TY - JOUR

T1 - Two Dimensional Convection Patterns in Large Aspect Ratio Systems

AU - Newell, Alan C.

N1 - Funding Information:
This work was supported in part by DOA Contract DAAG29-82-C-0068.

PY - 1983/1/1

Y1 - 1983/1/1

N2 - This chapter presents a mathematical framework for describing convection patterns. On the horizontal diffusion time scale TH, the convection field develops patches, of a circular nature surrounding a sink, in which the wavenumber is constant. The incompatibility of these patches is ironed out over the longer time scale of the aspect ratio times TH, and the process involves a gliding motion in which roll dislocations move in a direction perpendicular to the roll axis. The climb motion, where the dislocations move along the roll axis, occur on the scale TH as their role is to adjust wavelength, although small adjustments of order ε2 will be made on the ε-2TH scale.

AB - This chapter presents a mathematical framework for describing convection patterns. On the horizontal diffusion time scale TH, the convection field develops patches, of a circular nature surrounding a sink, in which the wavenumber is constant. The incompatibility of these patches is ironed out over the longer time scale of the aspect ratio times TH, and the process involves a gliding motion in which roll dislocations move in a direction perpendicular to the roll axis. The climb motion, where the dislocations move along the roll axis, occur on the scale TH as their role is to adjust wavelength, although small adjustments of order ε2 will be made on the ε-2TH scale.

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U2 - 10.1016/S0304-0208(08)72093-0

DO - 10.1016/S0304-0208(08)72093-0

M3 - Article

AN - SCOPUS:77956922432

SN - 0304-0208

VL - 81

SP - 205

EP - 231

JO - North-Holland Mathematics Studies

JF - North-Holland Mathematics Studies

IS - C

ER -