A TURBULENT FLUID MODEL FOR THE EVOLUTION OF ZONAL JETS IN A PREPLANETARY NEBULAR DISK

It is known that a turbulent, two-dimensional fluid at high Reynolds n umber under a suitable restoring force can evolve toward larger scales , that is, to waves and zonal jets. A two-dimensional disk of turbulen t fluid gravitationally bound to a central mass is considered as a mod el for a pre-planetary disk. It is found that for general conditions, azimuthal zonal jets can form in the disk. Planetesimals are assumed t o accrete between these jets. Their radial separation distances, s(r), should be roughly s(r) similar to pi{1/3[e/(1 - e(2))]}(1/2)r, where e is orbital eccentricity, and r is semimajor radius. In the corotatin g reference frame, jets alternate in direction, forming counterstreami ng pairs. For eccentricities comparable to Solar System planetary orbi tal eccentricities, jet pair separations roughly double with each succ essive jet pair. The predicted spacings are in better agreement with o bservation than predicitions by the Titius-Bode (TB) Rule. This model predicts that TB-like spacing should be common in extra-solar planetar y systems.