N ov 2 00 6 Comments on “ An Exact , Three - Dimensional , Time - Dependent Wave Solution in Local Keplerian

We analyze the scepticism on the hydrodynamic turbulence in Keplerian astrophysical disks expressed in Balbus and Hawley 2006 and show the failure of arguments of the paper. Recently Balbus and Hawley 2006 (BH06) have shown time-dependent three-dimensional nonlinear wave solution when considering a local Keplerian flow. Authors have demonstrated that the linear wave solution derived in Johnson and Gam-mie (2005) is actually also valid nonlinearly when considering a single plane wave. This solution can be used as a test for the dissipative properties of the numerical codes. The key message of BH06 is given in the abstract: " The existence of this solution argues against transient amplification as a route to turbulence in unmag-netized disks ". However, this message does not correctly describes the situation in unmagnetized astrophysical disks. In the latter case the determinative factor of local dynamics is vertical stratification of the flow, which is neglected by BH06: the stratification originates the modes of perturbations that are able to withstand stabilizing influence of Coriolis forces. Dynamics of local 3D perturbation modes in stably stratified Keplerian flow is studied in detail by Tevzadze at el. 2003 (T03). BH06 have omitted the key factors that provide the fundamental source of energy of the turbulence: the combined action of vertical gravity and Coriolis forces in 3D case results the conservation of the potential vorticity (see Eq. 11 of T03) that indicates the existence of a vortex/apperiodic mode in the perturbation spectrum of the system. This vortex mode is the primary in the transient amplification phenomenon. In the absence of any one of these (vertical gravity or Coriolis) forces vortex mode degenerates into the trivial solution of the system – it disappears.