Experimental And Theoretical Study Of Turbulence In Stably Stratified Flows

Stably stratified turbulence widely occurs in the ocean,atmospheric boundary layerand in many engineering applications. Stably stratified -ows have been investigatedextensively because they play a very important role in both theory and application.The main work of this paper is focused on the turbulent characteristics, especially onthe turbulent momentum counter-gradient transport features via the experimental andtheoretical investigations. The main results are given as follows:First, the system of experimental facilities on turbulent stratified -ow was con-structed in our laboratory, and experiments were conducted in stably stratified turbu-lence with a sharp interface, using Particle Dynamic Analysis (PDA ). The results showthat: (1) The width of turbulent mixing layer increases along the streamwise directionwhen the -ow develops in the -ow direction. The mixing layer appears to exhibit non-linear growth duo to the e-ects of shear and stratification.The o-set of the mixing layerto the side with the smaller inlet velocity is calculated quantitatively. The stronger themean shear rate,the larger the o-set of the mixing layer to the side with the smaller inletvelocity, while the stronger the stratification,the weaker the o-set of the mixing layer.The depth of the mixing layer is thinner and the di-erence of the thickness betweenupper mixing layer and lower mixing layer is smaller in the strong stratification .(2)The streamwise turbulent intensity is larger than the vertical one. The turbulent kineticenergies in both streamwise and vertical directions show a decaying scaling power lawin the range of 4 < x/M < 20. The decaying exponent for streamwise direction is from-0.68 to -1.29,for vertical one is from -1.22 to -1.55. The vertical component decaysfaster than the streamwise one regardless of the intensity of shear and stratification.(3)The probability density function (PDF) of -uctuating velocity is close to Gaussiandistribution at the center of the mixing layer. In the two sides of the mixing layer, thedegree of the deviation of the -atness and skewness of turbulent -uctuating velocityin the upper region with the smaller inlet velocity from the values of the Gaussiandistribution is less than that of the lower region with the larger inlet velocity. At theedges of the mixing layer, the -uctuating velocity shows asymmetric pdf. (4)Turbulentmomentum counter-gradient transport occurs only in the strong shear cases and is notfound at the center of mixing layer. The turbulent counter-gradient momentum trans-port is found to occur in the side of larger inlet velocity. The range of counter-gradientmomentum transport is in -2.8 < y/M < -1.4. Second, Hilbert-Huang transform (HHT) and arbitrary order Hilbert spectral areapplied to analyze the times series of velocities of stratified turbulence . The mo-mentum counter-gradient transport characteristic is firstly obtained in the space of fre-quency. It is found that: (1)There is a wide inertial subrange in the spectrum of the?uctuating velocity via applying HHT. The power law of the turbulent energy spec-trum is close to -7/3 in the non-stratified case with strong shear,but deviates form -7/3in the stratified case. (2)At the central region,the streamwise intermittency factor islarger than the vertical one. (3)Coherent structures play a principal role in turbulentmomentum transport.Vertical momentum transport is suppressed at the presence ofstratification. Local counter-gradient transport phenomena occur at certain modes(orat certain frequencies) , but the global counter-gradient momentum transport resultsfrom the total contributions of all modes (or all frequencies).Third, using two-scale direct interaction approximation (TSDIA), the energy spec-tra and the thermal intensity spectra in buoyancy-driven stratified ?ows are theoreti-cally investigated . (1)The theoretical representations for the turbulent energy spectraand thermal intensity spectra are explicitly deduced . (2)Di?erent scaling power laws,such as -5/3 law,-7/3 law, -9/3 law and -11/3 law corresponding to di?erent ?ow condi-tions, which are often observed in previous experiments are derived theoretically . (3)The results presented here overcome the defect of Lumley's result ,i.e., the turbulentspectra should be positive for small wave number.