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Unformatted text preview: APPH 4200
Physics of Fluids
More Fluid Waves/Instabilities (Ch. 7)
November 18, 2010 1.!
! Tides 2.! Jeans instability 1 Tides Thirty days of tide heights at Bridgeport Connecticut U.S.A. as calculated
from the Harmonic Constituent data aligned with 0h Sunday 1'st
September 1991. 2 10-component
Tide predicting machine, by Sir William Thomson in
The ﬁrst full sized machine for predicting tides,
combined ten tidal components (one pulley for each
component). It could trace the heights of the tides
for one year in about four hours. 3 The M2 tidal constituent. Amplitude is indicated by color, and the white lines are cotidal differing by 1 hr. The curved arcs
around the amphidromic points show the direction of the tides, each indicating a synchronized 6 hour period.
R. Ray, TOPEX/Poseidon: Revealing Hidden Tidal Energy en:GSFC,en:NASA. Redistribute with credit to R. Ray, and
NASA - Goddard Space Flight Center
NASA - Jet Propulsion Laboratory
Scientiﬁc Visualization Studio Semi-Diurnal Tide Map 4 Tides: Driven Shallow Water Waves 5 Surface Waves with a Lateral Force 6 (Same Eq using “integrated” velocity potential) 7 What is the lateral force? 8 Net Force with Period 2Ω 9 Driven Surface Waves 10 Star Formation 11 The Stability of a Spherical Nebula
J. H. Jeans PHILOSOPHICAL
1. The Stability of a Spherical Nebula.
By J. H. JEANS, B.A., Fellow of Trinity College, asnd Isaac Newton Student in the
University of Cambridge.
Communicated b)yProfessor G. H. DAvwN,
F. R.?S. _ead June 20, 1901. Revised February 28, 1902.
Received June 15,--R INTRODUUCTION. ? 1. object of the present paper can be best explained by referring to a sentence
which occurs in a paper by Professor G. H. DARWIN. This is as follows :
" The principal question involved in the nebular hypothesis seems to be the
stability of a rotating mass of gas; but, unfortunately, this has remained up to now
an untouched field of mathematical research. We can only judge of probable results
from the investigations which have been made concerning the stability of a rotating
mass of liquid."
In so far as the two cases are parallel, the argument by analogy will, of course, be
valid enough, but the compressibility of a gas makes possible in the gaseous nebula a
whole series of vibrations which have no counterpart in a liquid, and no infe:rence as
to the stability of these motions call be drawn from an examination of the behaviour
of a liquid. Thus, although there will be unstable vibrations in a rotating mass of
gas similar to those which are known to exist in a rotating liquid, it does not at all
follow that a rotating gas will become unstable, in the first place, through vibrations
T-IE 12 Jeans Instability: Driven Sound Waves 13 Linearized Self-Gravitational Response 14 Summary
• Linearization of dynamical equations provides a
powerful methodology to understand
disturbances • Harmonic analysis (ω) and modal analysis (k)
provide understanding of linear PDEs 15 ...
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This document was uploaded on 10/18/2011.
- Spring '09