By Steven N. Shore
This e-book is an creation to astrophysical hydrodynamics for either astronomy and physics scholars. It offers a accomplished and unified view of the overall difficulties linked to fluids in a cosmic context, with a dialogue of fluid dynamics and plasma physics. it's the in simple terms publication on hydrodynamics that addresses the astrophysical context. Researchers and scholars will locate this paintings to be an outstanding reference. Contents contain chapters on irrotational and rotational flows, turbulence, magnetohydrodynamics, and instabilities.
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Additional info for An Introduction to Astrophysical Hydrodynamics
Therefore there are six independent components of the stress tensor (which actually become only four because of the diagonal components in an isotropic medium like a fluid). Since the shear terms are due to the off-diagonal components, we can assume that the shear stress is linearly related to the shearing strain. Just arguing from dimensional considerations, we would expect to arrive for Tij, the off-diagonal part of the stress tensor, at something like T ~-pS for the shearing term. Here μ acts like a kind of spring constant measuring the displacement in the fluid as a result of the action of the stress on the medium.
This is a force that acts along the surface of an immersed body. Because it is along each surface, rather than normal to it, friction must be represented by offdiagonal components in the stress tensor. We can expect that any repre sentation of the fluid's tendency to resistance to motion through viscosity will therefore depend on the shear (see Fig. 1). For an inviscid fluid, the stress tensor is simply the one we have derived from kinetic theory, namely T = 3p (the trace of the stress tensor).
This friction is called the viscosity and gives rise to most of the interesting effects in fluids. 2 The Navier-Stokes Equation 35 effects. In fact, it is viscosity that produces the phenomenon of "wetting," the adhesion of a fluid to a surface, so the labels are most apt. This chapter is divided into two broad sections. The first is devoted to the classical treatment of viscosity. It introduces the extension to the equations of motion affected by the introduction of long-range coupling within the fluid caused by viscosity.
An Introduction to Astrophysical Hydrodynamics by Steven N. Shore