Fluid Dynamics

  1. Theoretical and Mathematical Aspects
    1. Dimensionless Numbers
      1. Importance and Role in Fluid Dynamics
        1. Scaling Analysis
          1. Model Simplification
          2. Reynolds Number
            1. Definition and Calculation
              1. Influence on Flow Regimes (Laminar vs. Turbulent)
              2. Mach Number
                1. Definition and Relation to Compressibility
                  1. Applications in Supersonic and Hypersonic Flows
                  2. Froude Number
                    1. Significance in Open Channel Flow
                      1. Applications in Ship Maneuverability
                      2. Prandtl Number
                        1. Relation between Momentum and Thermal Diffusivity
                          1. Impact on Convective Heat Transfer
                          2. Other Dimensionless Numbers
                            1. Euler Number
                              1. Weber Number
                                1. Knudsen Number
                              2. Stability Analysis
                                1. Linear Stability Theory
                                  1. Small Disturbance Analysis
                                    1. Stability of Parallel Flows
                                    2. Nonlinear Stability Theory
                                      1. Transition to Turbulence
                                        1. Bifurcation Analysis
                                        2. Instability Mechanisms
                                          1. Kelvin-Helmholtz Instability
                                            1. Rayleigh-Taylor Instability
                                              1. Tollmien-Schlichting Waves
                                            2. Potential Flow Theory
                                              1. Basic Assumptions
                                                1. Inviscid Flow
                                                  1. Irrotational Flow
                                                  2. Stream Function and Velocity Potential
                                                    1. Laplace's Equation in Fluid Dynamics
                                                      1. Applications in Aerodynamics
                                                      2. Flow Superposition
                                                        1. Source and Sink Flows
                                                          1. Doublet Flow
                                                          2. Complex Potential in Two-Dimensional Flows
                                                            1. Use of Conformal Mapping
                                                              1. Applications in Flow Around Cylinders
                                                            2. Vortex Dynamics
                                                              1. Vorticity and Circulation
                                                                1. Definition of Vorticity
                                                                2. Vortex Shedding
                                                                  1. Kármán Vortex Streets
                                                                    1. Implications in Structural Vibration and Aeroacoustics
                                                                    2. Vortex Rings
                                                                      1. Formation and Stability
                                                                        1. Interaction and Dynamics
                                                                        2. Vortex Breakdown
                                                                          1. Spiral and Bubble Modes
                                                                            1. Effects in Aerodynamics
                                                                          2. Boundary Layer Theory
                                                                            1. Boundary Layer Definition
                                                                              1. Laminar and Turbulent Layers
                                                                                1. Blasius Boundary Layer Solution
                                                                                2. Momentum Thickness and Displacement Thickness
                                                                                  1. Definitions and Calculations
                                                                                    1. Importance in Force Calculations
                                                                                    2. Boundary Layer Separation
                                                                                      1. Conditions Leading to Separation
                                                                                        1. Consequences and Control Methods
                                                                                        2. Wall Shear Stress and Skin Friction
                                                                                          1. Influence on Drag Force
                                                                                            1. Methods for Measurement and Estimation
                                                                                        9. Fluid Dynamics in Nature
                                                                                        First Page