Turbulent diffusion in a stratified fluid
Creators: name: Grigg, Harold Russel
Publisher: name: University of British Columbia
Year: 2011

description: In natural fluids, stratification of density is common. Observations of natural turbulence in the presence of a density stratification are difficult since the stratification usually occurs in regions not readily accessible. In the laboratory, maintenance of a stratification in a shear flow presents equal difficulties. Observations were made of isolated puffs of fluid injected vertically downwards into a uniform fluid of the same density, and into a stably stratified fluid of greater density. The observations demonstrate that such isolated puffs in uniform fluid are subject to the same decay laws as is the turbulent energy in an extended turbulent fluid. This implies that a turbulent field, made up of randomly oriented puffs of fluid of varying volumes and velocities, would display many of the characteristics of a fluid in which the turbulence is a result of shear flow, and that observations made on such puffs can be applied with some confidence to natural turbulence. The apparatus was so constructed that the detailed mixing between the injected fluid and the surrounding fluid resulted in the formation of a finely divided precipitate which rendered the puffs visible, and permitted measurements of their path by means of moving picture photographs. The results demonstrate that mixing with the surroundings occurs throughout the puff, which retains its identity and a relatively uniform density. Measurements of the rate of formation of precipitate permit an estimate of the rate at which the injected fluid became mixed with the entrained fluid. The density stratification had very little influence upon this rate until after the puff had reached its maximum penetration. The rate of horizontal spreading of the puff during its motion also showed little effect of the stratification. Measurement of the penetration and ultimate position of the center of a puff in a density stratification together with measurements of the position of the center of a puff in uniform fluid permit the calculation of a number of dimensionless ratios. These are displayed graphically as a function of a dimensionless number made up from the initial conditions of velocity, volume, density gradient, density, and the acceleration of gravity. This number resembles the reciprocal of a Richardson's number and is referred to as 1/Ri. The maximum conversion of initial kinetic energy to potential energy observed was 20 percent, being greatest for small values of 1/Ri. The portion of the initial energy which contributes to the breakdown of the stratification was found to be approximately 3 percent and nearly independent of 1/Ri. Some writers have thought the loss to density stratification would be much greater than this. A figure representative of the transport of properties during the history of a puff varied by a factor 35 over the possible range of initial conditions, being greater for high values of 1/Ri. An estimate of the possible effect of density stratification upon the production of turbulent energy shows that production is reduced by as much as a factor 10 for small 1/Ri. This arises from the reversal and rebound of the puff of fluid in the stratification.