"stability" of turbulent jet surface location

Al

Hi, can somebody please help with (sorry) basic understanding of the following:

turbulent jet (say round) entering almost vacuum (almost no friction) - VOF. Model: steady k-e (or RSM or k-w, not LES) with, of course, steady BC. Will the solution start to oscillate? If the formulation is unsteady with steady BC - will the jet surface start to be wavy?

Thanks a lot.