  Attempts to understand the dynamics of warped astrophysical discs have
garnered significant attention, largely motivated by the growing catalogue of
observed distorted systems. Previous studies have shown that the evolution of
the warp is crucially regulated by the internal flow fields established by the
undulating geometry. These are typically modelled as laminar horizontal,
shearing flows which oscillate back and forth at approximately the orbital
frequency. However this shearing motion is known to be susceptible to a
hydrodynamic, parametric instability of inertial waves which might modify the
warped dynamics. Whilst the linear growth phase is well understood, the
subsequent nonlinear saturation combined with the self-consistent feedback onto
the warp has not been studied. In this work, we implement a novel numerical
setup using the recent ring model framework of Fairbairn and Ogilvie, within
the Lagrangian code GIZMO. We formally identify several locally growing modes
in the simulation, as predicted by a three-mode coupling analysis of the
instability, and find decent agreement with the theoretical growth rates. We
understand the saturation mechanism as a wave breaking process which suppresses
the growth of shorter wavelength parametric couplings first, whilst allowing
the longest mode to dominate the final quasi-steady, wavelike turbulence. The
Reynolds stresses, transporting energy from the warp to the small scales, can
be effectively modelled using a time-dependent, anisotropic viscous alpha model
which closely captures the amplitude and phase evolution of the warp.
Consequently, this model might help inform future global studies which are
commonplace but typically don't resolve the parametric instability.
