About generalized scaling for passive scalars in fully developed turbulence

In this paper we use a simple normal form approach of scale invariant fields to investigate scaling laws of passive scalars in turbulence. The coupling equations for velocity and passive scalar moments are scale covariant. Their solution shows that passive scalars in turbulence do not generically follow a general scaling observed for velocity field because of coupling effects.

Drop migration of middle Reynolds number in a vertical temperature gradient

The experimental investigation of the thermocapillary drop migration in a vertical temperature gradient uns performed on ground. Silicon oil and pure soybean oil were used as experimental medium in drops and as continuous phases, respectively, in the present experiment. The drop migration, under the combined effects of buoyancy: and thermocapillarity, was studied for middle Reynolds numbers in order of magnitude O(10(1)). The drop migration velocities depending on drop diameters were obtained. The present experimental results show relatively small migration velocity in comparison with the one suggested by Young et nl. for linear theory of small Reynolds number. An example of flow patterns inside the drop was observed by PIV method.

A solution to the upward migration of an intrusion

The evolution of the upward migration of the magma is a nonlinear and unstable problem in mathematics. It is difficult to solve it. And using the numerical method, the solution is relatively tedious and time-consuming. This paper introduces a method of the instantaneous point source to solve the linear and unstable heat conduction equation during the infinite period of time instead of the solution of the nonlinear and unstable heat conduction equation. The results obtained by this method coincide with those by the numerical method, meaning that this method offers a simple way to solve the nonlinear and unstable heat conduction equation.

Turbulent passive scalar field of a small prandtl number

The statistical-mechanics theory of the passive scalar field convected by turbulence, developed in an earlier paper [Phys. Fluids 28, 1299 (1985)], is extended to the case of a small molecular Prandtl number. The set of governing integral equations is solved by the equation-error method. The resultant scalar-variance spectrum for the inertial range is F(k)~x−5/3/[1+1.21x1.67(1+0.353x2.32)], where x is the wavenumber scaled by Corrsin's dissipation wavenumber. This result reduces to the − (5)/(3) law in the inertial-convective range. It also approximately reduces to the − (17)/(3) law in the inertial-diffusive range, but the proportionality constant differs from Batchelor's by a factor of 3.6.

A passive scalar field convected by turbulence

Classical statistical mechanics is applied to the study of a passive scalar field convected by isotropic turbulence. A complete set of independent real parameters and dynamic equations are worked out to describe the dynamic state of the passive scalar field. The corresponding Liouville equation is solved by a perturbation method based upon a Langevin–Fokker–Planck model. The closure problem is treated by a variational approach reported in earlier papers. Two integral equations are obtained for two unknown functions: the scalar variance spectrum F(k) and the effective damping coefficient (k). The appearance of the energy spectrum of the velocity field in the two integral equations represents the coupling of the scalar field with the velocity field. As an application of the theory, the two integral equations are solved to derive the inertial-convective-range spectrum, obtaining F(k)=0.61 −1/3 k−5/3. Here is the dissipation rate of the scalar variance and is the dissipation rate of the energy of the velocity field. This theoretical value of the scalar Kolmogorov constant, 0.61, is in good agreement with experiments.