과제정보
The authors are thankful to reviewer for valuable suggestion to improve the manuscript.
참고문헌
- H.S. Dou, V. Ganesh, Short wave stability of homogeneous shear flows with varstile topography, Appl. Math. Mech. 35 (2014), 541-548. https://doi.org/10.1007/s10483-014-1811-7
- P.G. Drazin, W.H. Reid, Hydrodynamic stability, Stud. Appl. Math., Cambridge, 1981.
- L. Engevik, A Note on barotropic instability of the Bickley jet, J. Fluid Mech. 499 (2004), 315-326. https://doi.org/10.1017/S0022112003007110
- J.R. Gupta, R.G. Shandil, S.D. Rana, On the limitations of the complex wave velocity in the instability problem of heterogeneous shear flows, J. Math. Anal. Appl. 144 (1989), 367-376. https://doi.org/10.1016/0022-247X(89)90341-7
- F.J. Hickernell, An upper bound on the growth rate of a linear instability in a homogeneous shear flow, Studies in App. Math. 72 (1985), 87-93. https://doi.org/10.1002/sapm198572187
- L.N. Howard, Note on a paper of John. W. Miles, J. Fluid Mech. 10 (1961), 509.
- G.T. Kochar, and R.K. Jain, Note on Howard's semicircle, J. Fluid Mech. 91 (1979), 489-491. https://doi.org/10.1017/S0022112079000276
- H.L. Kuo, Dynamic instability of two dimension non divergent flow in a barotropic atmosphere, J. Meteorol. 6 (1949), 105.
- S. Lavanya, V. Ganesh, and G. Venkata Ramana Reddy, On the parabolic instability region for the Kuo problem, Advances in Mathematical Modelling, Applied Analysis and Computation 415 (2023), 311-317.
- S. Lavanya, V. Ganesh, and G. Venkata Ramana Reddy, Bounds on the growth rate for the Kuo problem, J. App. Math. and Informatics 41 (2023), 363-372.
- R.D. Lindzen, Planetary waves on Beta planes, Monthly Weather Review 95 (1967), 441-451. https://doi.org/10.1175/1520-0493(1967)095<0441:PWOBP>2.3.CO;2
- J.H. Miles, On the stability of heterogeneous shear flow, J. Fluid Mech. 10 (1961), 496.
- M. Padmini, M. Subbiah, Note on Kuo's problem, J. Math. Anal. Appl. 173 (1993), 659-665. https://doi.org/10.1006/jmaa.1993.1097
- J. Pedlosky, Geophysical Fluid Dynamics, Springer-Verlog, New York, Berlin, 1979.
- K. Reena Priya, V. Ganesh, Note on the Long wave stability of shear flows with variable bottom topography, International Journal of Mathematical Analysis 10 (2016), 757-766. https://doi.org/10.12988/ijma.2016.6349
- K. Reena Priya, V. Ganesh, On the criterion for long wave stability of shear flows, Int. J. Appl. Comput. Math. 4 (2018), 1-18. https://doi.org/10.1007/s40819-017-0445-y
- P.J. Schmid, and D.S. Henningson, Stability and Transition in shear flow, Springer, 2000.
- P.G. Shandil, Jagjit Singh, On linear instability of inviscid parallel shear flows in the β-plane, Ganita 54 (2004), 64.
- S. Sri Devi, H.S. Dou, V. Ganesh, A Unified instability region for the extended Taylor Goldstein problem of hydrodynamic stability, Adv. Appl. Math. Mech. 9 (2017), 1404-1419. https://doi.org/10.4208/aamm.OA-2016-0022
- M. Subbiah, and R.K. Jain, On the Taylor Goldstein Problem in hydrodynamic stability, Indian J. Pure Appl. Math. 18 (1987), 1016-1022.
- M. Subbiah, V. Ganesh, Bounds on the Phase speed and growth rate of the extended Taylor Goldstein Problem, Fluid Dynamics Research 40 (2008), 364-377. https://doi.org/10.1016/j.fluiddyn.2007.11.001
- R. Thenmozhy, N. Vijayan, On the linear stability of shear flows in the plane, International Journal of Mathematics Trends and Technology 66 (2020), 10-16.
- C.S. Yih, Stratified Flow, Academic Press, 1981.