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Second differential of the entropy as a criterion for the stability in low-dimensional climate models

The second differential of the entropy is used for analysing the stability of a thermodynamic climatic model. A delay time for the heat flux is introduced whereby it becomes an independent variable. Two different expressions for the second differential of the entropy are used: one follows classical irreversible thermodynamics theory; the second is related to the introduction of response time and is due to the extended irreversible thermodynamics theory. the second differential of the classical entropy leads to unstable solutions for high values of delay times. the extended expression always implies stable states for an ice-free earth. When the ice-albedo feedback is included, a discontinuous distribution of stable states is found for high response times. Following the thermodynamic analysis of the model, the maximum rates of entropy production at the steady state are obtained. A latitudinally isothermal earth produces the extremum in global entropy production. the material contribution to entropy production (by which we mean the production of entropy by material transport of heat) is a maximum when the latitudinal distribution of temperatures becomes less homogeneous than present values

漏 Quarterly Journal of the Royal Meteorological Society, 1999, vol. 125, n煤m. 553, p. 91-106

Royal Meteorological Society

Author: Pujol i Sagar贸, Toni
Llebot, Josep Enric
Date: 1999
Abstract: The second differential of the entropy is used for analysing the stability of a thermodynamic climatic model. A delay time for the heat flux is introduced whereby it becomes an independent variable. Two different expressions for the second differential of the entropy are used: one follows classical irreversible thermodynamics theory; the second is related to the introduction of response time and is due to the extended irreversible thermodynamics theory. the second differential of the classical entropy leads to unstable solutions for high values of delay times. the extended expression always implies stable states for an ice-free earth. When the ice-albedo feedback is included, a discontinuous distribution of stable states is found for high response times. Following the thermodynamic analysis of the model, the maximum rates of entropy production at the steady state are obtained. A latitudinally isothermal earth produces the extremum in global entropy production. the material contribution to entropy production (by which we mean the production of entropy by material transport of heat) is a maximum when the latitudinal distribution of temperatures becomes less homogeneous than present values
Format: application/pdf
ISSN: 0035-9009 (versi贸 paper)
1477-870X (versi贸 electr貌nica)
Document access: http://hdl.handle.net/10256/7716
Language: eng
Publisher: Royal Meteorological Society
Collection: Reproducci贸 digital del document publicat a: http://dx.doi.org/10.1002/qj.49712555307
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Is part of: 漏 Quarterly Journal of the Royal Meteorological Society, 1999, vol. 125, n煤m. 553, p. 91-106
Rights: Tots els drets reservats
Subject: Climatologia
Climatology
Entropia
Entropy
Termodin脿mica
Thermodynamic
Title: Second differential of the entropy as a criterion for the stability in low-dimensional climate models
Type: info:eu-repo/semantics/article
Repository: DUGiDocs

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