  When studying fluid-body interactions in the low-Froude limit, traditional
asymptotic theory predicts a waveless free-surface at every order. This is due
to the fact that the waves are in fact exponentially small---that is, beyond
all algebraic orders of the Froude number. Solutions containing exponentially
small terms exhibit a peculiarity known as the Stokes phenomenon, whereby waves
can 'switch-on' seemingly instantaneously across so-called Stokes lines,
partitioning the fluid domain into wave-free regions and regions with waves. In
three dimensions, the Stokes line concept must extend to what are analogously
known as 'Stokes-surfaces'. This paper is concerned with the archetypal problem
of uniform flow over a point source---reminiscent of, but separate to, the
famous Kelvin wave problem. In theory, there exist Stokes surfaces i.e.
manifolds in space that divide wave-free regions from regions with waves.
Previously, in Lustri & Chapman (2013) the intersection of the Stokes surface
with the free-surface, z=0, was found for the case of a linearised point-source
obstruction. Here we demonstrate how the Stokes surface can be computed in
three-dimensional space, particularly in a manner that can be extended to the
case of nonlinear bodies.
