The saturation of the VSI in protoplanetary discs via parametric instability

ABSTRACT The vertical shear instability (VSI) is a robust and potentially important phenomenon in irradiated protoplanetary discs (PPDs), yet the mechanism by which it saturates remains poorly understood. Global simulations suggest that non-linear evolution of VSI dominated radially propagating inertial wavetrains (called ‘body modes’), but these are known to be susceptible parametric instability. In this paper, we propose global via secondary instability, initiates redistribution energy from large scales smaller scale waves, finally into turbulent cascade. We present an analytic theory simple idealized model captures main physical mathematical details problem. addition, conduct numerical with snoopy code consolidate theory. argue challenging capture unless radial resolution very fine, possibly ?300 grid cells per height radius; thus likely far more disordered incoherent than current suggest.