Meridional circulation of gas into gaps opened by giant planets in three-dimensional low-viscosity disks

We examine the gas circulation near a gap opened by a giant planet in a protoplanetary disk. We show with high resolution 3D simulations that the gas flows into the gap at high altitude over the mid-plane, at a rate dependent on viscosity. We explain this observation with a simple conceptual model. From this model we derive an estimate of the amount of gas flowing into a gap opened by a planet with Hill radius comparable to the scale-height of a layered disk (i.e. a disk with viscous upper layer and inviscid midplane). Our estimate agrees with modern MRI simulations (Gressel, O., Nelson, R.P., Turner, N.J., Ziegler, U. [2013]. arXiv:1309.2871). We conclude that gap opening in a layered disk cannot slow down significantly the runaway gas accretion of Saturn to Jupiter-mass planets.