Statistical Model of Turbulent Dispersion Recapitulated

A comprehensive summary and update is given of Brouwers’ statistical model that was developed during the previous decade. The presented recapitulated model is valid for general inhomogeneous anisotropic velocity statistics that are typical of turbulence. It succeeds and improves the semiempirical and heuristic models developed during the previous century. The model is based on a Langevin and diffusion equation of which the derivation involves (i) the application of general principles of physics and stochastic theory; (ii) the application of the theory of turbulence at large Reynolds numbers, including the Lagrangian versions of the Kolmogorov limits; and (iii) the systematic expansion in powers of the inverse of the universal Lagrangian Kolmogorov constant C0, C0 about 6. The model is unique in the collected Langevin and diffusion models of physics and chemistry. Presented results include generally applicable expressions for turbulent diffusion coefficients that can be directly implemented in numerical codes of computational fluid mechanics used in environmental and industrial engineering praxis. This facilitates the more accurate and reliable prediction of the distribution of the mean concentration of passive or almost passive admixture such as smoke, aerosols, bacteria, and viruses in turbulent flow, which are all issues of great societal interest.

SIMULATION AND EARLY WARNING OF NATURAL AND TECHNOGENIC INFLUENCES IN COASTAL AREAS IN THE SEA OF AZOV

In this work, the waves and currents generated by prognostic wind in the Sea of Azov are investigated using a three-dimensional nonlinear sigma-coordinate model. The mathematical model was also used for studying the transformation of passive admixture in the Sea of Azov, caused by the spatiotemporal variations in the fields of wind and atmospheric pressure, obtained from the prediction SKIRON model. Comparison of the results of numerical calculations and the data of field observations, obtained during the action of the wind on a number of hydrological stations was carried out. The evolutions of storm surges, velocities of currents and the characteristics of the pollution region at different levels of intensity of prognostic wind and stationary currents were found. The results of a comprehensive study allow reliably estimate modern ecological condition of offshore zones, develop predictive models of catastrophic water events and make science-based solutions to minimize the possible damage.

SIMULATION AND EARLY WARNING OF NATURAL AND TECHNOGENIC INFLUENCES IN COASTAL AREAS IN THE SEA OF AZOV

In this work, the waves and currents generated by prognostic wind in the Sea of Azov are investigated using a three-dimensional nonlinear sigma-coordinate model. The mathematical model was also used for studying the transformation of passive admixture in the Sea of Azov, caused by the spatiotemporal variations in the fields of wind and atmospheric pressure, obtained from the prediction SKIRON model. Comparison of the results of numerical calculations and the data of field observations, obtained during the action of the wind on a number of hydrological stations was carried out. The evolutions of storm surges, velocities of currents and the characteristics of the pollution region at different levels of intensity of prognostic wind and stationary currents were found. The results of a comprehensive study allow reliably estimate modern ecological condition of offshore zones, develop predictive models of catastrophic water events and make science-based solutions to minimize the possible damage.

Some Problems of Statistical Modeling of Intermittent Turbulent Flows and Their Solutions

Some problems of statistical modeling of turbulent flows associated with the hydrodynamic effects of intermittency of various dynamic and scalar fields are identified, and a justification of their solutions is proposed. At first examines some problems of statistical modeling of large-scale (energy-containing) turbulence structure under the conditions of turbulent and nonturbulent fluid intermittency in the turbulent flow. This primarily applies to the problem of obtaining the differential equations of hydrodynamics for conditional statistical moments (conditional averages), i.e. for single-point statistical moments of each of the intermittent media of turbulent flow. To solve this problem is given a mathematically rigorous justification of conducting the operation of conditional averaging of the Navier-Stokes equations. As a result was obtained the system of differential equations for the conditional averages of turbulent and nonturbulent fluid. The main advantage of the obtained differential equations for the conditional averages is that these equations don’t contain the source terms. Therewith is given a physical substantiation of transformation process of nonturbulent fluid in turbulent, that occurs in a thin superlayer, which separates turbulent and nonturbulent fluid. Here also is given a justification of conducting the operation of total averaging of the partial derivates, which, as it turns out, is not a permutational and leads to a number of specific features in comparison with the unconditional averaging in RANS. Another problem associated with statistical modeling of inhomogeneous turbulent flows, i.e. flows with an inhomogeneous field of scalar substance. It is known that the dynamic field with turbulent fluid does not coincide with the inhomogeneous field of scalar substance. To solve this problem is proposed a method of calculating the statistical characteristics both of the turbulent fluid and the inhomogeneous field of a passive admixture concentration. It is shown, that the conditional averages of the passive admixture concentration are significantly different. In conclusion we consider the problem of statistical modeling of diffusional turbulent combustion of not pre-mixed chemically reacting gases, expressly the modeling by the known method PDF with involving the “reduced fuel concentration” as the passive impurity concentration. To solve this problem is given a justification of new differential equations, allowing to carry out calculations only of the conditional averages for the intersection region of the dynamic field of the turbulent fluid and the inhomogeneous field of the passive impurity concentration. Some results of such calculations, performed in the self-similar field of diffusion turbulent propane plume, are presented together with the experimental data available in literature.