Temperature Fluctuations in Homogeneous Turbulence at Four Point Correlations with Variable Prandtl Number

In this study the decay of temperature fluctuations in homogeneous turbulence before the final period is analyzed by using the correlation equations for fluctuating quantities at four point in the flow field.Throughout this work three-and four point-correlation equations are obtained.The correlation equations are converted into spectral form by their Fourier-transform.The set of equations are made to determinate by neglecting the quintuple correlations in comparison to the fourth-order correlation terms.Finally by integration of the energy spectrum over all wave numbers, we have obtained the decay of energy of temperature fluctuations for four point correlations.The obtained results have been shown by graphically at different Prandtl No. and at the different state of temperature.We also determined the values of the constant appear at the energy equation ( 38) by using the values of the parameters existing in it for different fluids and the effects of the parameters have been tried to shown by graphically.Keywords-Deissler's method, Four-point correlation, Decay before the temperature fluctuations, final period.T denotes the total energy and t is the time, W, X, Y and Z are arbitrary constants determined by initial conditions. Temperature Fluctuations in Homogeneous Turbulence at Four Point Correlations with Variable Prandtl No.…