When fluctuating temperature field is considered to be super imposed on a general field of eddy turbulence, the early period decay phenomena in regard to velocity, temperature and velocity-temperature are guided by three dynamical equations that are obtained here in a straightforward manner. The equations so obtained are simplified for the case of homogeneous turbulence and subsequently for the case of homogeneous and isotropic turbulence. § 1. IntroductionThe study of the behaviour of a turbulent scalar field e.g. temperature, concentration etc. superimposed on a turbulent velocity field is essential from the view point of turbulent mixing. Due to this, the extension of the theories propounded for the turbulent velocity field to the case of turbulent scalar fields are often desireable. Obukhoff [1] and Corrsin [2] have studied the small scale structure of the fluctuating scalar field with the help of Kolmogoroff's universal equillibrium hypothesis. O'Brien and Francis [3] presented the dynamical consequences of the quasinormality approximation (cf. Millionshtchikov, [4,5]) which states that the fourth-order moments are related to the second-order moments as in a normal distribution when applied to the behaviour of a scalar field. Following Chandrasekhar's [6] deductive theory of turbulence Jain [7] studied the fluctuating temperature field and compared his results with those of Corrsin [2]. Codreanu [8] obtained the equation for the spectrum of the scalar quantity using the method proposed by Malfliet [9]
This paper reports some results of turbulent boundary layer computation. The calculation is made assuming that law of the wall is valid throughout the boundary layer. Simple relations are proposed for friction for a smooth pipe and a flat plate at zero incidence. The results are compared with recent measurements. Encouraging results are obtained for both the cases of flows.
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