Vertical structure of the quasi-two-dimensional velocity field of a viscous incompressible flow and the problem of nonlinear friction
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An approximate theory is constructed to describe quasi-two-dimensional viscous incompressible flows. This theory takes into account a weak circulation in the vertical plane and the related divergence of the two-dimensional velocity field. The role of the nonlinear terms that are due to the interaction between the vortex and potential components of velocity and the possibility of taking into account the corresponding effects in the context of the concept of bottom friction are analyzed. It is shown that the nonlinear character of friction is a consequence of the three-dimensional character of flow, which results in the effective interaction of vortices with vertical and horizontal axes. An approximation of the effect of this interaction in quasi-two-dimensional equations is obtained with the use of the coefficient of nonlinear friction. The results based on this approximation are compared to the data of laboratory experiments on the excitation of a spatially periodic fluid flow.
KeywordsOceanic Physic Current Strength Ekman Layer Vertical Vorticity Viscous Incompressible Flow
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- 1.N. F. Bondarenko, M. Z. Gak, and F. V. Dolzhanskii, “Laboratory and Theoretical Models of a Plane Periodic Flow,” Izv. Akad. Nauk SSSR, Fiz. Atmos. Okeana 15, 1017–1026 (1979).Google Scholar
- 2.E. B. Gledzer, F. V. Dolzhanskii, and A. M. Oboukhov, Systems of Hydrodynamic Type and Their Application (Nauka, Moscow, 1981) [in Russian].Google Scholar
- 3.F. V. Dolzhanskii, “On the Influence of External Friction on the Stability of Plane-Parallel Flows of a Homogeneous Incompressible Fluid,” Izv. Akad. Nauk SSSR 23, 348–356 (1987).Google Scholar
- 5.F. V. Dolzhanskii and D. Yu. Manin, “Effect of the Ekman Turbulent Layer on the Dynamics of Large-Scale Motions,” Dokl. Akad. Nauk 322, 1065–1069 (1992).Google Scholar
- 8.S. D. Danilov and V. A. Dovzhenko, “Subcritical Flow in a System of Four Vortices,” Izv. Akad. Nauk, Fiz. Atmos. Okeana 31, 621–626 (1995).Google Scholar
- 9.A. M. Batchaev, “Self-Oscillations in an Elementary Cell of a Doubly Periodic Quasi-Two-Dimensional Flow,” Izv. Akad. Nauk, Fiz. Atm. Okeana 39, 445–457 (2003) [Izv., Atmos. Ocean. Phys. 39, 401–412 (2003)].Google Scholar