Experiments on entrainment in an annulus with and without velocity gradient across the density interface

Abstract

Abstract. The entrainment process in a two layer density stratified fluid column was studied experimentally by imposing external shear stress on one or both layers. The experiments have been conducted in an annular tank containing two water layers of different salt concentration and the shear stress was applied by means of rotating screens. The following quantities were measured: the screen velocity (which was kept constant during each experiment), the stress at the upper screen, and vertical profiles of circumferential velocity and density at different radial locations.When equal stress was imposed at the surface of the upper layer and at the bottom of the lower layer, entrainment took place from the two sides of the density interface at equal rate so that the interface was stationary in the central position between the two screens and there was no velocity gradient across the interface. The dependence of the entrainment coefficient on Richardson number obtained in these experiments was similar in form to that obtained in the shear-free experiments with an oscillating grid (e.g. Nokes 1988).When a shear stress was applied at the upper surface only, the upper layer depth increased with time and a velocity gradient existed at the interface. The influence of the interracial velocity gradient on the entrainment rate was studied by comparing the rates obtained with and without this velocity gradient. The entrainment rates were approximately the same for high values of the Richardson number while at low Richardson number the entrainment rate was much larger when a velocity gradient existed across the interface.The main results of this work are as follows: (i) Despite the curved geometry of the annular system, the dependence of the entrainment coefficient on Richardson number for shear-free interface experiments was found to be similar in form to that obtained for oscillating grid experiments.(ii) The entrainment across the interface is due to turbulent energy generated at some distance from the interface by an external source (i.e. shear stress induced by a screen) and due to turbulence produced locally at the interface by a velocity gradient. The relative contribution of each turbulence source to the total entrainment was found to depend on the stability of the interface.The numerous applications of turbulent mixing in nature and engineering, and the importance of this process from the basic point of view, have encouraged the research on turbulent mixing in stratified flows. Most of the studies have been performed in the laboratory as measurements in the field are more expensive and involve uncertainties arising from variations in the governing conditions. Although the scales of turbulence in the laboratory may be different from those in nature, the results obtained from such laboratory experiments have proved to be useful in understanding the basic mechanisms and even in predicting the growth rate of the mixed layer of the thermocline (e.g. Turner 1973).Previous laboratory experiments have been conducted primarily i...

Experimental investigation of turbulent entrainment in an annulus with moving sidewalls

“…The measurements of E and Hopfinger (1986) supported the value of the exponent n-~l.5, but Nokes (1988) performed detailed experiments resulting in n-~ 1.2. This result was also obtained by Chai and Kit (1991) in their special shear-free annulus experiments (for details see below).…”

“…The Richardson number was based on the same friction velocity and on the thickness of the upper mixed layer. The experimental results of Scranton and Lindberg (1983) and Chai and Kit (1991), have shown that when the interface is exposed to a velocity shear, the exponent of the entrainment law (1) is close to 1.8. The results of Kantha et al (1977) for moderate and large Richardson numbers, follow approximately the same power law (see Chai and Kit 1991, Fig.…”

“…13). Chai and Kit (1991) have also performed experiments in the same annulus but with two rotating screens, imparting shear stress on both layers. This configuration eliminated the velocity gradient across the interface and indeed, the exponent of the entrainment law was obtained n= 1.25, very close to that reported by Nokes (1988) for the oscillating grid experiments.…”

“…The experiments were carried out in a modified version of the annulus used by Chai and Kit (1991). The apparatus consists of an annular perspex channel, 2 m in diameter, 0.2 m wide and 0.35 m in height (Fig.…”

“…Calibration of each probe was made prior to each experiment against 7 salt solutions of known concentrations. More details about the construction of the probes can be found in Chai and Kit (1991).…”