Tham khảo tài liệu 'hydrodynamics advanced topics part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | 16 Hydrodynamics - Advanced Topics Fig. 5. Normalized ideal turbulent fluxes for P 1 using measured data. W is the measured peak of ự 2. z is the vertical distance from the interface. Adapted from Schulz et al. 2011a . Equation 32 is used to calculate covariances like f g f 3g f4g present in equations 3 . For example for ỡ 2 3 and 4 the normalized fluxes are given respectively by r g f 2 gf 1 - 2n 2 n 1 - n f g2 n 1 - n 1 v 2 -1 2 1 - n 3 n 3 34a n 1 - n I n 1 - n 1 - n 4 - n4 n 1 - n 1 - . r ĩ-n 7T n 7 2 -1 2 LvL As an ideal case for 1 perfect superposition equation 33 furnishes e g f J 20 y j g 1 - n e - -n e r 2e-1 ie 2e-1 I 4 1 - n -1 n 34b 34c 35 and the normalized covariances f 2g f 3g f 4g for ỡ 2 3 and 4 are then given respectively by 1 - 2n 1 - n 3 n 3 36a r g f 3 r g f 4 g f3 JfiJg 4 g f Vf V r g f e n 1 - n -L v 2--1 2 I rg f2 17 One Dimensional Turbulent Transfer Using Random Square Waves - Scalar Velocity and Velocity Velocity Interactions r f 3 r f 4 36b 36c Equations 34a and 36a can be used to analyze the general behavior of the flux f2 . These equations involve the factor 1 - 2n which shows that this flux changes its direction at n . For 0 n the flux f2 is positive while for n it is negative. In the mentioned example of gas-liquid mass transfer the positive sign indicates a flux entering into the bulk liquid while the negative sign indicates a flux leaving the bulk liquid. This behavior of f2 was described by Magnaudet Calmet 2006 based on results obtained from numerical simulations. A similar change of direction is observed for the flux f4 easily analyzed through the polynomial 1 - n 4 - n4 . The equations of items and confirm that the normalized turbulent fluxes are expressed as functions of n and p only while the covariances may be expressed as functions of n p Xf and V 2. Transforming the derivatives of the statistical equations Simple derivatives The governing differential equations 2 and 3 involve the .