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SUMMARY:Stochastic Rayleigh-B´enard Convective Adjustment - Darryl Holm (
 Imperial College London)
DTSTART:20220420T150000Z
DTEND:20220420T160000Z
UID:TALK172127@talks.cam.ac.uk
DESCRIPTION:&nbsp\;We discuss the initial value problem for Rayleigh-B&acu
 te\;enard convective adjustment (RBCA) in a vertical plane\, using the Eul
 er-Boussinesq equations in the vorticity representation\, neglecting visco
 sityand thermal diffusivity. This is a non-dissipative\, initial-value ver
 sion of the equations studied in[2]. The Hamiltonian structure of the mode
 l is used to characterise the equilibrium solutions of thenon-dissipative 
 system and derive their corresponding Taylor-Goldstein equations for linea
 r instability. Stochastic advection by Lie transport (SALT) is introduced 
 by following the approach of [1\, 3].The SALT equations enable uncertainty
  quantification and admit data assimilation methods based onparticle filte
 ring that can reduce the uncertainty in coarse-grained computational simul
 ations of convective adjustment. The Lagrangian Averaged (LA) SALT equatio
 ns for the RBCA initial value problemare discussed. The expectation equati
 ons of LA SALT for RBCA are similar in appearance to theoriginal dissipati
 ve Oberbeck-Boussinesq equations for diffusive\, viscous dynamics of Rayle
 igh-B&acute\;enardconvection. Finally\, deterministic dynamical equations 
 for the covariances and higher moments of thefluctuations away from the ex
 pected solution are derived
LOCATION:Seminar Room 2\, Newton Institute
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