Regular and singular components of periodic flows in the fluid interior |
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| Affiliation: | 1. School of Computing, University of Utah, 50 South Central Campus Dr., Room 3190, Salt Lake City, UT 84112, USA;2. Pearlstone Center for Aeronautical Engineering Studies, Department of Mechanical Engineering, Ben-Gurion University, Beer-Sheva, Israel;3. Division of Applied Mathematics, Brown University, Providence, RI, USA;1. Department of Mechanical Engineering, Columbia University, 500 West 120th Street, 220 SW Mudd, MC 4703, New York, NY 10027, USA;2. Department of Biomedical Engineering, Columbia University, 500 West 120th Street, 220 SW Mudd, MC 4703, New York, NY 10027, USA;3. Cartilage Biology and Orthopaedics Branch, National Institute of Arthritis, Musculoskeletal and Skin Diseases, National Institutes of Health, Bethesda, MD, USA;1. Coll. of Information Science and Engineering, Ocean Univ. of China, Qingdao 266071, P.R. China;2. Dept. of Information and Mathematics Sciences, Jiliang Univ, Hangzhou 310018, P.R. China;3. Coll. of Automation and Electronic Engineering, Qingdao Univ. of Science and Technology, Qingdao 266042, P.R. China |
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| Abstract: | The structure of infinitesimal periodic motions in the interior of a rotating compressible fluid which has been stratified using salt is analyzed taking account of dissipation effects. In the general case, the system of fundamental equations of motion belongs to the class of singularly perturbed equations, the solutions of that consist of functions which are regular and singular with respect to the dissipative coefficients that describe both propagating hybrid waves as well as several types of accompanying singular components including boundary layers. The thicknesses of the singular components are determined by the kinematic viscosity, the diffusion coefficient of the salt and the characteristic frequencies of the problem. In the model of a barotropic or homogeneous fluid, the singular components of spatial periodic flows combine together, which is indicative of degeneracy of the system of equations. Taking account of the full set of components, which are regular and singular with respect to the dissipative characteristics, enables one to construct exact solutions of problems of the generation and non-linear interaction of waves. |
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