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SUMMARY:Analysis of a rotationally constrained convection model - Yanqiu G
 uo ()
DTSTART:20220503T150000Z
DTEND:20220503T160000Z
UID:TALK172313@talks.cam.ac.uk
DESCRIPTION:This talk is about the analysis of an asymptotically reduced s
 ystem for rotationally constrained convection. The presence of a dominant 
 balance in equations for fluid flow can be exploited to derive a simpler s
 et of governing equations that permits analytical explorations. For rotati
 on dominated flows\, the geostrophic balance\noccurs: the pressure gradien
 t force is balanced by the Coriolis effect.\nThe Taylor-Proudman constrain
 t suggests that the dominant Coriolis force leads to flows that are organi
 zed into vertical plumes or columns whose horizontal scale is small compar
 ed to the layer height. Applying the asymptotic theory for small Rossby nu
 mber and tall columnar structures\, Julien and Knobloch derived a closed s
 et of reduced equations from the three-dimensional Boussinesq equations. A
 lso\, Sprague et al. numerically simulated this reduced model to study the
  equal populations of cyclonic and anticyclonic structures in rapid rotati
 ng convection. This reduced system is interesting yet challenging for anal
 ytical study. On the one hand\, the nonlinear convection term has a reduce
 d complexity since it contains only the horizontal gradient. On the other 
 hand\, the physical domain remains three dimensional\, while the regulariz
 ing viscosity acts in the horizontal direction only\, creating a major dif
 ficulty for establishing the global existence theory. Another difficulty a
 rises due to a linear term involving the vertical derivative of the stream
  function\, reflecting the balance of the Coriolis force by the pressure.\
 nI will present some of our results motivated by the global regularity pro
 blem. We show that the model is globally well-posed if regularized by a ve
 ry weak dissipation. I will also discuss the case of infinite Prandtl numb
 er convection\, and the situation when both of the Prandtl and Rayleigh nu
 mbers approach infinity. This is a joint project with Cao and Titi.
LOCATION:Seminar Room 2\, Newton Institute
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