The temporal instability of a two-dimensional perturbed wave in a coupled air-water shear flow is considered to study the generation and initial growth of wavelets by the air flow. A robust numerical method is developed to solve the coupled Orr-Sommerfeld equations and the interfacial conditions governing the linear viscous instability of the perturbed flow. Calculations of the growth rates and phase speeds of the unstable wavelets compare well with the early theoretical as well as numerical predictions, and also reveal that the discrepancy in the numerical results of Wheless and Csanady (1993) indeed are due to erroneous calculations. Dependence of the instability on the flow parameters is then studied systematically. Contrary to the previous findings, there is no apparent correlation between the maximum growth rate and the minimum phase velocity wavenumber.
Tsai, Wu-Ting and Lin, Mei-Ying
"Stability Analysis on the Initial Surface-Wave Generation with an Air-Sea Coupled Shear Flow,"
Journal of Marine Science and Technology: Vol. 12:
3, Article 9.
Available at: https://jmstt.ntou.edu.tw/journal/vol12/iss3/9