Hydrodynamics equations in geophysical problems. 1000-1M19RHG
Derivation of the Navier-Stokes equations.
Navier-Stokes equations as a dynamical system. Time asymptotics of solutions.
Boussinesq equations. Heat convection in fluids. Analysis of linear and nonlinear stability of solutions, their bifurcations, and heat transport.
Elements of Kolmogorov’s theory of turbulence.
Elements of geophysics. Analysis of the influence of rotation, density stratification and magnetic field on the fluid movement.
Type of course
Course coordinators
Learning outcomes
1. Knows what a dissipative autonomous dynamic system is.
2. Knows the terms: semigroup of operators, invariant set, absorbing set, attracting set, global attractor.
3. Knows the basic theorem about the existence of the global attractor.
4. Can derive Navier-Stokes equations.
5. Can prove the existence of a global attractor.
6. Knows what the energy distribution on harmonics is.
7. Is able to analyze the stability of solutions for Navier-Stokes and Boussinesq models.
8. Knows the elements of the Kolmogorov turbulence theory.
Social competence:
7. Understands the importance of dynamical systems as models of natural phenomena in mechanics, physics, chemistry, biology.
8. Can identify and describe a dissipative system, examine its structure and draw conclusions about the asymptotics of solutions in the context of applications.
9. Is well versed in the Navier-Stokest theory of equations and the problem of turbulence in fluids.
10. Is prepared to study original research papers and contribute to the field of study.
Assessment criteria
Assessment is based on an end-term exam.
Bibliography
1. Ch. Doering, J. Gibbon, Applied Analysis of the Navier-Stokes Equations. (Cambridge Texts in Applied Mathematics), 2005.
2. C. Foias, O. Manley, R. Rosa, R. Temam, Navier-Stokes Equations and Turbulence, Cambridge University Press, 2001.
3. P.Davidson, Turbulence. An Introduction for Scientists and Engineers, Oxford University Press, 2004.
4. J. Pedlosky, Geophysical Fluid Dynamics, Springer-Verlag, New York, 1979.
5. H. P. Greenspan, The Theory of Rotating Fluids, Cambridge University Press, New York, 1968.
6. P.H. Roberts, An introduction to magnetohydrodynamics, American Elsevier Pub. Co, 1967.
7. H.K. Moffatt, Magnetic Field Generation in Electrically Conducting
Fluids, Cambridge University Press, 1978.
Additional information
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