Joel E. Tohline
tohline@rouge.phys.lsu.edu
According to Landau and Lifshitz's (1975) eloquent discussion of the broad subject of Fluid Mechanics^{1}, the state of a moving fluid is determined by five quantities: the three components of the velocity v and, for example, the pressure P and the density r. For our discussions of astrophysical fluid systems throughout this Hypertext Book [H_Book], we will add to this the gravitational potential F. Accordingly, a complete system of equations of fluid dynamics should be six in number. For an ideal fluid these are:
[Equation I.C.1]
These equations relate the time ( t ) and spatial ( x ) variation of the variables
v | = | velocity, |
P | = | gas pressure, |
F | = | gravitational potential, |
r | = | mass density, |
e | = | specific internal energy, |
To complete the description of any specific astrophysical system, this set of differential equations must be supplemented by additional relations which (at least in the context of this H_Book) usually will be algebraic expressions motivated by the specific physics that is relevant to the chosen system.
^{2}If you need to be reminded what the dimensional units of any of these variables is, what the definition or form is of the various mathematical operators, or what the numerical value is of a particular physical constant in the above equations, click on the relevant highlighted text symbol and you'll find the answer on the page of definitions that accompanies this H_Book.
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