On an apriori estimate in the theory of hydrodynamical stability

1968 ◽  
pp. 267-269 ◽  
Author(s):  
V. I. Arnol′d
Keyword(s):  
Apriori Estimate ◽  
Hydrodynamical Stability

scholarly journals Asymmetrical Ejection of Matter in a Thermonuclear Model of a Supernova Explosion

1988 ◽  
Vol 101 ◽  
pp. 27-30
Author(s):  
V.M. Chechetkin ◽  
A.A. Denisov ◽  
A.V. Koldoba ◽  
Yu.A. Poveschenko ◽  
Yu.P. Popov
Keyword(s):  
Supernova Explosion ◽  
Recent Event ◽  
Simultaneous Production ◽  
Sn 1987A ◽  
Supernova 1987A ◽  
Explosion Mechanism ◽  
Red Giant ◽  
Carbon Burning ◽  
Hydrodynamical Stability ◽  
Main Factor

With the recent Supernova 1987a in the LMC, new and interesting possibilities have arisen for the solution of a problem relating to the explosion mechanism of supernovae. The presupernova was probably a B3Ia, the blue supergiant, and not a red giant as it was earlier thought likely. Calculations of the evolution, which have been made recently, show that the loss of hydrodynamical stability may be connected with carbon burning in the stellar core during the blue giant stage. This loss of stability of the CO core is the main factor in our explanation of the recent event of SN 1987a.Before we consider the thermonuclear model of a supernova based on a thermal flash in the degenerate CO core, let us dwell on the present situation in the theory of supernovae. The main problem in supernova theory is the simultaneity of births of a compact remnant and an expelled envelope. The compact remnant later becomes a neutron star. The expelled envelope determines the curve of brightness. Now, it is clear that a supernova explosion may result in either the total disruption of a star or in the simultaneous production of a compact remnant and an expelled envelope.

Nonlinear instability in plane Poiseuille flow: a quantitative comparison between the methods of amplitude expansions and the method of multiple scales

1981 ◽  
Vol 375 (1761) ◽  
pp. 155-167 ◽  
Keyword(s):  
Stream Function ◽  
Stokes Equations ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Navier Stokes ◽  
Plane Poiseuille Flow ◽  
Navier Stokes Equations ◽  
Order Of Magnitude ◽  
Model Equations ◽  
Hydrodynamical Stability

This paper shows that two different expansion procedures for hydrodynamical stability problems are equivalent. The method of multiple scales of Stewartson & Stuart (1971) is extended to calculate the stream function up to order ε 2 . Watson’s (1960) rigorous amplitude expansion of the solution of the Navier-Stokes equations is also used to calculate the stream function up to the same order of magnitude, and a complete equi­valence between the two results is found. An analysis of the Eckhaus model equations has been made and the results are equivalent.

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