Asymptotic Expansion of the Transient Capillary-Viscosity Green Function

摘要

The asymptotic expansion of the transient capillary-viscosity greenrnfunction at large distance r and large time t is considered in this paper.rnDifficulties arise when r / t approaches the minimum speed ofrncapillary-gravity waves ν_0.A cubic transform of the variable ofrnintegration is used to overcome the problem and uniformly validrnasymptotic approximations in terms of the Airy functions and itsrnderivatives are presented which span three separate domains for r / trngreater than, near , and less than ν_0. Calculations are performed tornillustrate the utility of the asymptotic results.