Abstract
In this paper, we are concerned with determining the explicit solution of a Sea-Breeze flow model by selecting a special viscosity function. Firstly, we examine the exact solution when the viscosity function is related to a nonnegative constant coefficient. Further, by employing suitable transformations and forcing terms, we transform the original second order differential equation corresponding to the Sea-Breeze flow model into the Bessel equation and derive the corresponding exact solution. Finally, we determine the exact solution when the viscosity function is related to a nonnegative quadratic function.
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Goler, R.A., Reeder, M.J.: The generation of the Morning Glory. J. Atmos. Sci. 61, 1360–1376 (2004)
Clarke, R.H., Smith, R.K., Reid, D.G.: The Morning Glory of the Gulf of Carpentaria: an atmospheric undular bore. Mon. Wea. Rev. 109, 1726–1750 (1981)
Goler, R.A.: Eastward-propagating undular bores over Cape York Peninsula. Mon. Wea. Rev. 137, 2632–2645 (2009)
Constantin, A., Johnson, R.S.: Atmospheric undular bores. Math. Ann. pp. 1–26 (2023)
Christie, D.R.: Long nonlinear waves in the lower atmosphere. J. Atmos. Sci. 46, 1462–1491 (1989)
Forbes, L.K., Belward, S.R.: Atmospheric solitary waves: some applications to the Morning Glory of the Gulf of Carpentaria. J. Fluid Mech. 321, 137–155 (1996)
Porter, A., Smyth, N.F.: Modelling the morning glory of the Gulf of Carpentaria. J. Fluid Mech. 454, 1–20 (2002)
Constantin, A., Johnson, R.S.: On the propagation of nonlinear waves in the atmosphere. Proc. R. Soc. A. 478, 20210895 (2022)
Marynets, K.: Sturm-Liouville boundary value problem for a Sea-Breeze flow. J. Math. Fluid Mech. 6, 25 (2023)
Zill, D.G.: Differential Equations with Boundary-Value Problems. Cengage Learning (2016)
Zaitsev, V.F., Polyanin, A.D.: Handbook of Exact Solutions of Ordinary Differential Equations. CRC Press, Boca Raton (2002)
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The authors are grateful to the referees for their careful reading of the manuscript and valuable comments. The authors thank the help from the editor too.
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Communicated by Adrian Constantin.
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This work is partially supported by the National Natural Science Foundation of China (12371163) and Guizhou Provincial Basic Research Program (Natural Science) [2023]034.
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Li, Z., Wang, J. Explicit solution for a Sea-Breeze flow model with special viscosity functions. Monatsh Math (2024). https://doi.org/10.1007/s00605-024-01975-x
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DOI: https://doi.org/10.1007/s00605-024-01975-x