Double-averaged velocity profile and its representative line for turbulent flows over two-dimensional fixed dunes

A laboratory study was conducted using particle image velocimetry (PIV) to measure flow velocity distributions over two-dimensional smooth and rough fixed dunes. It comprised 28 tests, each yielding 146 velocity profiles over one complete dune length. Two kinds of double-averaged velocity profiles were computed, one based on all the 146 lines of data (called global average), and the others from only some of them (called partial average). The results show that the global average velocity distribution is generally close to the partial average profile derived from evenly-distributed three or five lines along one dune length. Furthermore, the global average velocity profile can also be reasonably approximated using a single profile, measured at the representative line in this paper. The representative line is found to locate near the reattachment point. This result would be helpful to simplify measurements of general velocity distribution for a flow over dunes. The paper also applies the concept of representative line to the description of distributions of turbulence characteristics.