We consider the two-dimensional (2D) flow in a flat free-slip surface that
bounds a three-dimensional (3D) volume in which the flow is turbulent. The
equations of motion for the two-dimensional flow in the surface are neither
compressible nor incompressible but strongly influenced by the 3D flow
underneath the surface. The velocity correlation functions in the 2D surface
and in the 3D volume scale with the same exponents. In the viscous subrange the
amplitudes are the same, but in the inertial subrange the 2D one is reduced to
2/3 of the 3D amplitude. The surface flow is more strongly intermittent than
the 3D volume flow. Geometric scaling theory is used to derive a relation
between the scaling of the velocity field and the density fluctuations of a
passive scalar advected on the surface.Comment: 11 pages, 10 Postscript figure