Stratified flow over three-dimensional topography

In order to investigate flows over topography in an atmospheric context, we have studied experimentally the wake structure of axi-symmetric Gaussian obstacles towed through a linearly stratified fluid. Three dimensionless parameters govern the flow dynamics: F, the Froude number based on the topography height h; Re, the Reynolds number and the aspect ratio r = h/L, where L is the topography horizontal scale. Two-dimensional (2-D), saturated lee wave (SLW) and three-dimensional (3-D) regimes, as defined in Chomaz et al. (1993), are found to be functions of F and r only (Fig. 1) as soon as Re is larger than Re_c ≈ 2000. For F < 0.7 the flow goes around the obstacle and the motion in the wake is quasi-two-dimensional. This 2-D layer is topped by a region affected by lee wave motions with amplitude increasing with r and F. For 0.7 < F < 1/r, the flow is entirely dominated by a lee wave of saturated amplitude which suppresses the separation of the boundary layer from the obstacle. Above the critical value 1/r, the lee wave amplitude decreases with F and a recirculating zone appears behind the obstacle. Simultaneously, coherent large-scale vortices start to be shed periodically from the wake at a Strouhal number which decreases as 1/F until it reaches its neutral asymptotic value.