Dynamical eigenfunction decomposition of turbulent channel flow.

*(English)*Zbl 0721.76042Summary: The results of an analysis of low-Reynolds-number turbulent channel flow based on the Karhunen-Loève (K-L) expansion are presented. The turbulent flow field is generated by a direct numerical simulation of the Navier-Stokes equations at a Reynolds number \(Re_{\tau}=80\) (based on the wall shear velocity and channel half-width). The K-L procedure is then applied to determine the eigenvalues and eigenfunctions for this flow. The random coefficients of the K-L expansion are subsequently found by projecting the numerical flow field onto these eigenfunctions. The resulting expansion captures 90 % of the turbulent energy with significantly fewer modes than the original trigonometric expansion. The eigenfunctions, which appear either as rolls or shearing motions, possess viscous boundary layers at the walls and are much richer in harmonics than the original basis functions. Chaotic temporal behaviour is observed in all modes and increases for higher-order eigenfunctions. The structure and dynamical behaviour of the eigenmodes are discussed as well as their use in the representation of the turbulent flow.

##### MSC:

76F20 | Dynamical systems approach to turbulence |

##### Keywords:

Karhunen-Loève expansion; low-Reynolds-number turbulent channel flow; direct numerical simulation; Navier-Stokes equations; eigenvalues; eigenfunctions; trigonometric expansion; Chaotic temporal behaviour
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\textit{K. S. Ball} et al., Int. J. Numer. Methods Fluids 12, No. 6, 585--604 (1991; Zbl 0721.76042)

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