ThreeDimensionalConfigurations/Stability/RiemannEllipsoids - Revision history

Jet53man: /* Euler Equation */

2023-05-08T22:21:50Z

Euler Equation

← Older revision		Revision as of 18:21, 8 May 2023
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	{{ ~~Lebovitz89ahereafter~~ }}, §2, p. 223, Eq. (2)<br />		{{ Lebovitz89a }}, §2, p. 223, Eq. (2)<br />
	{{ LL96b }}, §2, p. 929, Eq. (2.1)		{{ LL96b }}, §2, p. 929, Eq. (2.1)
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Jet53man: /* Euler Equation */

2023-05-08T22:01:02Z

Euler Equation

← Older revision		Revision as of 18:01, 8 May 2023
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	{{ Lebovitz89ahereafter }}, §2, p. 223, Eq. (2)		{{ Lebovitz89ahereafter }}, §2, p. 223, Eq. (2)<br />
			{{ LL96b }}, §2, p. 929, Eq. (2.1)
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	In what follows, we will adopt the {{ Lebovitz89ahereafter }} variable notation.		In what follows, we will adopt the {{ Lebovitz89ahereafter }} variable notation.

	===Steady-State Unperturbed Flows===		===Steady-State Unperturbed Flows===

Jet53man: /* See Also */

2022-02-05T20:42:36Z

Jet53man: /* Steady-State Unperturbed Flows */

2022-02-05T00:42:28Z

Steady-State Unperturbed Flows

← Older revision		Revision as of 20:42, 4 February 2022
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	\frac{\partial}{\partial t} + (\mathbf{u} \cdot \nabla)		\frac{\partial}{\partial t} + (\mathbf{u} \cdot \nabla)
	\, .</math>		\, .</math>
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			{{ LBO67hereafter }}, §1, p. 294, Eq. (4)
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Jet53man: /* LHS */

2022-02-05T00:39:38Z

LHS

← Older revision		Revision as of 20:39, 4 February 2022
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	====LHS====		====LHS====
	With the assurance provided by {{ Lebovitz89ahereafter }} that <math>\Delta</math> commutes with the Lagrangian time-derivative, <math>D/Dt</math>, and that		With the assurance provided by {{ Lebovitz89ahereafter }} that <math>\Delta</math> commutes with the Lagrangian time-derivative, <math>D/Dt</math> — see also the paragraph immediately preceding Eq. (4) in {{ LBO67hereafter }} — and that
	<table border="0" align="center" cellpadding="3">		<table border="0" align="center" cellpadding="3">
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Jet53man: /* Lagrangian Displacement and Linearization */

2022-02-05T00:34:06Z

Lagrangian Displacement and Linearization

← Older revision		Revision as of 20:34, 4 February 2022
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	{{ Lebovitz89ahereafter }}, §2, p. 223, Eq. (3)		{{ Lebovitz89ahereafter }}, §2, p. 223, Eq. (3)<br />
			{{ LBO67hereafter }}, p. 293, Eq. (1)
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	{{ Lebovitz89ahereafter }}, §2, p. 224, Eq. (6)		{{ Lebovitz89ahereafter }}, §2, p. 224, Eq. (6)<br />
			{{ LBO67hereafter }}, p. 293, Eq. (2)
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	{{ Lebovitz89ahereafter }}, §2, p. 224, Eq. (7)		{{ Lebovitz89ahereafter }}, §2, p. 224, Eq. (7)<br />
			{{ LBO67hereafter }}, p. 294, Eq. (3)
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Jet53man: /* See Also */

2022-02-05T00:28:09Z

See Also

← Older revision		Revision as of 20:28, 4 February 2022
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	<ul>		<ul>
	<li>A library of ellipsoidal harmonics may be available from [https://en.wikipedia.org/wiki/George_Dassios George Dassios]</li>		<li>A library of ellipsoidal harmonics may be available from [https://en.wikipedia.org/wiki/George_Dassios George Dassios]</li>
			<li>{{ LBO67full }} titled, ''On the Stability of Differentially Rotating Bodies''</li>
			<li>{{ Lebovitz74full }} titled, ''The Fission Theory of Binary Stars. II. Stability to Third-Harmonics Disturbances''</li>
			<li>{{ Lebovitz89afull }} titled, ''The Stability Equations for Rotating, Inviscid Fluids:   Galerkin Methods and Orthogonal Bases''</li>
			<li>{{ Lebovitz89bfull }} titled, ''Lagrangian Perturbations of Riemann Ellipsoids''</li>
			<li>{{ LL96full }} titled, ''New Global Instabilities of the Riemann Ellipsoids''</li>
	<li>{{ Ou2006 }}</li>		<li>{{ Ou2006 }}</li>
	<li>{{ OTM2007full }}, ''Further Evidence for an Elliptical Instability in Rotating Fluid Bars and Ellipsoidal Stars.''</li>		<li>{{ OTM2007full }}, ''Further Evidence for an Elliptical Instability in Rotating Fluid Bars and Ellipsoidal Stars.''</li>
	~~<li>{{ Lebovitz74full }}, titled, ''The Fission Theory of Binary Stars. II. Stability to Third-Harmonics Disturbances''</li>~~
	~~<li>{{ Lebovitz89afull }} titled, ''The Stability Equations for Rotating, Inviscid Fluids:   Galerkin Methods and Orthogonal Bases''</li>~~
	~~<li>{{ Lebovitz89bfull }} titled, ''Lagrangian Perturbations of Riemann Ellipsoids''</li>~~
	</ul>		</ul>


	{{ SGFfooter }}		{{ SGFfooter }}

Jet53man: /* Summary */

2022-02-04T18:11:21Z

Summary

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 {{ LL96hereafter }}, &sect;3.1, p. 703, Eq. (17)
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Jet53man: /* Summary */

2022-02-04T18:02:39Z

Summary

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 {{ Lebovitz89ahereafter }}, &sect;2, p. 224, Eq. (11)<br />
 {{ Lebovitz89bhereafter }}, &sect;2, p. 227, Eq. (2)
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Jet53man: /* Steady-State Unperturbed Flows */

2022-02-04T17:33:38Z

Steady-State Unperturbed Flows

← Older revision		Revision as of 13:33, 4 February 2022
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	This relationship between structural variables in the context of steady-state unperturbed flows will be used below.		This relationship between structural variables in the context of steady-state unperturbed flows [[#Specifically_Perturb_Riemann_S-Type_Ellipsoids\|will be used below]].

	===Lagrangian Displacement and Linearization===		===Lagrangian Displacement and Linearization===

← Older revision		Revision as of 16:42, 5 February 2022
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	<ul>		<ul>
	<li>A library of ellipsoidal harmonics may be available from [https://en.wikipedia.org/wiki/George_Dassios George Dassios]</li>		<li>A library of ellipsoidal harmonics may be available from [https://en.wikipedia.org/wiki/George_Dassios George Dassios]</li>
			<li>{{ Lebovitz61full }} titled, ''The Virial Tensor and Its Application to Self-Gravitating Fluids''</li>
	<li>{{ LBO67full }} titled, ''On the Stability of Differentially Rotating Bodies''</li>		<li>{{ LBO67full }} titled, ''On the Stability of Differentially Rotating Bodies''</li>
	<li>{{ Lebovitz74full }} titled, ''The Fission Theory of Binary Stars. II. Stability to Third-Harmonics Disturbances''</li>		<li>{{ Lebovitz74full }} titled, ''The Fission Theory of Binary Stars. II. Stability to Third-Harmonics Disturbances''</li>