User:Tohline/ThreeDimensionalConfigurations/ChallengesPt2
Challenges Constructing Ellipsoidal-Like Configurations (Pt. 2)
This chapter extends an accompanying chapter titled, Construction Challenges (Pt. 1). The focus here is on an SCF technique that will incorporate specification of a Lagrangian flow-flied.
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Motivation
Usually, the density, <math>~\rho</math>, and the pair of axis ratios, <math>~b/a</math> and <math>~c/a</math>, are specified. Then, the Poisson equation is solved to obtain <math>~\Phi_\mathrm{grav}</math> in terms of <math>~A_1</math>, <math>~A_2</math>, and <math>~A_3</math>. The aim, then, is to determine the value of the central enthalpy, <math>~H_0</math> — alternatively, the thermal energy density, <math>~\Pi</math> — and the two parameters, <math>~\Omega_f</math> and <math>~\lambda</math>, that determine the magnitude of the velocity flow-field. Keep in mind that, as viewed from a frame of reference that is spinning with the ellipsoid (at angular frequency, <math>~\Omega_f</math>), the adopted (rotating-frame) velocity field is,
See Also
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© 2014 - 2021 by Joel E. Tohline |