Sufficient conditions of Rayleigh-Taylor stability and instability in equatorial ionosphere

doi:10.1007/s10483-016-2022-8

Applied Mathematics and Mechanics (English Edition) ›› 2016, Vol. 37 ›› Issue (2): 181-192.doi: https://doi.org/10.1007/s10483-016-2022-8

Sufficient conditions of Rayleigh-Taylor stability and instability in equatorial ionosphere

Sicheng WANG¹, Sixun HUANG^1,2

1. Institute of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101, China;
2. State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, China

收稿日期:2015-04-17 修回日期:2015-07-21 出版日期:2016-02-01 发布日期:2016-02-01
通讯作者: Sixun HUANG E-mail:huangsxp@163.com
基金资助:
Project supportedbythe National Natural Science Foundation of China (Nos. 41575026 and 41175025)

Sufficient conditions of Rayleigh-Taylor stability and instability in equatorial ionosphere

Sicheng WANG¹, Sixun HUANG^1,2

1. Institute of Meteorology and Oceanography, PLA University of Science and Technology, Nanjing 211101, China;
2. State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, State Oceanic Administration, Hangzhou 310012, China

Received:2015-04-17 Revised:2015-07-21 Online:2016-02-01 Published:2016-02-01
Contact: Sixun HUANG E-mail:huangsxp@163.com
Supported by:
Project supportedbythe National Natural Science Foundation of China (Nos. 41575026 and 41175025)

摘要/Abstract

摘要：

Rayleigh-Taylor (R-T) instability is known as the fundamental mechanism of equatorial plasma bubbles (EPBs). However, the sufficient conditions of R-T instability and stability have not yet been derived. In the present paper, the sufficient conditions of R-T stability and instability are preliminarily derived. Linear equations for small perturbation are first obtained from the electron/ion continuity equations, momentum equations, and the current continuity equation in the equatorial ionosphere. The linear equations can be casted as an eigenvalue equation using a normal mode method. The eigenvalue equation is a variable coefficient linear equation that can be solved using a variational approach. With this approach, the sufficient conditions can be obtained as follows:if the minimum systematic eigenvalue is greater than one, the ionosphere is R-T unstable; while if the maximum systematic eigenvalue is less than one, the ionosphere is R-T stable. An approximate numerical method for obtaining the systematic eigenvalues is introduced, and the R-T stable/unstable areas are calculated. Numerical experiments are designed to validate the sufficient conditions. The results agree with the derived suf-ficient conditions.

关键词: variational approach, Rayleigh-Taylor (R-T) instability, sufficient condition, equatorial iono-sphere

Abstract:

Key words: equatorial iono-sphere, Rayleigh-Taylor (R-T) instability, sufficient condition, variational approach

中图分类号:

76E25
65N25

Sicheng WANG, Sixun HUANG. Sufficient conditions of Rayleigh-Taylor stability and instability in equatorial ionosphere[J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(2): 181-192.

参考文献

[1] Woodman, R. F. Spread F-an old equatorial aeronomy problem finally resolved? Annales Geo-physicae, 27, 1915-1934(2009)
[2] Kelley, M. C. The Earth's Ionosphere: Plasma Physics and Electrodynamics, 2nd ed., Elsevier, London (2009)
[3] Huang, C. S., Le, G., de La Beaujardiere, O., Roddy, P. A., Hunton, D. E., Pfaff, R. F., and Hairston, M. R. Relationship between plasma bubbles and density enhancements: observations and interpretation. Journal of Geophysical Research: Space Physics, 119, 1325-1336(2014)
[4] Carter, B. A., Yizengaw, E., Retterer, J. M., Francis, M., Terkildsen, M., Marshall, R., Norman, R., and Zhang, K. An analysis of the quiet time day-to-day variability in the formation of post-sunset equatorial plasma bubbles in the Southeast Asian region. Journal of Geophysical Research: Space Physics, 119, 3206-3223(2014)
[5] Rayleigh, L. On the stability or instability of certain fluid motions. Proceedings of London Math-ematical Society, 11, 57-70(1880)
[6] Fjortoft, R. Application of integral theorems in deriving criteria of stability for laminar flows and for the baroclinic circular vortex. Geofys. Publ. Norske Vid.-Akad. Oslo, 17, 1-52(1950)
[7] Howard, L. N. Note on a paper of John W. Miles. Journal of Fluid Mechanics, 10, 509-512(1961)
[8] Drazin, P. D. and Reid, W. H. Hydrodynamics Stability, Cambridge University Press, Cambridge (1981)
[9] Yi, J. X. Fluid Dynamics (in Chinese), Higher Education Press, Beijing (1982)
[10] Zhao, G. F. and Zhou, H. Weakly nonlinear theory versus theory of secondary instability for plane poiseuille flow. Applied Mathematics and Mechanics (English Edition), 9(7), 617-623(1988) DOI 10.1007/BF02465691
[11] Xiong, J. G., Yi, F., and Li, J. The influence of topography on the nonlinear interaction of Rossby waves in the barotropic atmosphere. Applied Mathematics and Mechanics (English Edition), 15(6), 585-594(1994) DOI 10.1007/BF02450772
[12] Zhang, G., Xiang, J., and Li, D. H. Nonlinear saturation of baraclinic instability in the generalized Phillips model I: the upper bound on the evolution of disturbance to the nonlinearly. Applied Mathematics and Mechanics (English Edition), 23(1), 79-88(2002) DOI 10.1007/BF02437733
[13] Zeytounian, R. K. Theory and Applications of Nonviscous Fluid Flows, Springer, Berlin (2002)
[14] Huang, S. X. andWu, R. S. Methods of Mathematical Physics in Atmospheric Science (in Chinese), 3rd ed., China Meteorological Press, Beijing (2011)
[15] Ossakow, S. L., Zalesak, S. T., McDonald, B. E., and Chaturvedi, P. K. Nonlinear equatorial spread F: dependence on altitude of the F peak and bottomside background electron density gradient scale length. Journal of Geophysical Research, 84, 17-29(1979)
[16] Mendillo, M., Baumgardner, J., Pi, X., Sultan, P. J., and Tsunoda R. Onset conditions for equa-torial spread F. Journal of Geophysical Research, 97, 13865-13876(1992)
[17] Huang, C. S., Kelley, M. C., and Hysell, D. L. Nonlinear Rayleigh-Taylor instabilities, atmospheric gravity waves and equatorial spread F. Journal of Geophysical Research, 98, 15631-15642(1993)
[18] Sultan, P. J. Linear theory and modeling of Rayleigh-Taylor instability leading to the occurrence of equatorial spread F. Journal of Geophysical Research, 101, 26875-26891(1996)
[19] Rappaport, H. L. Field line integration and localized modes in the equatorial spread F. Journal of Geophysical Research, 101, 24545-24551(1996)
[20] Migliuolo, S. Nonlocal dynamics of the collisional Rayleigh-Taylor instability: application to the equatorial spread F. Journal of Geophysical Research, 101, 10975-10984(1996)
[21] Basu, B. On the linear theory of equatorial plasma instability: comparison of different descriptions. Journal of Geophysical Research, 107, 18-1-18-10(2002)
[22] Chakrabarti, N. and Lakhina, G. S. Collisional Rayleigh-Taylor instability and shear-flow in equa-torial spread-F plasma. Annales Geophysicae, 21, 1153-1157(2003)
[23] Sekar, R. Plasma instabilities and their simulations in the equatorial F region: recent results. Space Science Reviews, 107(1-2), 251-262(2003)
[24] Lee, C. C. Examine the local linear growth rate of collisional Rayleigh-Taylor instability during solar maximum. Journal of Geophysical Research, 111, A11313(2006)
[25] Aveiro, H. C. and Huba, J. D. Equatorial spread F studies using SAMI3 with two-dimensional and three-dimensional electrostatics. Annales Geophysicae, 31, 2157-2162(2013)
[26] Huba, J. D., Bernhardt, P. A., Ossakow, S. L., and Zalesak, S. T. The Rayleigh-Taylor instability is not damped by recombination in the F region. Journal of Geophysical Research, 101, 24553-24556(1996)
[27] Keskinen, M. J., Ossakow, S. L., and Fejer, B. G. Three-dimensional nonlinear evolution of equa-torial ionospheric spread-F bubbles. Geophysical Research Letters, 30, 1855-1858(2003)
[28] Scannapieco, A. J. and Ossakow, S. L. Nonlinear equatorial spread F. Geophysical Research Letters, 3, 451-454(1976)
[29] Zalesak, S. T. and Ossakow, S. L. Nonlinear equatorial spread F: spatially large bubbles resulting from large horizontal scale initial perturbations. Journal of Geophysical Research, 85, 2131-2142(1980)
[30] Basu, B. Nonlinear saturation of Rayleigh-Taylor instability in the presence of time-dependent equilibrium. Journal of Geophysical Research, 104(A4), 6859-6866(1999)
[31] Xie, H. and Xiao, Z. Numerical simulation of spread-F in low and mid-latitudes (in Chinese). Chinese Journal of Geophysics, 36(1), 18-26(1993)
[32] Picone, J. M., Hedin, A. E., Drob, D. P., and Aikin, A. C. NRLMSISE-00 empirical model of the atmosphere: statistical comparisons and scientific issues. Journal of Geophysical Research, 107, 15-1-15-16(2002)
[33] Bilitza, D. and Reinisch, B. W. International Reference Ionosphere 2007: improvements and new parameters. Advances in Space Research, 42, 599-609(2008)
[34] Zalesak, S. T. and Ossakow, S. L. Nonlinear equatorial spread F: the effect of neutral winds and background Pedersen conductivity. Journal of Geophysical Research, 87, 151-166(1982)
[35] Chapagain, N. P., Fisher, D. J., Meriwether, J. W., Chau, J. L., and Makela, J. J. Comparison of zonal neutral winds with equatorial plasma bubble and plasma drift velocities. Journal of Geophysical Research: Space Physics, 118, 1802-1812(2013)
[36] Kudeki, E., Akgiray, A., Milla, M., Chau, J. L., and Hysell, D. L. Equatorial spread-F initia-tion: posts-sunset vortex, thermospheric winds, gravity waves. Journal of Atmospheric and Solar-Terrestrial Physics, 69, 2416-2427(2007)
[37] Sekar, R. and Raghavarao, R. Role of vertical winds on the Rayleigh-Taylor mode instabilities of the night time equatorial ionosphere. Journal of Atmospheric and Terrestrial Physics, 49, 981-985(1987)
[38] Raghavarao, R., Suhasini, R., Mayr, H. G., Hoegy, W. R., and Wharton, L. E. Equatorial spread-F (ESF) and vertical winds. Journal of Atmospheric and Solar-Terrestrial Physics, 61, 607-617(1999)
[39] Sekar, R., Suhasini, R., and Raghavarao, R. Effects of vertical winds and electric fields in the non-linear evolution of equatorial spread-F. Journal of Geophysical Research, 99, 2205-2213(1994)
[40] Raghavarao, R., Sekar, R., and Suhasini, R. Non-linear numerical simulation of equatorial spread-F-effects of winds and electric fields. Advances in Space Research, 12, 227-230(1992)
[41] McClure, J. P., Hanson, W. B., and Hoffman, J. H. Plasma bubbles and irregularities in the equatorial ionosphere. Journal of Geophysical Research, 82, 2650-2656(1977)

Sufficient conditions of Rayleigh-Taylor stability and instability in equatorial ionosphere

Sufficient conditions of Rayleigh-Taylor stability and instability in equatorial ionosphere

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