  We show by numerical simulations that discretized versions of commonly
studied continuum nonlinear growth equations (such as the Kardar-Parisi-Zhang
equation and the Lai-Das Sarma equation) and related atomistic models of
epitaxial growth have a generic instability in which isolated pillars (or
grooves) on an otherwise flat interface grow in time when their height (or
depth) exceeds a critical value. Depending on the details of the model, the
instability found in the discretized version may or may not be present in the
truly continuum growth equation, indicating that the behavior of discretized
nonlinear growth equations may be very different from that of their continuum
counterparts. This instability can be controlled either by the introduction of
higher-order nonlinear terms with appropriate coefficients or by restricting
the growth of pillars (or grooves) by other means. A number of such
``controlled instability'' models are studied by simulation. For appropriate
choice of the parameters used for controlling the instability, these models
exhibit intermittent behavior, characterized by multiexponent scaling of height
fluctuations, over the time interval during which the instability is active.
The behavior found in this regime is very similar to the ``turbulent'' behavior
observed in recent simulations of several one- and two-dimensional atomistic
models of epitaxial growth. [pacs{61.50.Cj, 68.55.Bd, 05.70.Ln, 64.60.Ht}]
