Waves and spatially localized structures in turbulent viscous fluid flows. Numerical results

V. G. Priymak

Matematičeskoe modelirovanie, Tome 22 (2010) no. 2, pp. 3-28

Résumé

Direct Navier–Stokes simulation of fully turbulent and intermittent viscous incompressible fluid flows in an infinite circular pipe is performed. Calculations were carried out at Reynolds numbers $1800\le\mathrm{Re}\le4000$, based on the mean velocity and pipe diameter $D=2R$. Numerical Navier–Stokes solutions obtained belong to the class of streamwise periodic solutions with large periods $\lambda_\mathrm{max}=16\pi R$. It is demonstrated that the most energetic Fourier components of velocity fluctuations correspond to very low nonzero longitudinal wavenumbers. The structure of turbulent and inter-mittent flows as well as associated wave-like motions are investigated. The possibility and accu-racy of the velocity field approximation by the superposition of travelling and standing waves is analysed. It is shown that the parameters of such representation (wave amplitudes, phase veloci-ties, the position of wave front) are strongly dependent on the inclusion of low longitudinal wavenumbers in the Navier–Stokes simulation. Numerical solutions at $\mathrm{Re}=2200,2350$ describe equilibrium self-sustained flow regimes in which turbulent structures (turbulent puffs) sur-rounded by almost laminar flow propagate downstream while preserving their length. Space-time structure of turbulent puffs is compared with the existing experimental data. Propagation velocity of turbulent puffs and turbulence statistics inside and outside the puff are calculated.