Direct numerical simulations of the interaction of temporally evolving circular jets

Direct numerical simulations are performed to study turbulence generated by the interaction of multiple temporally evolving circular jets with jet Mach numbers $M_J=0.6$ and $1.6$ , and a jet Reynolds number of 3000. The jet interaction produces decaying, nearly homogeneous isotropic turbulence, where the root-mean-squared (r.m.s.) fluctuation ratio between the streamwise and transverse velocities is approximately 1.1, consistent with values observed in grid turbulence. In the supersonic case, shock waves are generated and propagate for a long time, even after the turbulent Mach number decreases. A comparison between the two Mach number cases reveals compressibility effects, such as reductions in the velocity derivative skewness magnitude and the non-dimensional energy dissipation rate. For the r.m.s. velocity fluctuations, $u_{rms}$ , and the integral scale of the streamwise velocity, $L_u$ , the Batchelor turbulence invariant, $u_{rms}^2 L_u^5$ , becomes nearly constant after the turbulence has decayed for a certain time. In contrast, the Saffman turbulence invariant, $u_{rms}^2 L_u^3$ , continuously decreases. Furthermore, temporal variations of $u_{rms}^2$ and $L_u$ follow power laws, with exponents closely matching the theoretical values for Batchelor turbulence. The three-dimensional energy spectrum $E(k)$ , where $k$ is the wavenumber, exhibits $E(k) \sim k^4$ for small wavenumbers. This behaviour is consistently observed for both Mach number cases, indicating that the modulation of small-scale turbulence by compressibility effects does not affect the decay characteristics of large scales. These results demonstrate that jet interaction generates Batchelor turbulence, providing a new direction for experimental investigations into Batchelor turbulence using jet arrays.