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SUMMARY:Craik-Leibovich Equation\, Distinguished Limits\, Drifts\, and Pse
 udo-Diffusion - Vladimir Vladimirov (Sultan Qaboos University\; University
  of York)
DTSTART:20170808T123000Z
DTEND:20170808T133000Z
UID:TALK74901@talks.cam.ac.uk
CONTACT:INI IT
DESCRIPTION:The Craik-Leibovich Equation (CLE) describes the Langmuir circ
 ulations in the upper layer of the oceans\, lakes\, etc. In this lecture w
 e consider CLE and the related notions of drifts and pseudo-diffusion. In 
 our approach\, CLE describes general vortex dynamics of oscillating flows\
 , not only the Langmuir circulations. A number of new results on CLE are p
 resented.  An important elements of our presentation is the systematic der
 iving of boundary conditions\, which represents a more difficult tusk than
  the deriving of averaged equations.  We also consider a &#39\;linearized&
 rsquo\; version of CLE\, which is different from that obtained by a straig
 htforward linearization of an averaged equation. A possible tree-timing pr
 ocedure for the generalisation of CLE is proposed. The effects of viscosit
 y and density stratification has been additionally re-examined. We also di
 scuss two generalisations of CLE. First one is a Magneto-Hydro-Dynamic ver
 sion of CLE.  It may have relation to the MHD dy namo and to the forming o
 f various flows and phenomena in stars\, galaxies etc. Second generalisati
 on deals with a version of CLE for compressible fluid\, where similar to C
 LE equations appears due to oscillations caused be acoustic waves. <br><br
 >Mathematically\, our consideration is based on a unified viewpoint. We us
 e the two-timing method\, Eulerian averaging\, and the concept of distingu
 ished limit. Such a consideration emphasises the generality\, simplicity\,
  and the rigour in all our derivations. We do not accept any additional as
 sumption and suggestions except the presence of small parameters and the a
 pplicability of rigorous asymptotic procedure. Our approach allows us to o
 btain the classical results much simpler than it has been done before\, an
 d hence a noticeable progress in the obtaining of new results can be achie
 ved. <br><span><br>Key Words: Craik-Leibovich Equation\, Lamgmuir Circulat
 ions\, Two-Timing Method\, Distinguished Limits\, Drift\, Pseudo-Diffusion
 .</span>
LOCATION:Seminar Room 1\, Newton Institute
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