Observations of inertial waves in a homogeneous rotating fluid

Observations of inertial waves generated by uniform horizontal flow over ridges and truncated axisymmetric obstacles in a homogeneous fluid rotating about a vertical axis are discussed and compared with linear theory. The dependence of the flow on obstacle shape, Ro, H, E and E is investigated. Here Ro = U/2ΩL is the Rossby number, H = Ro(D/L), E = v/2ΩL2 is the Ekman number, and ε = h/L is the non-dimensional height of the obstacle, where U is the basic velocity, Ω is the angular frequency, L is a streamwise length, D is the depth of the fluid, h is the height of the obstacle, and v is the kinematic viscosity. Previous linear analysis of this problem has been for the limit H fixed, Ro→0, referred to here as the small-Ro limit. However, it is shown that certain linear terms neglected in the small-Ro limit can be important for finite Ro, and are included in the analysis given here. The observed flow is then well described by linear theory for H/ε [Gt ] 1, particularly in the case of two-dimensional flow over a ridge. However, for H/ε [Gt ] 1 the flow field is dominated by a vertical columnar motion, which is not adequately described by the analysis.