Advanced fluid mechanics

• Explain and derive the basic conservation laws of fluid mechanics on differential form
• Apply tensor notation to describe flow kinematics and solve flow problems
• Explain and apply the analogy between momentum, heat and mass transfer
• Derive and solve simplified versions of the Navier-Stokes equations, such as the vorticity equation, Creeping/Stokes flow, potential flow, similarity solutions and the boundary layer equations
• Solve and analyze various corresponding simplified flow problems and identify problem formulations that even further simplify solutions of the reduced equations.
• Evaluate the validity and impact of the assumptions used to solve the flow problems
• Discuss the physical interpretation of these solutions
• Use the boundary layer approximation to solve simple boundary layer problems
• Apply the method of normal modes to simple problems of flow instability and identify flow settings with potential appearance of common instabilities
• Document a technical solution in writing in a short and precise form

Derivation of the continuity equation, the Navier-Stokes equation and the energy equation on differential form. Tensor notation for describing flow kinematics. Analogies between transfer of momentum, heat and mass. Flow in ducts, boundary layers, free shear flows, Creeping/Stokes flows, potential flows. Similarity solutions and vorticity formulation of the Navier-Stokes equation. Linear instability analysis and laminar to turbulent transition. Theory will also be discussed in relation to industrial problems.

41312/41102/02631/02633/28864, Knowledge of basic fluid mechanics and basic knowledge of Matlab, Python or similar.
Knowledge of mathematics, specifically for solving partial differential equations (e.g. the chain rule, partial differentiation and integration, basic vector calculus including familiarity with Stokes’ and Gauss’ theorems).

Lectures and problem solving. Feedback on exercises during the course.