Experiments on instability and turbulence in a stratified shear flow

Abstract

This is a study of turbulence which results from Kelvin—Helmholtz instability at the interface between two miscible fluids in a two-dimensional shear flow in the laboratory. The growth of two-dimensional ‘billows’, their disruption by turbulence, and the eventual decay of this turbulence and the re-establishment of a gravitationally and kinematically stable interface are described. Continuous measurements of density and horizontal velocity from both fixed and vertically moving probes have been made, and the records obtained are presented, together with photographs showing the simultaneous appearance of the flow, which serve to identify the physical nature of events seen in the records. The measurements show how the fine-structure of the density field described in earlier experiments is related to velocity fluctuations. The vertical length scales of the final mean velocity and density structure are found to be different, and to depend on the Richardson number at which instability first occurred. The eventual Richardson number at the centre of layer is, however, not dependent on the initial Richardson number and has a value of about one third. The implications of these results to the eddy diffusion coefficients, to the energy exchange, and to turbulence in the ocean and the atmosphere are discussed.

Role of mixing in the structure and evolution of a buoyant discharge plume

“…[37] The gradient Richardson number (Ri g = (À g r 0 @r @z ) / (( @u @z ) 2 )) is an effective tool for understanding the importance of stratification in a turbulent field [e.g., Thorpe, 1973;Koop and Browand, 1979]. Values of Ri g were found to be on the order of 10 À2 within the core of the plume for all passes, significantly lower than the critical value of 1/4 considered necessary for the development of instabilities in a stratified flow [Miles, 1961;Howard, 1961].…”

Dual Doppler Radar Observation of a Tropical Rainband Developed from Two Convective Clouds

“…The "head" of the rear and 12e. The erosion of the "head" would be caused mainly by the following two processes: entrainment into the developing cell which is suggested from the upward movement of air in the "head" , and mixing due to Kelvin-Helmholtz instability as suggested by Thorpe (1973) and Britter and Simpson (1978). The relationship between the development of the convective cells and the rear inflow will be discussed in detail in the next section.…”

Complimentarity of Different Approaches for Assessing Vertical Turbulent Exchange Intensity in Natural Stratified Basins

“…In the paper [9], where the analysis of high number of probing data and calculations of required functions ( ε and N ) in different areas of the ocean was carried out, a reliable correspondence to the model expressions (13) in the main pycnocline as well as to model expressions for ε from (15) in the upper stratified layer in 2 1 < ≤ β scale range was found. It should be pointed out that ) (N K dependence in this layer amounts to the following expression:…”

“…Using the results of laboratory experiments [13,14] and several mechanistic approaches in [15], the constancy of dynamical Richardson number f R (ratio of potential energy increase rate in the system to the rate of intake of energy spent on the mixing) in the acts of stratified flux shear instability and breaking of wave perturbations was determined. Several approximate values of f R (1/3 in [13] and 1/4 in [14]) and 0.2 value for assessment of the entire multiplier of the expression (3) right side in [16] were proposed for application in the calculations.…”

“…Several approximate values of f R (1/3 in [13] and 1/4 in [14]) and 0.2 value for assessment of the entire multiplier of the expression (3) right side in [16] were proposed for application in the calculations. If we choose 0.25 value for f R (which was done to draw up the correlation (2)), we will obtain the following expression for diffusion coefficient:…”