User:Dan Zimmerman/Draft Inertial Waves

Inertial waves are oscillations that can occur in fluid systems with overall rotation. Any fluid flow where the Coriolis acceleration is important could support inertial waves, as the Coriolis force is the restoring force for these oscillations. In an unbounded fluid, the inertial waves are propagating plane waves; for bounded fluids, they take the form of container modes.

Equations of Motion
The fluid velocity u in a frame rotating with constant angular speed Ω is given by

$$\frac{\partial\vec{u}}{\partial t}+\vec{u}\cdot\nabla\vec{u}+2\Omega\times\vec{u} = -\frac{1}{\rho}\nabla P - \nu\nabla\times(\nabla\times\vec{u})$$

where ρ is the fluid density, P is the pressure and ν is the kinematic viscosity.