Nonlinear interactions in strained axisymmetric high-Reynolds-number turbulence

Abstract

We present measurements, over a wide range of Reynolds numbers ($40\leq R_{\lambda} \leq 470$), of grid-generated turbulence subjected to axisymmetric strain, and of the subsequent evolution of the turbulence after the strain is released. The Reynolds number was varied by the use of both passive and active grids and the strain was produced by a 4:1 area-change axisymmetric contraction placed at various distances from the grid. The time scale ratio of the turbulence to that of the mean strain varied from approximately 10 to 30. The results show reasonable agreement with (linear) rapid distortion theory (RDT) for the velocity variances but, contrary to linear theory, the strained longitudinal, $u_{1}$, spectrum peaked at significantly higher wavenumber than the transverse, $u_{2}$, spectrum. The mismatch in peaks increased with increasing $R_{\lambda}$ and at the highest Reynolds number ($R_{\lambda} = 470$) the peak of the strained $u_{1}$-spectrum occurred at a wavenumber 200 times greater than that of the $u_{2}$-spectrum. As the flow relaxed toward isotropy after the contraction, further evidence of the non-locality in the flow field became apparent, with a second peak in the $u_{2}$-spectrum emerging at a similar wavenumber to the high-frequency peak in the $u_{1}$-spectrum. The strain also caused the longitudinal derivative skewness to change sign but as the flow evolved after the contraction the derivative skewness returned to its typical value of ${-}$0.4. We also show that single-point turbulence models are inadequate to describe the relaxation of the turbulence towards an isotropic state in the postcontraction region.

Effect of the shear parameter on velocity-gradient statistics in homogeneous turbulent shear flow

“…The results were supported by numerical experiments (Yeung, Brasseur & Wang 1995). Ayyalasomayajula & Warhaft (2006) also suggest a direct interaction of the large scales upon the small scales to explain results obtained in their irrotational axisymmetric strain experiment.…”

Inertial particle acceleration in strained turbulence

“…The sign change indicates a change in the small scale structure of turbulence, namely that vortex structures dominate sheet-like structures resulting in an inhibition of the energy cascade (Ayyalasomayajula & Warhaft (2006)). The right hand side of Figure 5 shows the longitudinal kurtosis, a measure of the flow intermittency.…”

Lagrangian acceleration timescales in anisotropic turbulence

“…The application of steady strain in a wind-tunnel flow by means of an axisymmetric converging duct in order to attenuate longitudinal velocity fluctuations [2] was originally theorized by Prandtl as the spanwise contraction of cylindrical vortices which diminish streamwise velocity fluctuations by conservation of angular momentum. From subsequent theoretical analyses [3,4] as well as experimental and direct numerical simulations (DNSs) the role of strain may be summarized by two essential points [5][6][7][8][9][10][11]. First, the large energy-containing scales experience an amplification of velocity fluctuations in the contracting direction and an attenuation in the elongating direction.…”