Fluid Dynamics

Nyuma: Partial-Differential-Equations, Multivariable-Calculus, Linear-Algebra

Icyiciro

1. Describing a flow

   3 Isomo
   ≋The continuum hypothesis and fields≋Eulerian and Lagrangian descriptions, the material derivative≋Kinematics: streamlines, pathlines and streaklines
   Kuri i

2. Mass, the stream function and vorticity

   3 Isomo
   ≋Conservation of mass, the continuity equation and incompressibility≋The stream function and two-dimensional incompressible flow≋Vorticity, circulation and Kelvin's circulation theorem
   Kuri i

3. Stress, pressure and ideal flow

   4 Isomo
   ≋The stress tensor and Cauchy's momentum equation≋Hydrostatics and pressure≋The Euler equations and Bernoulli's theorem≋Potential flow and the Laplace equation
   Kuri i

4. The Navier-Stokes equations

   3 Isomo
   ≋Viscosity, Newtonian fluids and the Navier-Stokes equations≋Exact solutions: Couette, Poiseuille and Stokes' first problem≋Dimensional analysis, the Reynolds number and the scaling symmetry
   Kuri i

5. Slow flow and thin layers

   2 Isomo
   ≋Stokes flow at low Reynolds number≋Boundary layers
   Kuri i

6. Vorticity, energy and turbulence

   3 Isomo
   ≋The vorticity equation and vortex stretching≋Energy: the energy equality, dissipation and enstrophy≋Turbulence and Kolmogorov 1941 (a heuristic theory)
   Kuri i

7. The Cauchy problem and weak solutions

   2 Isomo
   ≋The Cauchy problem: the Leray projection and local existence≋Weak solutions (Leray-Hopf) and Sobolev spaces for fluids
   Kuri i

8. Regularity and criticality

   2 Isomo
   ≋Regularity criteria: Ladyzhenskaya-Prodi-Serrin and Beale-Kato-Majda≋Partial regularity (Caffarelli-Kohn-Nirenberg) and criticality: 2D versus 3D
   Kuri i

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