ME-466: Instability

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Lectures in this course (63)

Parallel Flow Instability

Explores parallel flow instability, velocity ratio effect, and solving the Rayleigh equation.

Spatio-temporal Spectral Analysis

Covers spatio-temporal spectral analysis, dispersion relations, Fourier transforms, and group velocity.

Complex Fourier Space Analysis

Covers the analysis of instability in complex Fourier space and its application to mixing layers.

Viscous Jet Instability

Analyzes the instability of a non-viscous fluid jet and the effects of viscosity.

Stability Analysis of Shear Flows

Explores the stability analysis of shear flows, emphasizing conditions for flow instability and the impact of varying temperature profiles.

Weakly Nonlinear Approach: Bifurcations and Amplitude Equations

Explores weakly nonlinear approach, bifurcations, amplitude equations, critical slowing, and nonlinearities in dynamical systems.

Weakly Nonlinear Analysis: Multiple Time Scale Expansion

Explores weakly nonlinear analysis through multiple time scale expansion, emphasizing the period of a gravitational pendulum and non-resonance conditions.

Nonlinear Dynamics: Bifurcations and Stability

Explores nonlinear dynamics, bifurcations, stability, weakly nonlinear systems, saturation, Hopf bifurcation, and global stability analysis.

Foam Inducing Nonlinear Damping

Explores foam inducing nonlinear damping in oscillators, emphasizing the exacerbation of nonlinear effects by foam.

Fluid Dynamics: Instabilities and Turbulence

Covers fluid dynamics instabilities, turbulence, stability of airplanes, and key concepts.

Rayleigh-Taylor Instability

Explores Rayleigh-Taylor instability, perturbation linearization, boundary conditions, normal mode expansion, and Laplace equation solution.

Rayleigh-Plateau Instability

Explores the Rayleigh-Plateau instability in fluid flows, discussing surface tension effects and historical experiments related to this phenomenon.

Rayleigh-Benard Instability

Explores the Rayleigh-Benard instability, discussing flow instabilities due to buoyancy forces and the analysis of dispersion relations.

Marangoni Instability: Taylor Couette

Explores Marangoni effect, Benard-Marangoni instability, and Taylor Couette flow, focusing on surface tension variations.

Rayleigh-Taylor Instability: Mechanical Example

Covers the Rayleigh-Taylor instability, flow examples, and boundary conditions in a mechanical context.

Rayleigh Taylor: Normal Mode Expansion

Explores normal mode expansion, Laplace equation solution, and dispersion relation analysis in Rayleigh Taylor instability.

Instability Analysis: Linearized Equations and Dispersion Relation

Explores fluid instability through linearized equations and dispersion relation, analyzing stability based on wavenumber and frequency.

Rayleigh Benard: Instability and Boundary Conditions

Explores Rayleigh Benard convection, boundary conditions, instability, and solution ansatz.

Centrifugal Instabilities: Mechanism and Analysis

Explores centrifugal instabilities, focusing on the Rayleigh criterion and analysis process.

Fluid Mechanics: Boundary Layer Instability and Transition

Explores boundary layer instability, transition, and flow nonlinearities in fluid mechanics.

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