Notes from graduate course in Fluid Mechanics. There are several instances where a cogent explanation is lacking, not least due to a complete absence of diagrams. Hopefully, these issues will be resolved over time.
Lecture 15 - Kinematics: Local Linear Flows
Velocity gradient tensor. Classification of linear flows. Linear flow in Turbulence - flow below Kolmogorov length scale.
Lecture 21 - Kinematics: Surface gravity waves
Streamlines and streaklines in comoving frame and lab frame of reference. Perturbation expansion to obtain the Stokes drift.
Lecture 22 - Conservation of mass and the streamfunction
Mass conservation and consideration of incompressiblity. 2D Streamfunction in polar and general orthogonal system. Stokes streamfunction in spherical coordinate system.
Lecture 23 - Velocity field from dilation and vorticity fields
Multipole expansion. Biot-Savart Law.
Lecture 24 - Velocity field due to line vortex
Not yet written
Lecture 25 - Velocity of propagation of circular line vortex
Streamlines due to a thin circular line vortex. Velocity of propagation of a circular line vortex (thin vortex ring).
Lecture 30 - Lift in potential flows in 2D
Lift on circular cylinder in the presence of circulation. Lift on elliptic cylinder in the presence of circulation.