Overshooting: Mixing Length Yields Divergent Results

Details Overshooting: Mixing Length Yields Divergent Results Overshooting: Mixing Length Yields Divergent Results

Aug 1997

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1997apj...484l.161c&link_type=abstract

Astrophysical Journal Letters v.484, p.L161

Astronomy and Astrophysics

Astronomy

11

Convection, Hydrodynamics, Turbulence, Sun: Evolution, Stars: Evolution, Stars: Interiors

Scientific paper

Overshooting (OV) is the signature of the nonlocal nature of convection. To describe the latter, one needs five nonlocal, coupled differential equations to describe turbulent kinetic energies (total K and in the z-direction Kz), potential energy, convective flux, and rate of dissipation epsilon . We show analytically that if epsilon is assumed to be given by the local expression, epsilon = K3/2l-1 (mixing length l = alpha Hp or l = z/a, since the region is small in extent), the remaining differential equations exhibit singularities (divergences) for specific values of a within the range of values usually employed. No solution can be found. Thus, OV results from such an approach are quite accidental, as they stem from an arbitrary fine tuning of a.

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