Turbulence At A Non-Turbulent/turbulent Density Interface In A Mean Shear-free Stably Stratified Two-layer Fluid

Since flow near the density interface is complex,this thesis is concerned with turbulence at a non-turbulence/turbulent density interface in a mean shear-free stably stratified two-layer fluid using the statistical theory of turbulence,spectral analysis and Rapid Distortion Theory,and the flow characteristics near the interface and the effect of density interface on turbulence are given.Further extended calculations made for the non-dimensional Eulerian frequency spectra of the horizontal and vertical velocities,and the root-mean-square horizontal and vertical velocities for both arbitrary and infinite Richardson number(Ri)for Case ?.the density interface thickness(h)is negligible;Case II.h is very thin,respectively.For Case?,(1)for arbitrary and infinite Ri,the effect of a density interface on the large scale eddies is more significant than on the small scale eddies;the distortion of turbulence by a density interface is more significant in the vertical direction than in the horizontal direction;(2)For arbitrary Ri,if the non-dimensional frequency is large,the non-dimensional Eulerian frequency spectra of both the horizontal and vertical velocities satify the-5/3 power law at the density interface and within the turbulent layer.However,they are not converged into the same line,suggesting that turbulence at the density interface is partially transferred into internal waves.For Case II,(i)a density interface has no effect on the non-dimensional Eulerian frequency spectra of the horizontal velocity;a transitional zone of the non-dimensional Eulerian frequency spectrum of the vertical velocity,which does not satisfy the-5/3 power law but has an increasing power law,is present within the turbulent layer;(ii)the non-dimensional Eulerian frequency spectrum of the vertical velocity satisfies the-5/3 power law while a decreasing power law is present at a density interface;(iii)a transitional zone of the non-dimensional Eulerian frequency spectrum of the vertical velocity decreases and is shifted to the left side with increasing distance from the interface,suggesting that the energy within the transitional zone decreases after taking h into account;when the non-dimensional frequency increases,the non-dimensional Eulerian frequency spectrum of the vertical velocity satisfies the-5/3 power law,suggesting that the density interface has no effect on the small scale eddies after taking h into account;far from the density interface,a transitional zone disappears;(iv)the power of the non-dimensional Eulerian frequency spectrum of the vertical velocity at the density interface decreases,suggesting that the energy is focused within the low non-dimensional frequency zone after taking h into account;(v)when h increases,the non-dimensional Eulerian frequency spectrum of the vertical velocity decreases with the same amplitude within the whole non-dimensional frequency range of the linear internal waves at the density interface,while the non-dimensional Eulerian frequency spectrum of the vertical velocity only decreases within the linear low dimensional frequency range and its decreasing amplitude decreases with increasing non-dimensional frequency;furthermore,the vertical amplitude that the density interface affects the horizontal and vertical root mean square velocities decreases with increasing Richardson number.Based on the one-dimensional K-? model of stratified turbulence proposed by Baumert(2005),the conversion of TKE and internal wave energy under two kinds of density distributions was calculated,which indicate that stratification can significantly reduce turbulent kinetic energy and rapidly convert it into internal wave energy.By using the mixture model of three-dimensional multi-phase flow and combining with large eddy simulation and dynamic mesh technique in Fluent,the numerical simulation of the mean shear-freestably stratified two-layer fluid is carried out.The interaction between density interface and turbulence is further studied and compared with the theoretical calculation and the experimental measurement.The results show the generation and evolution of oscillating-grid turbulence and reflect the early stage of interaction between turbulence and density interface.The modeled vertical distribution of horizontal and vertical root mean square velocities under the density interface is in good agreement with theoretical calculation and experimental measurement.