Inverse energy cascade in a turbulent round jet

Large eddy simulation of turbulent free round jet has been performed to study statistical properties of turbulence, including third-order structure functions. It has been shown the presence of a zone within the jet initial region where the spectral flux of turbulent energy is directed from smaller scales toward larger ones and the longitudinal third-order structure function becomes positive. Energy spectra calculated in this zone demonstrate the $E\left(k\right)\sim k^{-3}$ law specific for two-dimensional turbulence.

Figure 1

Distributions of dimensionless structure function $D_{LLL}/\left(\ell U_{\text{jet}}^3/D_{\text{jet}}\right)$ obtained in experiment [11, 12, 20] (left) and in LES (right) in longitudinal section of the jet (only positive values shown).

Figure 2

LES fields of dimensionless structure function $D_{LLL}^{\ast }\equiv D_{LLL}/\left(\ell U_{\text{jet}}^3/D_{\text{jet}}\right)$ (shaded contours, only positive values shown) and the turbulent kinetic energy (isocurves).

Figure 3

Typical vortex structure of the jet visualized with ${\lambda }_2$ criterion (shaded pixels indicate ${\lambda }_2<0$).

Figure 4

Radial profiles of dimensionless structure function $D_{LLL}^{\ast }$ (solid lines) and flatness $K_L$ (dashed lines) at several cross-sections of the jet.

Figure 5

Radial profiles of dimensionless turbulent energy fluxes $-{\Pi }^{\ast }\left(k_1\right)$ (curve 1), $-{\Pi }^{\ast }\left(k_2\right)$ (curve 2), and dimensionless structure function $D_{LLL}^{\ast }$ (curve 3), at the jet sections: (a) $x/D_{\text{jet}}=2.6$; (b) $x/D_{\text{jet}}=9.1$

Figure 6

Power spectra of turbulent energy at several points across the jet, in sections (a) $x/D_{\text{jet}}=2.5$, (b) 3.0, (c) 5.0, and (d) 8.0.