Patterns in Rotating Patterns in Rotating Rayleigh-BRayleigh-Bénard énard

Convection at High Convection at High Rotation RatesRotation Rates

Presented by: P. L. MutyabaPresented by: P. L. Mutyabapmutyaba@clunet.edupmutyaba@clunet.edu

P. L. Mutyaba, Terri Kimmel, Janet D. ScheelP. L. Mutyaba, Terri Kimmel, Janet D. Scheel

California Lutheran UniversityCalifornia Lutheran University

Rayleigh-BRayleigh-Bénard Convection énard Convection (RBC)(RBC)

http://www.chemistrydaily.com/chemistry/upload/1/12/Convection_cells.png

Rotation,Rotation,ΩΩ

RRaa

Side View

Square Patterns in RBCSquare Patterns in RBC

BulkBulkSquareSquare

PeripheryPeripheryTraveling waveTraveling wave

Overhead View

Previous ResearchPrevious Research ExperimentsExperiments

Rotation ratesRotation rates170170

Cylindrical cellsCylindrical cellsAspect ratio 5 and 3Aspect ratio 5 and 3(radius to depth ratio)(radius to depth ratio)

Bajaj et al.(1998)Bajaj et al.(1998)

Previous ResearchPrevious Research Numerical SimulationsNumerical Simulations

Aspect Ratio 5 and 3Aspect Ratio 5 and 3 ΩΩ = =274 274

Aspect Ratio 3Aspect Ratio 3 ΩΩ = =180180

ObservationsObservations Traveling wave affects bulkTraveling wave affects bulk SSáánchez-nchez-ÁÁlvarez et al.lvarez et al.

(2005)(2005)

Current ResearchCurrent Research

GoalsGoalsAccurately simulate experiments Accurately simulate experiments

Investigate interaction between the traveling wave Investigate interaction between the traveling wave

and bulkand bulk

Study effect of centrifugal forces on square pattern Study effect of centrifugal forces on square pattern

formation formation

Methods Boussinesq Equations

Code written by Paul Fischer (Argonne) Experimentally realistic boundary conditions

No slip for the velocity

0u

u

uuuu

and ,)(

r,ˆ2ˆ-p

-)(

2

22

t

t zzg

Periodic Cell Periodic Cell Random initial Random initial

conditionsconditions

ParametersParametersAspect Ratio is 5, Aspect Ratio is 5,

ΩΩ = 274, = 274, εε==0.020.02

Oscillating RollsOscillating Rolls

KKL InstabilityL Instability90 °90 °

Periodic Cell Periodic Cell Non-random initial Non-random initial

conditioncondition Super-imposed Super-imposed

rolls, fade in and rolls, fade in and

outout

Not a transient Not a transient

statestate

Traveling wave is Traveling wave is

not necessary. not necessary.

ResultsResultsAspect Ratio = 5, Aspect Ratio = 5, ΩΩ=170, =170, εε=0.09=0.09

Coriolis and Coriolis and centrifugal forcescentrifugal forces

ResultsResults

Coriolis force onlyCoriolis force only

Aspect Ratio = 5, Aspect Ratio = 5, ΩΩ=170 , =170 , εε =0.09 =0.09

DiscussionDiscussionThe inclusion of the centrifugal and Coriolis The inclusion of the centrifugal and Coriolis forces provides better agreement with forces provides better agreement with experiment. (Aspect Ratio = 5, experiment. (Aspect Ratio = 5, ΩΩ=170, =170, εε=0.09=0.09))

Bajaj et al.(1998)Bajaj et al.(1998) Coriolis and Coriolis and centrifugal forcescentrifugal forces

Coriolis forceCoriolis force

DiscussionDiscussionThe inclusion of the Coriolis force only provides The inclusion of the Coriolis force only provides better agreement with other numerical better agreement with other numerical simulations. (Aspect Ratio = 5,simulations. (Aspect Ratio = 5,ΩΩ=274,=274,εε =0.004, =0.004, εε=0.02=0.02 ) )

SSáánchez-nchez-ÁÁlvarez et al.lvarez et al.(2005)(2005)

Coriolis and Coriolis and centrifugal forcescentrifugal forces

Coriolis forceCoriolis force

The oscillating rolls may be KThe oscillating rolls may be Küppers-üppers-

Lortz Instability with a switching angle of Lortz Instability with a switching angle of

90 °.90 °.

The centrifugal force should be included The centrifugal force should be included

in order to numerically model the RBC in order to numerically model the RBC

experimentsexperiments..

ConclusionConclusion

The effects of the fictitious forces on the growth The effects of the fictitious forces on the growth

rates of the modes are necessary to understand rates of the modes are necessary to understand

pattern formation.pattern formation.

The cause of the square patternsThe cause of the square patterns

The oscillation of the square bulkThe oscillation of the square bulk

Future WorkFuture Work

AcknowledgementsAcknowledgements Dr. Janet ScheelDr. Janet Scheel

Terri KimmelTerri Kimmel

Sam WaltonSam Walton

Katelyn WhiteKatelyn White

Dr. Michael CrossDr. Michael Cross

The Swenson FamilyThe Swenson Family