G. G. Chernykh

On Corrsin equation closure

Corrsin equation closure is done using the gradient hypothesis relating a two-point third-order correlation moment to a two-point second-order correlation function of a passive scalar field. A numerical locally isotropic turbulence model based on a closed system of Kolmogorov and Yaglom equations is constructed. A similarity solution of the Corrsin equation, which corresponds to infinitely high Reynolds and Peclet numbers, is constructed under assumption of constancy of Corrsin and Loitsiansky invariants. A numerical model of turbulence dynamics and temperature fluctuations behind a heated grid in a wind tunnel, which is based on Karman-Howarth and Corrsin closed equations, is developed.

On numerical modeling of the dynamics of turbulent wake behind a towed body in linearly stratified medium

Two numerical models of the dynamics of a turbulent wake behind a towed body in a linearly stratified medium are compared, namely, the model based on direct numerical integration of Navier-Stokes equations in the Oberbeck-Boussinesq approximation and the mathematical model with applying a semiempirical turbulence model of the second order. The calculation results of the two models are similar to the known experimental data and are in good agreement.

Experimental and numerical modeling of the turbulent wake of a self-propelled body

The development of the turbulent axisymmetric wake of a self-propelled body is modeled experimentally and numerically. Experimentally, the self-propulsion regime was implemented in the wake of a body of revolution whose hydrodynamic resistance was completely compensated by the pulse of a swirling jet rejected from its trailing part, and the jet-induced swirling was counterbalanced by the rotation of a part of the body surface in the opposite direction. The second-order semiempirical turbulence model that includes the differential equation of motion. the transfer of the normal Reynolds stresses, and the dissipation rate was used to describe this wake mathematically, and the nonequilibrium algebraic relations were used to determine the tangential stresses. A satisfactory agreement between the calculation results and the experimental data is shown. Degeneration of the distant turbulent wake is investigated numerically.

Numerical simulation of momentumless turbulent wake dynamics in linearly stratified medium

This paper presents comparison of two numerical models of the momentumless turbulent wake dynamics behind a body of revolution in a linearly stratified medium, namely, the model based on direct (DNS) numerical integration of Navier–Stokes equations in the Oberbeck–Boussinesq approximation and the mathematical model with application of a semi-empirical turbulence model of the third order. The results of calculations by these two models agree with the known experimental data.

Self-similar degeneration of the turbulent wake behind a body towed in a passively stratified medium

A mathematical model of the far turbulent wake behind a towed body in a passively stratified medium, based on the known semi-empirical e-ɛ model of turbulence, is considered. A grouptheoretical analysis of the model is performed. With the help of the method of B-determining equations, the model is reduced to a system of ordinary differential equations, which is solved numerically. The resultant solution is compared with a self-similar solution obtained by direct numerical integration of the differential equations at large distances from the body.

Numerical Modeling of Internal Waves Generated by Turbulent Wakes Behind Self-Propelled and Towed Bodies in Stratified Media

A flow that arises in a turbulent wake behind a body that moves in a stratified fluid is rather peculiar. With a relatively weak stratification a turbulent wake first develops essentially in the same way as in a homogeneous fluid and extends symmetrically. However, buoyancy forces oppose vertical turbulent diffusion. Therefore a wake has a flattened form at large distances from the body and, finally, ceases to extend in a vertical direction. Because of turbulent mixing the fluid density within the wake is distributed more uniformly than outside it. unperturbed state of a stable stratification. As a result, convective flows, which give rise to internal waves in an ambient fluid, arise in the plane perpendicular to the wake axis. Turbulent wakes behind bodies of revolution in stratified fluids have been considered in many publications [1–7]. Analyzing these works we note that the results of the numerical modeling of internal waves generated by turbulent wakes are incomplete. There are, in particular, no data on the numerical analysis of the characteristics of the internal waves generated by drag wake in stratified media, and there are no data on comparison of characteristics of the internal waves generated by the wakes behind the self-propelled and towed bodies. In the present work an attempt is made at filling the gaps available in the numerical modeling.

Dynamics of a Swirling Turbulent Wake past a Sphere

Using a mathematical model, which includes the averaged motion equations, differential transport equations of normal Reynolds stresses and dissipation rate, we carried out numerical modeling of evolution of a swirling turbulent wake with nonzero total excess momentum and angular momentum. The calculations were done to very large distances from the body. For small distances from the body the calculated profiles of averaged motion velocities and intensities of turbulent fluctuations of the longitudinal velocity component are in good agreement with the known experimental data of the Lavrent’ev Institute of Hydrodynamics, SB RAS. A simplified model of the flow is constructed.

Dynamics of a momentumless turbulent wake in a shear flow

Numerical modeling and investigation of the dynamics of a momentumless turbulent wake in a horizontally homogeneous shear flow are performed. The obtained data demonstrate transformation of the turbulized region in awake under the action of a shear flow, and also substantial generation of turbulence energy by averaged motion, which leads to slower turbulence degeneracy at large time values after passage of the body. Some considerations on flow similarity by shear Froude number are presented along with calculation results illustrating this similarity.

Numerical simulation of turbulent wakes with variable total excess momentum

Numerical simulation of the dynamics of plane and axisymmetric turbulent wakes in a homogeneous fluid is performed using the modified e ∼ ɛ model. The calculation results are in good agreement with the known experimental data. Asymptotic decay of axisymmetric turbulent wakes with small nonzero total excess momentum is numerically simulated.

Numerical modeling of 3D convection in the upper mantle of the Earth beneath lithosphere of central Asia

The constructed 3D numerical model of thermal convection in the upper mantle of the Earth is based on applying the vector potential-vorticity variables and the fractional step method. Detailed testing of the model is carried out. Results of 3D modeling of convection beneath cratons of central Asia are presented. The calculation results illustrate the structure of convection flows.