Abstract
The problem of finding optimal perturbations, which are perturbations with a maximum ratio of the final energy to the initial energy, is considered in the Eady model of baroclinic instability. The solution to the problem uses explicit expressions for the energy functional, which are functions of parameters of an initial perturbation. For perturbations with zero potential vorticity, the basic parameters are the amplitudes of the initial buoyancy distributions at the boundaries of the atmospheric layer and a phase shift between these distributions. Dependences of the optimal phase shift and maximum energy ratio on the wave number and time optimization are determined using an analysis for extremum. The parameters of the optimal perturbations are compared with those of the growing normal modes. It is found that only one exponentially growing mode is an optimal perturbation.
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References
E. T. Eady, “Long waves and cyclone waves,” Tellus 1 (3), 35–52 (1949).
J. Pedlosky, Geophysical Fluid Dynamics (Springer, Berlin–New York, 1987).
B. F. Farrell, “Optimal excitation of baroclinic waves,” J. Atmos. Sci. 46, 1193–1206 (1989).
B. F. Farrell and P. J. Ioannou, “Generalized stability theory. Part 1: Autonomous operators’,” J. Atmos. Sci. 53, 2025–2040 (1996).
H. Mukougawa and T. Ikeda, “Optimal excitation of baroclinic waves in the Eady model,” J. Meteorol. Soc. Jpn. 72, 499–513 (1994).
M. C. Morgan, “A potential vorticity and wave activity diagnosis of optimal perturbation evolution,” J. Atmos. Sci. 58, 2518–2544 (2001).
M. C. Morgan and C. C. Chen, “Diagnosis of optimal perturbation evolution in the Eady model,” J. Atmos. Sci. 59, 169–185 (2002).
H. Vries and J. D. Opsteegh, “Resonance in optimal perturbation evolution. Part 1: The two-layer Eady model,” J. Atmos. Sci. 64, 673–694 (2007).
H. Vries and J. D. Opsteegh, “Resonance in optimal perturbation evolution. Part 2: Effects of non-zero PV gradient,” J. Atmos. Sci. 64, 695–710 (2007).
H. C. Davies and C. H. Bishop, “Eady edge waves and rapid development,” J. Atmos. Sci. 51, 1930–1946 (1994).
E. Heifetz, C. H. Bishop, B. J. Hoskins, and J. Methven, “The counter -propagating Rossby wave respective on baroclinic instability. Part 1: Mathematical basis,” Q. J. R. Meteorol. Soc. 130, 211–231 (2004).
E. Heifetz, C. H. Bishop, B. J. Hoskins, and J. Methven, “The counter -propagating Rossby wave respective on baroclinic instability. Part 2: Application to the Charney model,” Q. J. R. Meteorol. Soc. 130, 233–258 (2004).
Kalashnik M. V. “Resonant and quasi-resonant excitation of baroclinic waves in the Eady model,” Izv., Atmos. Ocean. Phys. 51 (6), 576–584 (2015).
C. D. Thorncroft and B. J. Hoskins, “Frontal cyclogenesis,” J. Atmos. Sci. 47, 2317–2336 (1990).
J. Jencner and M. Ehrendorfer, “Resonant continuum modes in the Eady model with rigid lids,” J. Atmos. Sci. 63, 765–773 (2005).
M. G. Akperov and I. I. Mokhov, “A comparative analysis of the method of extratropical cyclone identification,” Izv., Atmos. Ocean. Phys. 46 (5), 574–590 (2010).
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Original Russian Text © M.V. Kalashnik, O.G. Chkhetiani, 2018, published in Izvestiya Rossiiskoi Akademii Nauk, Fizika Atmosfery i Okeana, 2018, Vol. 54, No. 5, pp. 487–496.
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Kalashnik, M.V., Chkhetiani, O.G. Optimal Perturbations with Zero Potential Vorticity in the Eady Model. Izv. Atmos. Ocean. Phys. 54, 415–422 (2018). https://doi.org/10.1134/S0001433818050055
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DOI: https://doi.org/10.1134/S0001433818050055