The structure and origin of confined Holmboe waves*

We describe and elucidate the origin of confined Holmboe waves (CHWs), which are apparently previously unreported long-lived coherent structures in a sustained stratified shear flow generated in the laboratory by exchange flow through an inclined square duct. We use a combination of (i) novel time-resolved, volumetric measurements of the three-component velocity and density fields simultaneously; (ii) a linear stability analysis solving for three-dimensional perturbations about the two-dimensional streamwise-averaged experimental flow. We show that the lateral confinement by the duct walls is an important ingredient of the confined Holmboe instability, which gives rise to the CHW, with implications for many inherently confined geophysical flows. Our results suggest that the CHW is an example of an experimentally observed, inherently nonlinear, robust, long-lived coherent structure which has developed from a linear instability. We conjecture that the CHW is a promising candidate for a class of exact coherent states underpinning the dynamics of more disordered, yet continually forced stratified shear flows.