An experimental investigation of turbulent flows over a hilly surface

Gentle topographic variations significantly alter the mass and momentum exchange rates between the land surface and the atmosphere from their flat-world state. This recognition is now motivating basic studies on how a wavy surface impacts the flow dynamics near the ground for high bulk Reynolds numbers ( Re h ) . Using detailed flume experiments on a train of gentle hills, we explore the spatial structure of the mean longitudinal ( u ) and vertical ( w ) velocities at high Re h . We show that classical analytical theories proposed by Jackson and Hunt (JH75) for isolated hills can be extended to a train of gentle hills if the background velocity is appropriately defined. We also show that these theories can reproduce the essential 2D structure of the Reynolds stresses. The basic assumptions in the derivation of the JH75 model are also experimentally investigated. We found that the linearization of the advective acceleration term and the mixing length proposed in JH75 are reasonable within the inner layer. We also show that the measured variability in the linearized mean longitudinal advective acceleration term can explain much of the measured variability in the entire nonlinear advective acceleration term for the longitudinal mean momentum balance.