Seminars

3pm Thursday 8 October 2009, Seminar room M345
School of Mathematical Sciences Colloquium
On Langmuir circulation and generalized Lagrangian mean theory
Prof William R.C. Phillips (Swinburne University of Technology)

Langmuir circulation form in the surface layers of oceans, lakes and ponds when winds of moderate strength blow over them, and manifest as a parallel series of counter rotating vortices that more or less align with the wind. Since they act at the surface to concentrate flotsam, seaweed and air bubbles into streaks, they are clearly visible, and satellite photographs suggest they are present over 15-20% of the ocean at any time. In cross section they range from circa that of noodles to that of a sports stadium and because of their dynamics and range of scales are a key ingredient in the formation of the ocean mixed layer, a layer circa 100m deep which absorbs atmospheric gases and solar heat, and which in turn affects the weather. In view of their importance it is prudent to have a credible robust dynamic model of them and to this end we employ instability theory to show they arise as a consequence of shear, be it current or wind induced and differential drift, caused by the quadratic interaction of surface gravity waves, via an instability mechanism we term CLg, or generalized Craik-Leibovich. Since multiple length and time scales enter this theory, with averaging over the smaller scales, a conservative wave mean flow theory is necessary to proceed and we herein employ the generalized Lagrangian mean theory of Andrews & McIntyre. In this seminar we discuss generalized Lagrangian mean theory and how we used it with instability theory to construct a set of evolution equations, the CLg equations, that are a credible metaphor for the aetiology of Langmuir circulation over scales ranging from those in ponds to those in the open ocean.