Open AccessTime‐dependent thermal convection ‐ a possible explanation for a multiscale flow in the Earth's mantle
Author(s) -
Hansen Ulrich,
Ebel Adolf
Publication year - 1988
Publication title -
geophysical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0952-4592
DOI - 10.1111/j.1365-246x.1988.tb05895.x
Subject(s) - convection , mantle convection , rayleigh number , geophysics , geology , thermal , mantle (geology) , mechanics , convection cell , natural convection , combined forced and natural convection , thermodynamics , physics , lithosphere , seismology , tectonics
Summary The temporal evolution of thermal convection in stress‐free, base‐heated boxes is investigated by means of a finite‐element model. It is shown that the aspect ratio and also the initial conditions have a tremendous influence on the evolution. In boxes of aspect ratio A, significantly greater than unity (1.8<λ<3), the onset of time‐dependence occurs at much lower values of the Rayleigh number Ra than predicted from studies which assumed square boxes (λ= 1). While steady‐state solutions can be obtained by a particular choice of initial conditions, stationary convection breaks down for less restrictive conditions. It is also demonstrated, that the long held view, that convection cells with λ= 1 would break down into smaller units, is not valid. At Ra ‐ 10 6 elongated convection cells of λ= 3 with superimposed boundary‐layer instabilities are found in the long‐term range of the temporal evolution. Regarding the Earth's mantle, the model of a time‐dependent multiscale flow can basically explain the coexistence of different scales of convection in the mantle.