Physics / research
Instability, mixing, and turbulent flow
Study the onset of fluid instabilities, turbulent energy transfer, and closure limits without treating unresolved turbulence questions as settled.
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Module 01 research
Instability, mixing, and turbulent flow
Study the onset of fluid instabilities, turbulent energy transfer, and closure limits without treating unresolved turbulence questions as settled.
- 01
Linear stability of parallel flows
Construct a perturbation eigenproblem, interpret its growth convention, and identify what an inviscid stability criterion actually establishes.
32 min - 02
Kelvin–Helmholtz shear instability
Derive and interpret the ideal vortex-sheet growth rate while separating shear energy, gravity, surface tension, and finite-thickness effects.
31 min - 03
Rayleigh–Taylor density instability
Connect adverse density stratification with gravitational energy release, derive the linear growth rate, and identify capillary stabilization.
30 min - 04
Rayleigh–Bénard convection
Balance buoyant feedback against thermal and momentum diffusion, and connect convection thresholds to specified boundary conditions.
34 min - 05
Orr–Sommerfeld equation and transient growth
Retain viscosity in the parallel-flow eigenproblem and show concretely why stable eigenvalues do not exclude temporary disturbance-energy growth.
36 min - 06
Turbulent energy cascade and Kolmogorov scaling
Relate energy flux across three-dimensional turbulent scales to inertial-range estimates and the viscous cutoff, with assumptions made explicit.
35 min - 07
Structure functions and intermittency
Use velocity increments and high-order moments to distinguish typical fluctuation size from rare intense events, without claiming unresolved exponent predictions.
33 min - 08
Reynolds averaging and closure problems
Derive the mean momentum correction from velocity correlations, calculate turbulent production, and distinguish an exact average from an empirical closure.
35 min - 09
Two-dimensional turbulence and inverse cascades
Use simultaneous inviscid energy and enstrophy conservation to understand dual-cascade constraints and why planar flow differs from generic 3D turbulence.
35 min - 10
Turbulence measurements and resolution limits
Design a turbulence measurement around sensor response, sampling, spatial averaging, and statistically converged observables rather than attractive spectra alone.
34 min