The motion of an initially quiescent, incompressible, stratified and/or rotating
uid of semi-infinite extent due to surface forcing is considered. The stratification
parameter N and the Coriolis parameter f are constant but arbitrary and all possible
combinations are considered, including N = 0 (rotating homogeneous fluid), f = 0
(non-rotating stratified fluid) and the special case N = f. The forcing is suction or
pumping at an upper rigid surface and the response consists of geostrophic flows and
inertial-internal waves. The response to impulsive point forcings (Green's functions)
is contrasted with the response to finite-sized circularly symmetric impulsive forcings.
Early-time and large-time behaviour are studied in detail. At early times transient
internal waves change the vortices that are created by pumping/suction at the surface.
The asymptotically remaining vortices are determined, a simple expression for what
fraction of the initial energy is converted into internal waves is derived, as well as
wave energy fluxes and the dependence of the flux direction on the value of N/f.
The internal wave field is to leading order in time a distinct pulse, and rules for the
arrival time of the pulse, its amplitude, its motion along a ray of constant frequency
and decay with time, are given for the far field. A simple formula for the total wave
energy distribution as a function of frequency is derived for when all waves have
propagated away from the forcing.