Physics of Convection Motivation: Convection is the engine that turns heat into motion. Examples from Meteorology, Oceanography and Solid Earth Geophysics Basic Equations, stationary convection, time-dependence, influence of mechanical inertia, volumetric effects ..
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Physics of Convection " Motivation: Convection is the engine that turns heat into motion. " Examples from Meteorology, Oceanography and Solid Earth Geophysics.
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Physics of Convection
Motivation: Convection is the engine that turns heat into motion. Examples from Meteorology, Oceanography and
Atmospheric phenomena: - Large scale Headly-cells => horizontal transport - Thermals which result in Cumulus and Cumulo-Nimbus
clouds = > vertical transport from surface to the Tropospause- characteristic: Inertia & Coriolis forces
Oceanographic processes:
- Large scale water exchange Arctics-Tropics
- El Nino - Double Diffusive
Convection (e.g. Polynoyas)
- characteristic: density determined by temp. & salinity
Solid Earth & Planets: - Convection in the Earth mantle - MHD - convection in the Earth core generating mag. field - Magama chambers -characteristic: no inertia(mantle), multicomponent
Basic scenario:
Non dimensional equation for time-dependent convection in a constant-property Boussinesq fluid:
with:
scaled by:
where:
How to solve the equations:
- Problem: coupled system i.e v depends on T and T depends on v
- Analytic: -linearize equation -see if infinitesimal disturbance gets amplified
=> critical value for Ra ~ 600, independent of Pr
- first instablities have a roll pattern
- other patterns also exist like: square patter, hexagon pattern, cross-roll pattern ...
- no extrema principal
Higher Rayleigh numbers:
Numerical Simulation:
Solve the equations by a numerical method(e.g. finite element, fd, spectral, fv...)
+ variables are available at any point in space+ high viscosity, rotation, spherical geometry are easily realized
- long 3D timeseries are still expensive- small-scale features can not be resolved
Rayleigh
Prandtl
Time-dependent convection:
- onset of time-dependence from boundary layer theory
- At high Pr. : large scale coherent structures with superimposed boundarie layer instabilities (BLI's) which are drifting with the main flow
- with incrasing Ra the strength of the major up- and downwelling decreases
Influence of the Prandtl number:
- The Prandtl number measures the ratio of mechanical inertia