Angular Momentum in Geophysical Turbulence: Continuum Spatial Averaging Method

ISBN-13: 9789048164783 / Angielski / Miękka / 2010 / 245 str.

Victor N. Nikolaevskiy

Opis

Turbulence theory is one of the most intriguing parts of fluid mechanics and many outstanding scientists have tried to apply their knowledge to the development of the theory and to offer useful recommendations for solution of some practical problems. In this monograph the author attempts to integrate many specific approaches into the unified theory. The basic premise is the simple idea that a small eddy, that is an element of turbulent meso-structure, possesses its own dynamics as an object rotating with its own spin velocity and obeying the Newton dynamics of a finite body. A number of such eddies fills a coordinate cell, and the angular momentum balance has to be formulated for this spatial cell. If the cell coincides with a finite difference element at a numerical calculation and if the external length scale is large, this elementary volume can be considered as a differential one and a continuum parameterization has to be used. Nontrivial angular balance is a consequence of the asymmetrical Reynolds stress action at the oriented sides of an elementary volume. At first glance, the averaged dyad of velocity components is symmetrical, == However, if averaging is performed over the plane with normal nj, the principle of commutation is lost. As a result, the stress tensor asymmetry j is determined by other factors that participate in the angular momentum balance. This is the only possibility to determine a stress in engineering."

Spis treści

* Preface. Introduction. * 1: Angular Momentum In A Viscous Fluid. 1.1. Dynamics of viscous fluids. 1.2. Angular momentum in hydrodynamics (review). 1.3. Angular momentum of a fluid element. 1.4. Micro and macro-scales. * 2: Space Averaging And Macroequations. 2.1. Spatial averaging principles. 2.2. Chain of turbulence balance equations. 2.3. Angular momentum balance. 2.4. Evolution of moment of inertia. * 3: Turbulence As Open Thermodynamic System. 3.1. Energy and entropy balances. 3.2. Constitutive laws for turbulent fluids. 3.3. Kinetic analysis of turbulence. 3.4. Turbulent problem formulation. * 4: Turbulent Wakes In The Atmosphere. 4.1. Turbulent wake of a body. 4.2. Asymmetrical dynamics of a suspension. 4.3. Turbulence of heterogeneous fluids. 4.4. Turbulent flow with intermittency. * 5: Geophysical Turbulence. 5.1. Tornado as a localized phenomenon. 5.2. Ocean currents on the equator. 5.3. Global ocean circulation. 5.4. Towards the problem of a magnetic dynamo. * 6: Vortex Symmetry In Statistical Theory. 6.1. Homogeneity and symmetry concepts. 6.2. Tensorial moments of a velocity pulsation field. 6.3. Turbulence with reflection symmetry. 6.4. Turbulence with angular symmetry. * 7: Vector-Director Concept In Turbulence. 7.1. Dynamics equations. 7.2. Energy and constitutive laws. 7.3. Wind velocity profile at a ground surface. 7.4. Flows between plates. * 8: Literature. * 9: Index.