Consider a continuous dynamical system for which partial
information about its current state is observed at a sequence of
discrete times. Discrete data assimilation inserts these observational
measurements of the reference dynamical system into an approximate
solution by means of an impulsive forcing. In this way the
approximating solution is coupled to the reference solution at a
discrete sequence of points in time. This paper studies discrete data
assimilation for the incompressible two-dimensional Navier--Stokes
equations. In both cases we obtain bounds on the time interval
between subsequent observations which guarantee the convergence of the
approximating solution obtained by discrete data assimilation to the
reference solution.