In order to interpret the physical feature of Bessho form translating-pulsating source Green function, the phase function is extracted from the integral representation and stationary-phase analysis is carried out in t...In order to interpret the physical feature of Bessho form translating-pulsating source Green function, the phase function is extracted from the integral representation and stationary-phase analysis is carried out in this paper. The complex characteristics of the integral variable and segmentation of the integral intervals are discussed in m complex plane. In θ space, the interval [-π/2+φ,-π/2+φ-iε] is dominant in the near-field flow, and there is a one-to-one correspondence between the real intervals in m space and the unsteady wave patterns in far field. If 4τ>1(τ is the Brard number), there are three kinds of propagation wave patterns such as ring-fan wave pattern, fan wave pattern and inner V wave pattern, and if 0<4τ<1, a ring wave pattern, an outer V and inner V wave pattern are presented in far field. The ring-fan or ring wave pattern corresponds to the interval [-π+α,-π/2+φ] for integral terms about k2, and the fan or outer V wave pattern and inner V wave pattern correspond to [-π+α,-π/2) and(-π/2,-π/2+φ] respectively for terms about k1. Numerical result shows that it is beneficial to decompose the unsteady wave patterns under the condition of τ≠0 by converting the integral variable θ to m. In addition, the constant-phase curve equations are derived when the source is performing only pulsating or translating.展开更多
基金financial support from the National Natural Science Foundation of China under Grant No. 50879090the Key Program of Hydrodynamics of China under Grant No.9140A14030712JB11044
文摘In order to interpret the physical feature of Bessho form translating-pulsating source Green function, the phase function is extracted from the integral representation and stationary-phase analysis is carried out in this paper. The complex characteristics of the integral variable and segmentation of the integral intervals are discussed in m complex plane. In θ space, the interval [-π/2+φ,-π/2+φ-iε] is dominant in the near-field flow, and there is a one-to-one correspondence between the real intervals in m space and the unsteady wave patterns in far field. If 4τ>1(τ is the Brard number), there are three kinds of propagation wave patterns such as ring-fan wave pattern, fan wave pattern and inner V wave pattern, and if 0<4τ<1, a ring wave pattern, an outer V and inner V wave pattern are presented in far field. The ring-fan or ring wave pattern corresponds to the interval [-π+α,-π/2+φ] for integral terms about k2, and the fan or outer V wave pattern and inner V wave pattern correspond to [-π+α,-π/2) and(-π/2,-π/2+φ] respectively for terms about k1. Numerical result shows that it is beneficial to decompose the unsteady wave patterns under the condition of τ≠0 by converting the integral variable θ to m. In addition, the constant-phase curve equations are derived when the source is performing only pulsating or translating.
