Jet53man at 16:25, 30 July 2021

2021-07-30T16:25:50Z

Jet53man: /* Introduction */

2021-07-30T15:58:47Z

Introduction

← Older revision		Revision as of 11:58, 30 July 2021
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	==Introduction==		==Introduction==
			{\| class="PGEclass" style="float:left; margin-right: 20px; border-style: solid; border-width: 3px border-color: black"
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			! style="height: 125px; width: 125px; background-color:white;" \|
			<font size="-1">[[H_BookTiledMenu#Stability_Analysis\|<b>(poor attempt at)<br />Reconciliation</b>]]</font>
			\|}
	===Eulerian Approach===		===Eulerian Approach===
	In a [[~~User:Tohline/~~SSC/~~Stability_Eulerian_Perspective~~#Stability_of_Spherically_Symmetric_Configurations_.28Eulerian_Perspective.29\|related discussion]], we have shown that, from a standard Eulerian perspective, the perturbation and linearization of the [[~~User:Tohline/~~PGE#Principal_Governing_Equations\|principal governing equations]] leads to an equation of continuity (EOC), equation of motion (EOM), and Poisson equation of the form,		In a [[SSC/StabilityEulerianPerspective#Stability_of_Spherically_Symmetric_Configurations_.28Eulerian_Perspective.29\|related discussion]], we have shown that, from a standard Eulerian perspective, the perturbation and linearization of the [[PGE#Principal_Governing_Equations\|principal governing equations]] leads to an equation of continuity (EOC), equation of motion (EOM), and Poisson equation of the form,
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	<math>~s \equiv \frac{\rho_1}{\rho_0} \, ,</math>		<math>~s \equiv \frac{\rho_1}{\rho_0} \, ,</math>
	</div>		</div>
	this becomes what we have [[~~User:Tohline/~~SSC/~~Stability_Eulerian_Perspective~~#EulerianWaveEquation\|referred to elsewhere as the Eulerian Wave Equation]].		this becomes what we have [[SSC/StabilityEulerianPerspective#EulerianWaveEquation\|referred to elsewhere as the Eulerian Wave Equation]].

	===Lagrangian Approach===		===Lagrangian Approach===
	In [[~~User:Tohline/~~SSC/Perturbations#Spherically_Symmetric_Configurations_.28Stability_.E2.80.94_Part_II.29\|another related discussion]], we have shown that, from a standard Lagrangian perspective, the perturbation and linearization of the principal governing equations leads to an equation of continuity (EOC), and equation of motion (EOM) ''already combined'' with the Poisson equation of the form,		In [[SSC/Perturbations#Spherically_Symmetric_Configurations_.28Stability_.E2.80.94_Part_II.29\|another related discussion]], we have shown that, from a standard Lagrangian perspective, the perturbation and linearization of the principal governing equations leads to an equation of continuity (EOC), and equation of motion (EOM) ''already combined'' with the Poisson equation of the form,
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	which, after rearrangement of terms, gives what we have [[~~User:Tohline/~~SSC/Perturbations#2ndOrderODE\|referred to elsewhere as the Adiabatic Wave (or Radial Pulsation) Equation]].		which, after rearrangement of terms, gives what we have [[SSC/Perturbations#2ndOrderODE\|referred to elsewhere as the Adiabatic Wave (or Radial Pulsation) Equation]].

	===Rosseland's Approach===		===Rosseland's Approach===
	[[~~User:Tohline/~~SSC/~~Perspective_Reconciliation~~#Rosseland.27s_Derivation_of_the_Wave_Equation\|Rosseland's approach]] is to <font color="red">take the total time-derivative of the EOM — even before linearizing any of the governing equations — then combine it strategically with the EOC and (integrated) Poisson equation</font> to obtain,		[[SSC/PerspectiveReconciliation#Rosseland.27s_Derivation_of_the_Wave_Equation\|Rosseland's approach]] is to <font color="red">take the total time-derivative of the EOM — even before linearizing any of the governing equations — then combine it strategically with the EOC and (integrated) Poisson equation</font> to obtain,

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Jet53man: Created page with "FORCETOC =Reconciling Eulerian versus Lagrangian Perspectives= ..."
2021-07-30T15:53:34Z
Created page with "FORCETOC  =Reconciling Eulerian versus Lagrangian Perspectives= <table border="1" cellpadding="8" align="center" width="90%"> <tr>..."
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Jet53man at 16:25, 30 July 2021

Jet53man: /* Introduction */