Using the nonlinear gyrokinetic code package GENE/GIST F. Jenko, W. Dorland, M. Kotschenreuther, and B. N. Rogers, Phys. Plasmas 7, 1904 2000; P. Xanthopoulos, W. A. Cooper, F. Jenko, Yu. Turkin, A. Runov, and J. Geiger, ibid. 16, 082303 2009, we study the turbulent transport in a broad family of stellarator designs, to understand the geometry dependence of the microturbulence. By using a set of flux tubes on a given flux surface, we construct a picture of the two-dimensional structure of the microturbulence over that surface and relate this to relevant geometric quantities, such as the curvature, local shear, and effective potential in the Schrödinger-like equation governing linear drift modes.