  We derive a self-similar description for the 2D streamline topology and flow
structure of an axi-symmetric, thermally driven wind originating from a disc in
which the density is a power law function of radius. Our scale-free solution is
strictly only valid in the absence of gravity or centrifugal support;
comparison with 2D hydrodynamic simulations of winds from Keplerian discs
however demonstrates that the scale-free solution is a good approximation also
in the outer regions of such discs, and can provide a reasonable description
even for launch radii well within the gravitational radius of the flow.
Although other authors have considered the flow properties along streamlines
whose geometry has been specified in advance, this is the first isothermal
calculation in which the flow geometry and variation of flow variables along
streamlines is determined self-consistently. It is found that the flow
trajectory is very sensitive to the power-law index of radial density variation
in the disc: the steeper the density gradient, the stronger is the curvature of
streamlines close to the flow base that is required in order to maintain
momentum balance perpendicular to the flow. Steeper disc density profiles are
also associated with more rapid acceleration, and a faster fall-off of density,
with height above the disc plane. The derivation of a set of simple governing
equations for the flow structure of thermal winds from the outer regions of
power law discs offers the possibility of deriving flow observables without
having to resort to hydrodynamical simulation.
