Turbulent Mixing And Fractal Dimension Across A Density Interface In A Stably Straitified Fluid

Laboratory mixing box experiments were undertaken to examine turbulent mixing and fractal dimension at a density interface in a stably stratified two component fluid (fresh on salt), subjected to shear-free turbulence induced by an oscillating grid within the salt water layer. Geometrical shapes of the density interfaces were visualized by adding fluorescein and dye into the salt water layer. Both videos and photographs were made of the two-dimensional vertical cross-sections and three-dimensional density interfaces. Firstly, measurements were made of the mean height of the density interface and density of the salt water layer. Calculations were made of the entrainment rate and overall Richardson number (Rio). Secondly, videos and photographs of the visualized density interfaces were used to qualitatively analyze the mixing mechanisms across the density interface. Finally, using the box counting method, the fractal dimensions of the two-dimensional and three-dimensional interfaces were calculated to quantitatively understand their relationship with turbulence across a density interface. The relationship between the entrainment rate and the overall Richardson number, i.e., the entrainment law, follows the power law, taking the form of either E=KRio-3/2 or E=KRio-7/4. Four different mixing mechanisms corresponding to the different Ri0 are identified:(a) eddy impingement (Rio<15); (b) local Kelvin-Helmholtz instabilities (15< Rio<30); (c) the generation and breaking of interfacial waves (30< Rio<82); and (d) molecular diffusion (Rio>82). Fractal structures are present on both the two-dimensional and three-dimensional density interfaces. The fractal dimension of the three-dimensional density interface is 1 larger than that of the two-dimensional interface which is embedded in the three-dimensional interface. The fractal dimension of the two-dimensional section is related to that of the original three-dimensional interface. The fractal dimension decreases with an increasing overall Richardson number. The density interfaces become smoother with decreasing turbulence.