the dispersion, under gravity, of a column of fluid supported on a rigid horizontal plane

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Part III. the dispersion, under gravity, of a column of fluid supported on a rigid horizontal plane