Relevance of two- and three-dimensional disturbance field explained with linear stability analysis of Orr-Sommerfeld equation by compound matrix method. (15th July 2021)

• Record Type: Journal Article
• Authors: Maddipati, Raj; Sengupta, Tapan K.; Sundaram, Prasannabalaji
• Is Part Of: Computers & fluids. Volume 225(2021)
• Publication Date: 2021-07-15
• Subjects: Neutral curves -- Orr-Sommerfeld equation -- Spanwise wall excitation -- Spatio-temporal analysis; 00-01 -- 99-00; Fluid dynamics -- Data processing -- Periodicals; 532.050285
• DOI: 10.1016/j.compfluid.2021.104965
• Languages: English
• ISSNs: 0045-7930

Abstract

Abstract: Three-dimensional Orr-Sommerfeld equation is analyzed by compound-matrix method to explain the relevance of two- and three-dimensional wall excitations with respect to three-dimensional direct simulation results presented in Sharma and Sengupta, Effect of frequency and wavenumber on the three-dimensional routes of transition by wall excitation, Phys. Fluids, 31 (6), 064107 (2019). Physical variables are considered in a finite spanwise domain which allows us to consider spanwise wavenumber β as the higher harmonics of fundamental spanwise mode β 0 defined by the spanwise domain. Linear stability analysis is performed for various cases with different spanwise wavenumber and neutral curves are generated in both spatial and temporal frameworks. Even though the neutral curves appear different, the critical Reynolds number remains same for all spanwise excitation wavenumbers. The significance of neutral curve in either spatial, or temporal or spatio-temporal frameworks is explained for both modal and non-modal component of the response field. It is shown that as spanwise wavenumber of input excitation increases, the critical Reynolds number increases, while the spatial amplification rate α i decreases. Thus, this establishes that increasing three-dimensionality of input excitation will shown enhanced stability of the flow, and helps one to understand the three-dimensional direct simulation of receptivity analysis for wall excitation reported very recently.