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تسجيل مستخدم جديدA two-dimensional mixing length theory of convective transport
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The helioseismic observations of the internal rotation profile of the Sun raise questions about the two-dimensional (2D) nature of the transport of angular momentum in stars. Here we derive a convective prescription for axisymmetric (2D) stellar evolution models. We describe the small scale motions by a spectrum of unstable linear modes in a Boussinesq fluid. Our saturation prescription makes use of the angular dependence of the linear dispersion relation to estimate the anisotropy of convective velocities. We are then able to provide closed form expressions for the thermal and angular momentum fluxes with only one free parameter, the mixing length. We illustrate our prescription for slow rotation, to first order in the rotation rate. In this limit, the thermodynamical variables are spherically symetric, while the angular momentum depends both on radius and latitude. We obtain a closed set of equations for stellar evolution, with a self-consistent description for the transport of angular momentum in convective regions. We derive the linear coefficients which link the angular momentum flux to the rotation rate ($Lambda$- effect) and its gradient ($alpha$-effect). We compare our results to former relevant numerical work.
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Stellar convection is customarily described by Mixing-Length Theory, which makes use of the mixing-length scale to express the convective flux, velocity, and temperature gradients of the convective elements and stellar medium. The mixing-length scale
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Turbulent convection is certainly one of the most important and thorny issues in stellar physics. Our deficient knowledge of this crucial physical process introduces a fairly large uncertainty concerning the internal structure and evolution of stars.
A striking example is overshoot at the edge of convective cores. Indeed, nearly all stellar evolutionary codes treat the overshooting zones in a very approximative way that considers both its extent and the profile of the temperature gradient as free parameters. There are only a few sophisticated theories of stellar convection such as Reynolds stress approaches, but they also require the adjustment of a non-negligible number of free parameters. We present here a theory, based on the plume theory as well as on the mean-field equations, but without relying on the usual Taylors closure hypothesis. It leads us to a set of eight differential equations plus a few algebraic ones. Our theory is essentially a non-mixing length theory. It enables us to compute the temperature gradient in a shrinking convective core and its overshooting zone. The case of an expanding convective core is also discussed, though more briefly. Numerical simulations have quickly improved during recent years and enabling us to foresee that they will probably soon provide a model of convection adapted to the computation of 1D stellar models.
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