James W. Rottman

Gravity currents produced by instantaneous releases of a heavy fluid in a rectangular channel

Results of laboratory experiments are presented in which a finite volume of homogeneous fluid was released instantaneously into another fluid of slightly lower density. The experiments were performed in a channel of rectangular cross-section, and the two fluids used were salt water and fresh water. As previously reported, the resulting gravity current, if viscous effects are negligible, passes through two distinct phases : an initial adjustment phase, during which the initial conditions are important, and an eventual self-similar phase, in which the front speed decreases as t-4 (where t is the time measured from release). The experiments reported herein were designed to emphasize the inviscid motion. From our observations we argue that the current front moves steadily in the first phase, and that the transition to the inviscid self-similar phase occurs when a disturbance generated at the endwall (or plane of symmetry) overtakes the front. If the initial depth of the heavy fluid is equal to or slightly less than the total depth of the fluid in the channel, the disturbance has the appearance of an internal hydraulic drop. Otherwise, the disturbance is a long wave of depression. Measurements of the duration of the initial phase and of the speed and depth of the front during this phase are presented as functions ofthe ratio of the initial heavy fluid depth to the total fluid depth. These measurements are compared with numerical solutions of the shallow-water equations for a two-layer fluid.

Unsteady gravity current flows over obstacles: some observations and analysis related to the phase II trials

Abstract The Phase II trials at Thorney Island were designed to provide a few full-scale results of the interaction of heavy gas clouds with surface-mounted obstacles. In this paper, we interpret some preliminary observations from the Phase II trials by reviewing and developing the theory of two-layer fluid flows over obstacles and comparing these results with visual observations of the field trials. The results are preliminary, and largely qualitative, because the concentration and other quantitative measurements are not yet available.

Steep standing waves at a fluid interface

An algorithm is formulated for computing perturbation-series solutions for standing waves on the interface between two semi-infinite fluids of different but uniform densities. Using a comppter, the series solutions are computed to fifth order for a general value of r , the ratio of the density of the upper fluid to that of the lower fluid (0 ≤ r ≤ l), and to 21st order for five specific values of this ratio: r = 0, 10 −3 , 0·1, 5·0, 1·0. The series for the period, the energy, and the interface profile of the waves are summed using Pade approximants. The maximum wave height for each of the above five density ratios is estimated from the locations of the poles of the Pade approximants for the wave period and the wave energy. At maximum height the interface appears to be vertical at a point on the interface that is very near the crest for r = 10 −3 and approaches the midpoint between the crest and the trough as r approaches 1·0.

The initial and gravity-spreading phases of heavy gas dispersion: Comparison of models with phase I data

Abstract The aim of this paper is to compare theoretical models with the observed behaviour of the heavy gas clouds in the Phase I Thorney Island field trials for small times after release. The approach we adopt is to divide the early-time motion into two phases: an initial phase, in which the motion is a strong function of the release conditions, and a gravity-spreading phase, in which motion is mainly horizontal and driven by buoyancy and the mean ambient flow. The results of idealised computations and experiments modelling these two phases are compared with the measurements and observations of the Phase I trials. We find that in the initial phase, all the field trials are strongly buoyancy dominated, and therefore, that the flow field due to the containment vessel has only a minor effect on the initial motion of the cloud. The initial motion mostly consists of the generation of a radially spreading vortex ring. We perform idealised calculations that predict the time after release when this vortex ring is formed. In the gravity-spreading phase, we show that conventional gravity current theory fairly accurately describes the motion. As the ring expands, it leaves mixed fluid behind so that by the end of the gravity-spreading phase a fairly uniform well-mixed cloud remains. This is when “box-models” become the appropriate description. We also consider the effects of shear in the mean wind profile on the radially spreading gravity current. We show that shear is responsible for the upwind current front having the shape of a thin wedge and the downwind front having a thick shape with a nearly vertical leading edge. The behaviour of these two fronts explains the elongation of the cloud along the mean wind direction.

The Initial Development of Gravity Currents from Fixed Volume Releases of Heavy Fluids

This paper describes some laboratory experiments of the initial development of gravity currents resulting from the instantaneous release of a fixed-volume of one fluid into a cross flow of another fluid of lesser density. Two limiting cases are considered in detail: the release of a cylindrical volume of neutrally-buoyant fluid into a uniform cross flow and the release of a cylindrical volume of heavy fluid into still surroundings. The results of the experiments are interpreted in terms of simple models.

Some Physical Processes Involved in the Dispersion of Dense Gases

In this paper we attempt to provide a theoretical framework for the formulation of mathematical models of dense gas dispersion in the atmosphere. Our approach is to divide the evolution of a released dense gas cloud into four phases, during each of which different physical processes governing the behaviour of the cloud are most important. These processes are identified and recent attempts to uhderstand them are discussed. We also give scaling arguments for the order and duration of the different phases as functions of the atmospheric and release conditions.

Some new highest-wave solutions for deep-water waves of permanent form

The classical series expansion procedure of Michell is used to calculate some new highest-wave solutions. These solutions are shown to correspond to the types of gravity waves studied recently by Chen & Saffman (1980). Results are presented for wave profiles, phase speeds, and kinetic and potential energies.

Numerical calculations of steady gravity-capillary waves using an integro-differential formulation

A new integro-differential equation is derived for steady free-surface waves. Numerical solutions of this equation for periodic gravity-capillary waves on a fluid of infinite depth are presented. For the two limiting cases of gravity waves and capillary waves, our results are in excellent agreement with previous calculations. For gravity-capillary waves, detailed calculations are performed near the wave-number at which the classical second-order perturbation solution breaks down. Our calculations yield two solutions in this region, which in the limit of small amplitudes agree with the results obtained by Wilton in 1915; one solution has the small amplitude behaviour of a gravity wave and the other that of a capillary wave, but the numerical results show that at large amplitudes both waves have the characteristics of capillary waves. The calculations also show that the wavenumber range in which two solutions exist increases with increasing wave height.