Advanced Fluid Dynamics

Topics

• Eulerian and Lagrangian Descriptions of Fluid Motion
• Kinematics, Strain and Vorticity
• Kinematic Transport Theorem and Consequences
• Forces in the Fluid, Stresses and Cauchy’s Law
• Momentum Conservation Law
• Stress and Strain, Navier-Stokes Equations
• Vorticity Theorems for Homogeneous and Stratified Fluids
• Rayleigh Problem – Where Does Vorticity Come From?
• Scaling and Approximations
• Slow Spreading of a Mud Layer on an Incline
• Selective Withdrawal into a Line Sink, Boundary Layer Approximation and Similarity Solution
• Stokes Flow Past a Sphere
• Mechanics of Aerosols
• Inviscid Irrotational Flows of a Homogeneous Fluid
• Bernoulli’s Theorems for Inviscid Homogeneous Fluids
• Example of Steady Boundary Layer; The Laminar Jet
• Effects of Variable Pressure Gradient
• Kármán’s Momentum Integral Approximation
• An Application to Transient Boundary Layer Along a Flat Plate
• Unsteady Boundary Layers
• Gust and Separation
• Thermal Energy; Mountain Wind
• Buoyant Plume from a Steady Source of Heat
• Homogenization and Dispersion in Oscillatory Flows in a Pipe
• Heruristic Argument of Kelvin-Helmholtz Instability; Linearized Analysis of K-H Instability; K-H Instabilty of a Continuously Stratified Fluid
• Rayleigh’s Inviscid Theory of Instability of Parallel Flows; Fjortoft’s Theorem
• Viscous Effects on Parallel Flow Instability
• Porous Media and Darcy’s Law; Homogenization and Micro-Mechanical Basis of Darcy’s Law
• Saffman-Taylor Instability and Viscous Lingering; Convection in a Porous Layer with a Geothermal Gradient (Rayleigh Number)
• Horton-Rogers-Lapwood Instability
• Rotating Coordinates and Coriolis Force
• Vorticity Theorem in Rotating Fluid; Shallow-Sea Approximation
• Steady Wind-Induced Flow in a Shallow Sea
• Nonuniform Forcing on the Sea Surface-Ekman Pumping
• Wind-Forced Waves in a Two-Layered Sea
• Coastal Upwelling