The method of multiple time scales is used to obtain an approximate description of the linear
propagation of near-inertial oscillations (NIOs) through a three-dimensional geostrophic
flow. This 'NIO equation'uses a complex field, M (x, y, z, t), related to the demodulated
horizontal velocity by M z= exp (if 0 t)(u+ iv), where f 0 is the inertial frequency. The three
processes of wave dispersion, advection by geostrophic velocity and refraction (geostrophic
vorticity slightly shifts the local inertial frequency) are all included in the formulation. The NIO …

The method of multiple time scales is used to obtain an approximate description of the linear
propagation of near-inertial oscillations (NIOs) through a three-dimensional geostrophic
flow. This NIO equation uses a complex field, M (x, y, z, t), related to the demodulated
horizontal velocity by M z= exp (if 0 t)(u+ iv), where f 0 is the inertial frequency. The three
processes of wave dispersion, advection by geostrophic velocity and refraction (geostrophic
vorticity slightly shifts the local inertial frequency) are all included in the formulation. The NIO …