Abstract
An outgrowth of studies of instability of the Ekman boundary layer has been consideration of the stability of a linear variation of wind with height (a constant thermal wind). A closely related linear shear flow was solved with several approximate conditions by D. K. Lilly as an approximation to the “parallel flow” of the Ekman boundary layer. Lilly’s results are confirmed and extended to the case of a constant thermal wind shear in the free atmosphere. The mechanism of energy transfer from the mean shear flow to roll vortices with their axes parallel to the shear is interesting and appears to be a new type of instability.
This instability is studied by direct numerical integration of the equations of motion. The unstable cells have their axes parallel to the thermal wind and even in neutral stratification the cells have a significant tilt. Computations at Ri = 0.1 continue to show instability, but with increased tilt of the convective cells.
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References
Faller, A. J. (1963). An experimental study of the instability of the laminar Ekman boundary layer. J. Fluid Mech., 15, 560–576.
Faller, A. J. and Kaylor, R. (1965). Investigations of stability and transition in rotating boundary layers. Tech. Note BN-427, Inst. Fluid Dyn. and Appl. Math., U. of Md., and The Dynamics of Fluids and Plasma, S. I. Pai, Editor (Academic Press, New York, 1966 ).
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Faller, A.J., Kaylor, R. (1969). Instability of the Thermal Wind. In: Pao, YH., Goldburg, A. (eds) Clear Air Turbulence and Its Detection. Springer, Boston, MA. https://doi.org/10.1007/978-1-4899-5615-6_5
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DOI: https://doi.org/10.1007/978-1-4899-5615-6_5
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