Statistics – Computation
Scientific paper
Aug 1986
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1986gapfd..36..161k&link_type=abstract
Geophysical and Astrophysical Fluid Dynamics (ISSN 0309-1929), vol. 36, no. 2, 1986, p. 161-177.
Statistics
Computation
10
Boundary Conditions, Boundary Value Problems, Computational Fluid Dynamics, Convective Flow, Magnetic Field Configurations, Periodic Variations, Two Dimensional Flow, Boussinesq Approximation, Rayleigh Number, Standing Waves, Traveling Waves
Scientific paper
The effect of an imposed horizontal magnetic field on two-dimensional convection in a plane layer heated from below is studied in the presence of periodic boundary conditions in the horizontal. An amplitude equation describing the transitions between traveling and standing waves and steady convection near a particular multiple bifurcation is derived. When the first instability is oscillatory, two solution branches bifurcate simultaneously from the conduction solution, corresponding to traveling and standing waves. The branch of traveling waves is stable throughout and terminates on the steady-state branch in a steady-state bifurcation as the Rayleigh number is increased. Beyond this point stable overturning convection is found. Standing waves are unstable. The results are indicative of the larger amplitude behavior of the system.
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