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Planets by Lynn M. Stone

By Lynn M. Stone

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2 2 0 0 2 1/2 Appendix: Langmuir Waves as Perturbations of the Distribution Function We will not deal very much with particle kinetics or plasmas in this book. But it is impossible to pass up the opportunity to illustrate an example of how the distribution function can be used, with moment methods and the Vlasov equation so fresh in your mind. The other reason for this appendix is that it is the best way to introduce an important quantity, the plasma frequency, and also to illustrate how perturbations on the distribution function result in dispersion relations.

3 Dissipation and Viscous Coupling The leitmotif of this chapter is that viscosity is intrinsically dissipative of momentum and energy. To see the consequences of viscous coupling of the fluid to its environment, or to internal dissipation, we need to find how the energy losses depend on the stresses within the fluid. We assume that the flow is driven by the stress 7] which contains the viscosity. We will generalize this discussion, without regard to the details of 2Jy, because the only condition we need to place on the stress is that it is symmetric in its indices.

You will meet with this problem again when we discuss Alfven waves, in the sense that the medium becomes anisotropic in the presence of a magnetic field and the difference in the viscous coef­ ficients is like the propagation of a magnetosonic wave. 4 T h e Reynolds Number If we start with the Navier-Stokes equation, we see that we can form a dimensionless number from the scales of length and time. The equation of motion, with or without viscosity, is ultimately a force equation. It there­ fore has the dimensions MLT~ , or MU L~ .

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