This is just a classic (but very large) example of a turbulent jet.
The SRB is even used as an example in this textbook.
Turbulent eddies of many sizes and shapes are observed due to the
presence of the smoke as a tracer of the turbulent motion. There is
a general tendency for the length scale of the turbulent motion to
increase as the eddies move along the jet. Induced by the motion of
the eddies, fluid from the surrounding environment is drawn into the
jet through a process called turbulent entrainment. The extent of the
turbulent zone increases and the concentration of the tracer decreases
with distance from the source as the source fluid is diluted by the
fluid entrained from the surroundings. The jet in this example produces
a thrust (three million pounds) for the rocket engine.
Turbulent Jets and Plumes (sadly, the sample chapter cuts off before the picture)