Open AccessAn interpretation of the Nusselt‐Rayleigh number relationship for convection in a spherical shell
Author(s) -
Iwase Yasuyuki,
Honda Satoru
Publication year - 1997
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1997.tb01874.x
Subject(s) - nusselt number , rayleigh number , convection , natural convection , mechanics , spherical shell , combined forced and natural convection , rayleigh–bénard convection , shell (structure) , downwelling , thermodynamics , geometry , physics , classical mechanics , materials science , mathematics , geology , reynolds number , turbulence , composite material , oceanography , upwelling
SUMMARY Recent studies on the relationship between the Nusselt ( Nu ) and Rayleigh ( Ra ) numbers for base‐heated convection in a spherical shell with a constant viscosity show that the power‐law index is around 1/4, which is different from the value of 1/3 predicted by a simple boundary layer theory. We show that such a difference may be caused by the flow pattern due to the geometry. The flow pattern of the convection in a spherical shell at relatively low Ra , at least, less than 10 6 , is characterized by narrow upwelling and broad downwelling, which is similar to the opposite flow pattern of internally heated convection. Convection in the internally heated case predicts the power‐law index of 1/4. We demonstrate this relationship based on the concept of ‘local’ Rayleigh ( Ra1 ) and Nusselt ( Nu1 ) numbers