In the second talk of the afternoon of 17 July,
Julian Hunt talked about a range of topics motivated by the problem of wind-wave interaction. He started with a review of Jeffrey’s 1926 paper. Despite 50 years of intense research, there is still disagreement about how idealised mathematical models apply to real air flow over real waves. Classical models like Miles (1957) and Lighthill (1962) are invalid for viscous, turbulent flow when the growth rate is asymptotically small. But analytical viscous turbulent shear flow models, also with critical layers, are valid in this limit and agree more closely with experimental wind profile data. The second part of the talk concerned recent long tsunami-like waves, especially waves where the leading part of the wave is depressed, which was a characteristic feature of the tsunamis that approached the coast-lines of SEAsia in 2004 and Japan in 2011. As such waves travel from the source region, a non-linear Kortweg-de Vries model of Grimshaw, Lam & Hunt (2014) is proposed as a model. It shows how when a depression wave is followed by an elevation (a ‘breather’) there is a transition at a location which can be estimated when the peak elevation catches up with the peak depression and nearly doubles in height before it then decreases and travels in front of the depression. The model results are compared with experiments done at Arizona State University with good agreement (Klettner et al. 2012). At the end he mentioned some recent significant measurements of velocity fields near the eye of a hurricane that have been obtained by Chinese researchers. A video of the talk is available here.