Mathematical approaches in description of turbulent flows 1100-MADTF

Topics:
1.The basic concepts.
a. The equations of hydrodynamics, averaging and Reynolds decomposition,
b. The Reynolds stress and its effect on large scale flows; turbulent viscosity
2.The simplest theory of weak turbulence and calculation of the Reynolds stress
3. Strong turbulence – fully nonlinear
a. General description of isotropic and axisymmetric turbulence from symmetry considerations and group theory,
• The energy cascade
• The evolution equations for the correlation tensor
b. The Markovianized one-point two-scale approach,
c. Renormalization of the hydrodynamic equations,
• Turbulent viscosity and large-scale flow
d. The Two-Scale Direct Interaction Approach (TSDIA),
e. The stochastic description of the dynamics of particle trajectories, passive scalars and streamlines.

Prerequisites (description)

Requirements: 1. Knowledge of the theoretical basics of hydrodynamics. 2. Knowledge of the basics of statistics. 3. Good knowledge of vector calculus 4. Knowledge of methods for solving differential equations.

Course coordinators

Krzysztof Mizerski

Assessment criteria

Conditions for completing the course: Students will be required to pass an oral exam at the end of the course.

Bibliography

Literature: The lecture will not be fully based on any particular book and its aim will be to present mathematical methods applied to describe complex, nonlinear turbulent flows in an accessible form. Therefore, there is no single textbook, but the recommended literature includes (will be sent to students in electronic form):
[1] A. Yoshizawa 1998, Hydrodynamic and magnetohydrodynamic turbulent flows, Springer.
[2] G.K. Batchelor 1982, The theory of homogeneous turbulence, Cambridge University Press.
[3] P.A. Davidson 2015, Turbulence: an introduction for scientists and engineers, Oxford University Press.
[4] W.D. McComb 2014, Homogeneous isotropic turbulence; phenomenology, renormalization and statistical clossures, Oxford University Press.
[5] K. Gawędzki 2008, Soluble models of turbulent transport, in: Non-equillibrium statistical mechanics and turbulence by J. Cardy, G. Falkovich & K. Gawędzki, Cambridge University Press.

Additional information

Additional information (registration calendar, class conductors, localization and schedules of classes), might be available in the USOSweb system:

Description of 1100-MADTF in USOSweb