| 1. |
|
|
| 2. |
- Morra, Pierluigi, et al.
(författare)
-
The colour of forcing statistics in resolvent analyses of turbulent channel flows
- 2020
-
Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 907
-
Tidskriftsartikel (refereegranskat)abstract
- In resolvent analyses of turbulent channel flows it has been common practice to neglect or model the nonlinear forcing term that forms the input of the resolvent. However, the spatiotemporal structure of this term is mostly unknown. Here, this nonlinear forcing term is quantified. The Fourier transform of its two-point space-time correlation, its cross-spectral density (CSD), is computed. The CSD is evaluated for two channel flows at friction Reynolds numbers Re-tau = 179 and Re-tau = 543 via direct numerical simulations (DNS). The CSDs are computed for energetic structures typical of buffer-layer and large-scale motions, for different temporal frequencies. It is found that the forcing is structured and that its solenoidal part, which is the only one affecting the velocity field, is the combination of an oblique streamwise vortical forcing and a streamwise component that counteract each other, as in a destructive interference. It is shown that a rank-2 approximation of the forcing, with only the most energetic spectral proper orthogonal decomposition (SPOD) modes, leads to the bulk of the response. Moreover, it is found that the nonlinear forcing term has a non-negligible projection onto the linear sub-optimal forcings of resolvent analysis, which demonstrates that the linear optimal forcing is not representative of the nonlinear forcing. Finally, it is clarified that the Cess eddy-viscosity-modelled forcing improves the accuracy of resolvent analysis prediction because the modelled forcing projects onto the linear sub-optimal forcings similarly to DNS data.
|
|
| 3. |
- Nogueira, Petronio A. S., et al.
(författare)
-
Forcing statistics in resolvent analysis : application in minimal turbulent Couette flow
- 2021
-
Ingår i: Journal of Fluid Mechanics. - : Cambridge University Press (CUP). - 0022-1120 .- 1469-7645. ; 908
-
Tidskriftsartikel (refereegranskat)abstract
- An analysis of the statistics of the nonlinear terms in resolvent analysis is performed in this work for turbulent Couette flow at Reynolds number 400. Data from a direct numerical simulation of a minimal flow unit is used to compute the covariance matrix of the velocity. From the same data, we computed the nonlinear terms of the Navier-Stokes equations (treated as forcing), which allowed us to compute the covariance matrix of the forcing. The quantitative relation between the two covariances via the resolvent operator is confirmed here for the first time, accounting for relevant signal processing issues related to the windowing procedure for frequency-domain quantities. Such exact correspondence allowed the eduction of the most relevant force components for the dominant structures in this flow, which participate in the self-sustaining cycle of turbulence: (i) streamwise vortices and streaks, and (ii) spanwise-coherent fluctuations of spanwise velocity. The results show a dominance by a subset of the nonlinear terms for the prediction of the full statistics of streamwise vortices and streaks; a single term is seen to be dominant for spanwise motions. A relevant feature observed in these cases is that the forcing covariance is dominated by its first eigenfunction, showing that nonlinear terms also have a coherent structure at low frequencies in this flow. Different forcing components are also coherent between them, which leads to constructive and destructive interferences that greatly modify the flow response. These are key features of forcing 'colour' for the present flow.
|
|
| 4. |
|
|
