Mixing and Dispersion of Wastes by Wind and Wave Action

Masch, Frank D.

doi:10.1016/b978-1-4832-8391-3.50046-4

Cited by 6 publications

(5 citation statements)

References 20 publications

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“…We have formulated the problem such that all parts of the current system, including the averaged current u h , the wave drift us and the Langmuir circulations, represented by ?, b and uu h , may be of comparable intensity. There are some indications, however, that at least in some circumstances the dimensionless shear U;(z) may be somewhat larger than us and the other components of the current (Masch 1963) and their gradients. If we take the parameter A as a measure of UL(x), then ( 3 5 d ) provides an estimate of its magnitude: where 0; is O(1).…”

Section: A Perturbation Solutionmentioning

confidence: 70%

A rational model for Langmuir circulations

1976

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A realistic theoretical model of steady Langmuir circulations is constructed. Vorticity in the wind direction is generated by the Stokes drift of the gravity-wave field acting upon spanwise vorticity deriving from the wind-driven current. We believe that the steady Langmuir circulations represent a balance between this generating mechanism and turbulent dissipation.Nonlinear equations governing the motion are derived under fairly general conditions. Analytical and numerical solutions are sought for the case of a directional wave spectrum consisting of a single pair of gravity waves propagating at equal and opposite angles to the wind direction. Also, a statistical analysis, based on linearized equations, is developed for more general directional wave spectra. This yields an estimate of the average spacing of windrows associated with Langmuir circulations. The latter analysis is applied to a particular example with simple properties, and produces an expected windrow spacing of rather more than twice the length of the dominant gravity waves.The relevance of our model is assessed with reference to known observational features, and the evidence supporting its applicability is promising.

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Section: A Perturbation Solutionmentioning

confidence: 70%

A rational model for Langmuir circulations

1976

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“…Notwithstanding its environmental importance, however, the present understanding of this flow is still rather limited, being based on a relatively small number of often inconclusive laboratory studies undertaken in combined wind and water, or air-sea interaction, tunnels. Results obtained in these experimental systems by Forssbland (1974), Tichner (1958), Masch (1963), Baines & Knapp (1965), Goossens (1979), Koutitas & O'Connor (1980) and Goossens, van Pagee & Tessel (1982) have been found to be highly three-dimensional on both the air side and the water side of the interface due to sidewall friction effects. Among other consequences, this leads to velocity distributions in the centreplane, i.e.…”

Section: Introductionmentioning

confidence: 83%

The structure of turbulent shear-induced countercurrent flow

Tsanis

Leutheusser

1988

J. Fluid Mech.

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Countercurrent flow is a generalized plane Couette flow in which a shear-induced drift current is opposed by a pressure-driven return flow such that the resulting mass flux is zero. This type of flow is encountered in both environmental fluid mechanics and tribology. Measurements are described that were undertaken in steady turbulent countercurrent flow, generated in a novel type of apparatus between smooth walls, at Reynolds numbers, expressed in terms of surface velocity and depth of the flow, from 200 to 20000; the critical Reynolds number of laminar to turbulent transition as determined herein is approximately 1750. The laboratory facility is explained, and experimental data are presented on mean velocities, pressure gradient, turbulence intensities, Reynolds stresses, and energy spectra. It is found that the velocity distributions follow the universal law of the wall in the drift current, but that the flow is undeveloped in the return portion of the flow. The non-dimensional longitudinal pressure gradient increases with Reynolds number, and a semi-empirical law of resistance is proposed and experimentally verified. Turbulence intensities in the drift current increase toward the shearing surface but are essentially constant in the opposing pressure-driven flow. The distribution of the Reynolds stress is found to be consistent with previous measurements obtained in this type of flow using different apparatus, but only approximately follows the theoretically linear distribution. Energy spectra in the shear-induced portion of the flow involve higher frequencies closer to the shearing surface than in the return current. There, the spectral energy is essentially the same throughout the flow, reflecting the constancy of turbulent intensity in this region.

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“…It has been a common practice in the study of turbulent diffusion t o relate the diffusion coefficient, K, t o a mixing length ( and a characteristic velocity, uo'. Following the argument of Masch (1964), the dispersion coefficient can be written as If one assumes that the contribution from the current velocity t o mixing is small relative to wave motion at the Strait of Canso, uo' becomes proportional only to the resultant orbital velocity of the particles within the waves u'. The path of the particle motion within a wind wave near the water surface was measured by Johnson (1960).…”

Section: Mathematical Modelmentioning

confidence: 99%

“…The values of K thus calculated correlate well with wind velocity in the form of K a U"'" as indicated in figure 1. The laboratory data of Masch (1964) are represented by…”

Section: Comparison Of Calculated and Experimental Kmentioning

confidence: 99%

“…When the wind speed reaches a certain value, waves begin to form, and at a sufficiently high value, waves become unstable and break into whitecaps, causing increased water mixing at the surface and, eventually, dispersion. The most recent laboratory investigations on the effect of wind speeds on dispersion were performed by Johnson and Rice (1952) and Masch (1964). Johnson and Rice studied the motions of a number of individual particles in a laboratory channel with a wind speed of 42.6 ft/sec by recording their relative positions in particular frames.…”

Section: Introductionmentioning

confidence: 99%

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Dispersion of Pollutants in the Strait of Canso1

Wang

McMillan

Chen

1976

J American Water Resour Assoc

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By using the method of successive approximations, the one‐dimensional diffusion equation was solved for the distribution of pollutant from an instantaneous point source in a semi‐infinite body of water under the influence of wind‐generated waves. The solution was obtained with the aid of an expression developed in this study to relate the dispersion coefficient to wind speed, characteristics of a wind‐generated wave, and drift current velocities. The results indicate that the wave causes the local concentration to oscillate with respect to time around a mean concentration distribution curve. The period of the oscillation is about that of the wave, and its amplitude is always less than 7 percent of the mean. The effect of a chemical reaction is to reduce the level of pollutant concentration, the magnitude of the reduction being dependent upon both the rate constant and the order of reaction. The case of simultaneous dumping of one pollutant at different sites was also considered.

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Mixing and Dispersion of Wastes by Wind and Wave Action

Cited by 6 publications

References 20 publications

A rational model for Langmuir circulations

A rational model for Langmuir circulations

The structure of turbulent shear-induced countercurrent flow

Dispersion of Pollutants in the Strait of Canso1

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