The Ekman spiral for two types of eddy viscosities

Abstract

This paper further investigates the classical problem of the wind in the steady atmospheric Ekman layer. For the case of eddy viscosity being subjected to a quadratic function, we construct an explicit solution, where the used approach is different from Delia [Analytical atmospheric Ekman-type solutions with height-dependent eddy viscosities. J Math Fluid Mech. 2021;23:Article ID 18]. For the case of eddy viscosity being related to two-value piecewise-constant, we give a formula to compute the surface deflection angle by the constructed solution.

Keywords:

• Ekman layer
• variable eddy viscosity
• explicit solution
• deflection angle

2010 Mathematics Subject Classification:

• 34B05

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China [grant number 11661016], Training Object of High Level and Innovative Talents of Guizhou Province [grant number (2016)4006], Guizhou Data Driven Modeling Learning and Optimization Innovation Team [grant number [2020]5016], Discipline and Master's Site Construction Project of Guiyang University by Guiyang City Financial Support Guiyang University [grant number 2021-xk04], the Slovak Research and Development Agency under the contract No. APVV-18-0308, and the Slovak Grant Agency VEGA Nos. 1/0358/20 and 2/0127/20.