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A B S T R A C T
The onset of convection i n a horizontal f l u i d layer, heated f r o m below, i r , exemine8 by meam of perturbation amlysie. !l!he msrilting elgenva3ue ayeten of eguations iu 801~8d by manu of a new e&enrrion of a Fourier series technique. !Two ~ eof coupled t ~ effects are investigated:
( i ) tharad buoyancy und surface-tension effecte, snd ( l i ) thermal buoyancy and eolute buoyancy effects.
For the f i r ~ t Bet of effects the rasgnstotrydroc¶ymmtc problen is 00 atudied.
For t h e surfaco-tension problem, attention i r focutsed on t h e case where the lower boundary 18 a r i g i d conductor and the upper free surface i s subJect to s general thermal condition* It i s found t h a t f o r t h i r care the surface-tension and buoyancy forces reinforce each other and cue t i g h t l y coupled. Cells foraaed by rrur9ace tension are apprQximatev the s i z e as t h 0 0 ~ formed by buoyeurcy.
me
stre- line patterns produced by the two agencies acting separately are sgain 8blihU'.When the f l u i d 9s e k t r l c a l l y conducting anB is fn t h e presence of a mrticsl. magnetic field, it i r , found that the field dtwa~rs has a s % a b l k i z I ~ effect* When convection eella are formed i n the presence of uuch a f i e l d , their horlsontal dimemiom are less than f o r c e l l s
forraha i n the absence of the fiela. The magnetic fielcl accentuates
the difYerence batween the ceUa induced by raurface tension and thoae by buoyancy, Wthu. reduce6 the coupling between the Ue-
stabilizing forces. Increase of magnetic f i e l d cswea the buoyancy c e l l pattern t o bscoms mare syrmnatricsrl, but caumee t h e stre-8
in aurfaee-tembn cella t o become bunched near the &ace. When me magnetic fie&& 58 large, the t r a m i t i o n from one type of c e l l t o the other type is oxtrenraly rudbn, st least when the upper eurface is a good t h e r w l conductor.
It has been found that, on the model comida~red, there can be no oscillatory l n ~ t a b 3 . U ~ f o r t h i s problem. However, dlmenaiond tmalymis reveels that, f o r a sufficisatly flsxible upper rrwf'sca,
mi c j ht
oscillatory Inotability &euU i n fact occur.
]N.mUy t h e tb11~)haUm prablam, whem tk cbneity vsriara with both temperature anB the concentration of solute, l a stud.tcb8.
!Rm eigenvdue equation l r r tkow found f o r general, b u n b y coniiitions, The b g r e e of coupUng between the the& and the solute effects
Prgain depend8 on t h e u j d l a r i f y batman cospectlon c e l h caused by the two agencies &dag sepamtaly. (For one
