  We model the time evolution of gaps in tidal streams caused by the impact of
a dark matter subhalo, while both orbit a spherical gravitational potential. To
this end, we make use of the simple behaviour of orbits in action-angle space.
A gap effectively results from the divergence of two nearby orbits whose
initial phase-space separation is, for very cold thin streams, largely given by
the impulse induced by the subhalo. We find that in a spherical potential the
size of a gap increases linearly with time for sufficiently long timescales. We
have derived an analytic expression that shows how the growth rate depends on
the mass of the perturbing subhalo, its scale and its relative velocity with
respect to the stream. We have verified these scalings using N-body simulations
and find excellent agreement. For example, a subhalo of mass 10^8 Msun directly
impacting a very cold thin stream on an inclined orbit can induce a gap that
may reach a size of several tens of kpc after a few Gyr. The gap size
fluctuates importantly with phase on the orbit, and it is largest close to
pericentre. This indicates that it may not be fully straightforward to invert
the spectrum of gaps present in a stream to recover the mass spectrum of the
subhalos.
