Turbulence and Mixing

Strong and weak turbulence. Navier-Stokes equation and its integrals of motion. Descriptions of turbulent diffusion via Brownian motion of a particle, and via convective-diffusive equation. Dimensionless numbers: Reynolds, Scmidt,Prandtl, Kubo and Peclet numbers. Kolmogorov turbulence and power laws. Forward and reverse cascade. Richardson's and Batchelor's laws. Intermittency and structure functions. Lagrangean statistics of material elements and Lyapunov exponents. Compressible velocity fields. Particles in turbulence. Nucleation of droplets in warm clouds. The problem of magnetic dynamo. Self-organized criticality. Interdisciplinary applications of the theory of trubulence.

NB! This course will take place in autumn semester 2025/2026 which starts on 1st of September and ends on 25th of January (you can find that information under Start date section). TalTech's timetables for Autumn semester 2025 will be published at the end of June via tunniplaan.taltech.ee. Switch the page to English and use "Search" and "Open detailed search" to find your course. NB! Some courses are taught by several lecturers during the same semester. Make sure that the course name and lecturer/teacher infromation of your course match with the information given in the Course Catalogue.

Knows the basic models, methods and results of the theory of turbulence, and is able to use these in his/her professional work.

Final assessment can consist of one test/assignment or several smaller assignments completed during the whole course. After declaring a course the student can re-sit the exam/assessment once. Assessment can be graded or non-graded. For specific information about the assessment process please get in touch with the contact person of this course. For specific information about grade transfer please contact your home university

None.

• Uriel Frisch, "Turbulence: The Legacy of A. N. Kolmogorov", CUP 1995

lectures, exercises