COURSES

Goals

The objective of the course is to deliver to the students the existing knowledge of fluid dynamics. Students will be acquainted with fundamentals of fluid dynamics of compressible and mostly incompressible flows. They will learn about laminar and turbulent flows, basic conservation laws which represent fundamentals for the geophysical fluid flows (physical oceanography). Students will develop the ability to solve independent research and development tasks in the field of fluid dynamics, including the setup of a fluid problem to be resolved, analytical tools to find a solution in simple flows and numerical approach to resolve more complex ones.

Curriculum

Fluids. Perfect gas and liquids. Hydrostatics of compressible media. Surface and body forces. Gauss’ and Stokes’ theorems. Kinematics of fluids. What are flows? Fluid particles, streamlines, streak lines, particle paths, Euler and Lagrangian time derivative. Decomposition of relative motion in straining rate and rotation. Vorticity and circulation. Conservation laws. Volume and mass conservation, continuity equation, Euler and Navier-Stokes equation of motion. Mechanical energy equation. Thermodynamic laws for fluids. Bernoulli equation. Irrotational flow. 2D flows, velocity potential and stream function. 3D potential flows and axisymmetric stream function. Sources and sinks, doublet. Flow past half-body, cylinder and sphere. 2D flows and conformal mapping. Gravity waves. Linear (potential) theory of surface waves in deep and shallow waters. Group and phase velocity. Stokes’ drift. Internal waves in continuously stratified fluids, energy of internal waves. Laminar flows. Analogy between heat and vorticity diffusion, diffusion of vortex street, decay of line vortex. Boundary layers. Boundary layer on a flat plate, flow past a cylinder and sphere, separation of flow. Secondary flows and perturbation techniques. Instabilities. Normal modes. Kelvin-Helmholtz instability, double-diffusive instability, stability of inviscid parallel flows.Turbulent flows. Subgrid-scale processes and Reynolds averaging. Eddy viscosity and mixing length in a stratified fluid flow. Turbulent boundary layers, shear flows, coherent structure in a wall layer. Large eddy simulations (LES) techniques. Computational fluid dynamics. Finite difference, finite element and finite volume methods. Central difference scheme, leap-frog method.