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Initial and boundary layer analyses are performed to obtain the asymptotically correct initial and boundary conditions for the Levermore flux-limited diffusion approximation to the equation of radiative transfer.
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This work shows how analogous, one-dimensional (1D) mass and momentum boundary layer analyses can predict filtration flux.
The boundary layer equations are (1).
The significant differences from traditional boundary layer flows are highlighted.
Boundary layer studies suggest that the velocity and temperature boundary layer thicknesses are lower for higher Reynolds numbers.
A boundary layer flow was indirectly detected.
The boundary layer saturation is Eq. 18.
The diffusion boundary layer thickness was varied between 0.0025 and 0.1 cm.
The lower mantle thermal boundary layer thickness is also derived by assuming the boundary layer Rayleigh number is critical and that νLM = 2 νUM, which was found by Driscoll and Bercovici (2014) to produce a nominal Earth model.
Thermal boundary layer temperature jumps are Δ TUM = TUM − Tg and Δ TLM = Tcmb − TLM, and thermal boundary layer depth is δ. Figure B1 shows an example whole-planet geotherm T r) at four times in the evolution.
The top of the daytime boundary layer is referred to as the mixed-layer inversion.
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