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On Linear Growth Rates in Thermohaline Convection with Viscosity Variations


Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India
     

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In the present paper it is proved that the complex growth rate (where and are real and imaginary parts of p ) of an arbitrary oscillatory motions of growing amplitude, neutral or unstable, for thermohaline convection configuration of Veronis type (Veronis, G., J. Mar. Res., 23(1965)1), with the viscosity variations must lie inside a semicircle in the right half of the prpiplane whose centre is at the origin and radius equals . A similar theorem is also proved for thermohaline convection of Stern type (Stern, M.E., Tellus 12(1960)172). Furthermore the above results are uniformly valid for all combinations of rigid and free bounding surfaces. The results obtain herein, in particular, also yield sufficient conditions for the validity of the ‘principle of the exchange of the stabilities’ for the respective configurations.

Keywords

Thermohaline Instability, Oscillatory Motions, Veronis Type, Stern Type, Variable Viscosity.
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  • On Linear Growth Rates in Thermohaline Convection with Viscosity Variations

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Authors

Jyoti Prakash
Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India
Kanu Vaid
Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India

Abstract


In the present paper it is proved that the complex growth rate (where and are real and imaginary parts of p ) of an arbitrary oscillatory motions of growing amplitude, neutral or unstable, for thermohaline convection configuration of Veronis type (Veronis, G., J. Mar. Res., 23(1965)1), with the viscosity variations must lie inside a semicircle in the right half of the prpiplane whose centre is at the origin and radius equals . A similar theorem is also proved for thermohaline convection of Stern type (Stern, M.E., Tellus 12(1960)172). Furthermore the above results are uniformly valid for all combinations of rigid and free bounding surfaces. The results obtain herein, in particular, also yield sufficient conditions for the validity of the ‘principle of the exchange of the stabilities’ for the respective configurations.

Keywords


Thermohaline Instability, Oscillatory Motions, Veronis Type, Stern Type, Variable Viscosity.

References