The leading order equivalence of Oseen’s and Imai’s representations

Adamu, Hamid; Chadwick, Edmund

Abstract

Consider the far-field behind a body in a steady, two-dimensional uniform flow field. In the far-field the Oseen linearisation is valid, and in the far-field wake Imai’s asymptotic expansion is applicable. The fundamental solution Green’s function of the Oseen equation which represents a point force is called the Oseenlet. The drag and lift Oseenlets are given in [1], and from this representation we determine the corresponding Oseenlet vorticity and Oseenlet stream function. Imai [2] gives the velocity, vorticity and stream function in the far-field wake behind a body in terms of an asymptotic expansion. We shall show that the first terms in Imai’s expansion are the same as the drag and lift Oseenlets when approximated in the wake. This demonstrates that Imai’s and Oseen’s treatments are the same
to leading order, and from this we infer that the next order terms in Imai’s expansion will correspond to the approximation of the next order terms in Oseen’s linearisation. Future work will be to use Imai’s result to infer the next order terms in the Oseen linearisation.

Citation

Adamu, H., & Chadwick, E. The leading order equivalence of Oseen’s and Imai’s representations. In C. Fresneda-Portillo (Ed.), Proceedings of the 12th UK Conference on Boundary Integral Methods UKBIM12

• Conference Name: 12th UK Conference on Boundary Integral Methods
• Conference Location: Oxford Brooks University
• Start Date: Jul 8, 2019
• End Date: Jul 9, 2019
• Online Publication Date: Jul 1, 2019
• Deposit Date: Jul 3, 2023
• Publicly Available Date: Jul 5, 2023
• Publisher: Oxford Brookes University
• Book Title: Proceedings of the 12th UK Conference on Boundary Integral Methods UKBIM12
• ISBN: 9781999741297
• Publisher URL: https://radar.brookes.ac.uk/radar/items/dd58e98a-6942-456f-98a5-0203f2a159e0/1/