稳定分层二层流非湍流/湍流层无平均剪切密度界面处的湍流

Turbulence at Non-turbulent/Turbulent Density Interface in a Mean Shear-free Stably Stratified Two-layer Fluid

采用湍流统计理论、谱分析和快速畸变理论研究稳定分层二层流非湍流/湍流层无平均剪切密度界面处的湍流.分别在密度界面厚度(h)可忽略和很薄两种情况下,推导出任意理查森数(Ri)Ri→∞时,湍流层中水平、垂直方向速度的欧拉频谱和水平、垂直方向均方根速度的积分表达式.在h可忽略情况下:(1)任意Ri,Ri→∞时,密度界面对大尺度涡的影响显著,而对小尺度涡几乎无影响;距离密度界面越近,湍流层中水平方向均方根速度增大而垂直方向均方根速度减小;(2)任意Ri且在无量纲频率较大时,密度界面处、湍流层中水平、垂直方向速度的欧拉频谱满足-5/3幂次律,但是,它们不收敛于同一直线,表明密度界面处部分湍流转化为内波.在h很薄的情况下:(1)在水平方向上密度界面对湍流无显著的影响;湍流层中垂直方向速度的欧拉频谱出现过渡区,不满足-5/3幂次律,其幂次律增大,表明湍流过渡区的能量减少,但是,密度界面对线性小尺度涡仍几乎无影响;(2)距离密度界面越远,密度界面厚度对湍流的影响减弱并且偏向于线性中尺度涡;当远离密度界面时,过渡区消失,表明考虑密度界面厚度后密度界面对湍流的影响范围有限;(3)密度界面处垂直方向速度的欧拉频谱的幂次律减小,表明密度界面处线性内波的能量向线性低频区集中;(4)随着密度界面厚度增加,密度界面处垂直方向速度的欧拉频谱在整个线性内波频域里等幅度减小,湍流层中垂直方向速度的欧拉频谱只在线性低频区域减小且减小的幅度随着频率增大而减小;密度界面对湍流层中水平、垂直方向均方根速度影响的垂向范围随Ri增大而减小.

This paper is concerned with the turbulence at a non-turbulent/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.Further extended calculations are made for the non-dimensional Eulerian frequency spectra of the horizontal and vertical velocities,and the horizontal and vertical root-mean-square velocities for both arbitrary and infinite Richardson number (Ri)for Case I,the density interface thickness (h)is negligible ;Case II,h is very thin,respectively.For Case Ⅰ,(1)for arbitrary and infinite Ri,the effect of a density interface on 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 satisfy the -5/3power law at the density interface and within the turbulent layer.However,they are not converged into the same line,suggesting that the turbulence at the density interface is partially transferred into internal waves.For Case Ⅱ,(i)a density interface has no the effect on non-dimensional Eulerian frequency of the horizontal velocity;a transitional zone of the non-dimensional Eulerian frequency spectrum of the vertical velocity,which does not satisfy the -5/3power 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 -5/3power law while a decreasing powerlaw is present at the 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 -5/3power 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 deceases 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 non-dimensional frequency range and its decreasing amplitude decreases with increasing non-dimensional frequency;furthermore,the vertical range within which the density interface affects the horizontal and vertical root mean square velocities decreases with increasing Richardson number.