Flow instability

Flow instability occurs when disturbances in a moving fluid grow rather than decay, potentially changing the flow’s structure or triggering turbulence.

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Linear stability analysis: A method that tests whether small disturbances to a system grow or decay by examining its linearized equations. It predicts whether infinitesimal disturbances to a base flow grow.
Fluid mechanics: The study of fluids at rest and in motion, including forces, transport, and deformation. Flow instability is a central question within the broader study of fluid motion.
Couette flow: Fluid motion between surfaces driven by their relative movement, often studied between parallel plates or rotating cylinders. Its stability changes with geometry and forcing, making it a classic test case.
Hydrodynamic stability: The study of whether disturbances to fluid motion grow, decay, or remain bounded. It names the broader framework in which flow instability is assessed.
Reynolds number: A dimensionless ratio of inertial to viscous forces in fluid motion. It helps characterize when disturbances can overcome viscous damping.
Navier–Stokes equations: Partial differential equations expressing conservation of momentum for viscous fluid motion. Their solutions describe how disturbances evolve in many ordinary flows.
Poiseuille flow: Pressure-driven flow through a channel or pipe, with velocity varying across the cross-section. Its persistence despite linear instability illustrates the limits of simple predictions.
Linear stability: Stability assessed by tracking infinitesimal disturbances in a linearized model. A flow stable under this test may still amplify larger disturbances.
Nonlinear instability: Instability driven by finite-amplitude disturbances or nonlinear interactions, even when infinitesimal disturbances decay. It explains why linear stability alone may not guarantee a robust flow.
Velocity profile: The variation of fluid velocity across a position, such as the height of a channel or distance from a wall. Its shape supplies the base flow that disturbances can destabilize.