Basic properties of free stratified flows
Results of analytical studies of the governing equations of stratified rotating fluids based on the unification of theories of continuous and discrete groups, perturbations and modern numerical visualizations are described. Symmetries of basic systems and their simplified versions, different approximations and constitutive turbulent models are compared. A new method to calculate discrete groups analytically, which does not need a preliminary search for continuous groups, is developed. As an example of the practical use of the developed algorithm, a complete classification of cellular and roll structures of Bénard convection is presented. A complete classification of 3D periodic motions in compressible viscous stratified and rotating fluids, including regular (wave) and singular elements, is performed by perturbation methods. In all cases, in a viscous fluid, besides waves there are two different periodic boundary layers. In a homogeneous fluid the split boundary layers are merged, thus forming a joint doubly-degenerate structure. Stratification and rotation reduce the degeneration of the 3D periodic boundary layers. Calculations of a 3D periodic wave beam emitted by an oscillating part of a sloping plane are visualized by a computer-graphics method. The existence of thin extended components on the edges of the 3D wave cone is demonstrated.
Keywordsboundary layers complete equations continuous and discrete groups exact solutions internal waves
Unable to display preview. Download preview PDF.
- 1.L. D. Landau and E. M. Lifshitz, Course of theoretical physics, In: Vol. 6: Fluid Mechanics. Moscow: (1986) 136 pp; New York: Pergamon (1987).Google Scholar
- 5.Ovsiannikov L.V. (1994). Programme SUBMODELS. Gas dynamics. J. Appl. Math. Mech. 58(4):30–55Google Scholar
- 6.V. G. Baidulov and Yu. D. Chashechkin, Invariant properties of the equations of motion of stratified fluids. Dok. Phys. 47(12) (2002) 888–891. (Translated from Dokl. Akad. Nauk 387(6) 760–763.)Google Scholar
- 7.E. V. Bruyatskii, Turbulentnye Stratifitsirovannye Struinye Techeniya. (in Russian, Turbulent Stratified Jet Flows). Kiev: Naukova Dumka (1986) 296 pp.Google Scholar
- 8.Rodi W. (1980). Turbulence Models and Their Application in Hydraulics – A State of the Art Review. SBF Report 80/T/125. University of Karlsruhe, KarlsruheGoogle Scholar
- 11.A. V. Kistovich and Yu. D. Chashechkin, Types of discrete symmetries of convection in a plane fluid layer. Dok. Phys. 47(6) (2002) 458–460. (Translated from Dokl. Akad. Nauk 384(5), 630–633.)Google Scholar
- 17.S. A. Gabov and A. G. Sveshnikov, Zadachi Dinamiki Stratifitsirovannykh Zhidkostei. (in Russian, Problems of Stratified Fluids Dynamics). Moskva: Nauka (1986) 288 pp.Google Scholar
- 20.Yu. V. Kistovich and Yu. D. Chashechkin, A new mechanism of the non-linear generation of internal waves. Dokl. Phys. 47(2) (2002) 163–167. (Translated from Dokl. Akad. Nauk 382(6) 772–776).Google Scholar