text: The evolution of the RTI follows four main stages.  In the first stage, the perturbation amplitudes are small when compared to their wavelengths, the equations of motion can be linearized, resulting in exponential instability growth.  In the early portion of this stage, a sinusoidal initial perturbation retains its sinusoidal shape.  However, after the end of this first stage, when non-linear effects begin to appear, one observes the beginnings of the formation of the ubiquitous mushroom-shaped spikes (fluid structures of heavy fluid growing into light fluid)  and bubbles (fluid structures of light fluid growing into heavy fluid).  The growth of the mushroom structures continues in the second stage and can be modeled using buoyancy drag models, resulting in a growth rate that is approximately constant in time.  At this point, nonlinear terms in the equations of motion can no longer be ignored.  The spikes and bubbles then begin to interact with one another in the third stage.  Bubble merging takes place, where the nonlinear interaction of mode coupling acts to combine smaller spikes and bubbles to produce larger ones.  Also, bubble competition takes places, where spikes and bubbles of smaller wavelength that have become saturated are enveloped by larger ones that have not yet saturated.  This eventually develops into a region of turbulent mixing, which is the fourth and final stage in the evolution.  It is generally assumed that the mixing region that finally develops is self-similar and turbulent, provided that the Reynolds number is sufficiently large.