A Note on the Stability of a Finite-amplitude Wave Solution of the Generalized Landau Equation

Niino, Hiroshi

doi:10.2151/jmsj1965.60.5_1024

Cited by 5 publications

(4 citation statements)

References 8 publications

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“…Это можно сделать двумя способами. Во первых, можно учесть медленное пространственное изме нение амплитуды гармонического (по х) возмущения [104]. В этом слу чае задача сводится к уравнению Ландау -Гинзбурга и можно изучить устойчивость стационарного решения от носительно периодических возмущений (модуляционная неустойчи вость) .…”

Section: 4unclassified

Stability and vortex structures of quasi-two-dimensional shear flows

Dolzhanskii¹,

Krymov²,

Manin³

1990

Usp. Fiz. Nauk

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Section: 4unclassified

Stability and vortex structures of quasi-two-dimensional shear flows

Dolzhanskii¹,

Krymov²,

Manin³

1990

Usp. Fiz. Nauk

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“…respectively. From the relationship S(-d, -l) =S(d , l) (Niino, 1982), it is found that the stability of the finite-amplitude wave does not change when the sign of * is reversed.…”

Section: The Coefficients Of the Generalized Landau Equation Shown Inmentioning

confidence: 99%

“…5.1.4 The stability of the finite-amplitude wave As stated in Introduction, for a given supercritical Reynolds number, a finite-amplitude wave of wavenumber k0 is stable in the wavenumber range given by S(k1-kc)<k0-kc<S(k2-kc), (5.1) where k1 and k2 (k1<k2) are the wavenumbers of the neutral waves for the given Reynolds number (Stuart and DiPrima, 1978;Niino, 1982). The wavenumber range and the neutral curve is schematically shown in Fig.…”

Section: The Coefficients Of the Generalized Landau Equation Shown Inmentioning

confidence: 99%

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A Weakly Non-linear Theory of Barotropic Instability

Niino¹

1982

Journal of the Meteorological Society of Japan

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The stability of non-divergent horizontal shear flows in a homogeneous rotating fluid is investigated by means of a weakly non-linear theory. Velocity profiles of the shear flows considered in this paper are given by U(y)=tanh y and U(y)=sech2 y, where y is the coordinate in the cross-stream direction. The effect of variation of the Coriolis parameter * (beta effect) and that of the Ekman friction at the bottom surfaces are included.The coefficients of the generalized Landau equation, which describes temporal and spatial modulation of the amplitude of periodic waves, are calculated for various values of /*=d*/dy. It is found that the barotropic instability of the shear flows belongs to so-called supercritical type for all values of * used in this study. Therefore, we can expect a steady-state configuration betweenn a finite-amplitude wave and the distorted flow for a supercritical Reynolds number.The stability of the finite-amplitude steady wave with respect to so-called side-band modes is also examined. It is found that, for a given supercritical Reynolds number, the finiteamplitude wave is stable if the wavenumber k0 satisfies the inequality S(k1-kc)

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Modulational instability of plane waves in a two-dimensional jet and wake

Fujimura¹,

Yanase²,

Mizushima³

1988

Fluid Dyn. Res.

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The modulational instability problem is reformulated by the amplitude expansion method. A generalized version of the Stewartson-Stuart equation is derived, which is applicahle to any supercritical state as long as the amplitude of the disturhance is small. The modulational instahility of plane waves in a two-dimensionaljet and wake is investigated on the basis of this equation, and it is found that the plane waves are stahle to side-band disturhances in supercritical states except in the close neighbourhood of the critical state.

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A Note on the Stability of a Finite-amplitude Wave Solution of the Generalized Landau Equation

Abstract: The stability analysis of a finite-amplitude wave solution of the generalized Landau equation due to Stuart and DiPrima (1978) is extended. For a given supercritical stability parameter, a finite-amplitude wave of wavenumber ko is stable if ko satisfies -S(k1-kc)< ko -kc Show more

Cited by 5 publications

References 8 publications

Stability and vortex structures of quasi-two-dimensional shear flows

Stability and vortex structures of quasi-two-dimensional shear flows

A Weakly Non-linear Theory of Barotropic Instability

Modulational instability of plane waves in a two-dimensional jet and wake

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