At high collision energy, turbulence has been seen at relativistic heavy-ion collisions. We examine the turbulence characteristics in this system and found that the initial and pre-equilibrium phases of the collision show considerable departures from isotropic turbulence. Since the anisotropic fluctuations are subleading to the isotropic fluctuations, the Kolmogorov spectrum can be obtained even during the initial phases. However, departures from isotropic turbulence are indicated by the energy spectrum and temperature fluctuations. We analyse the energy density spectrum in the transverse and longitudinal planes by dividing the sphere into multiple planes since there is a significant momentum anisotropy between the two planes. We observe that the scaling exponent of the spectra is different in the two planes. This shows that the geometrical anisotropy is reflected in the anisotropic turbulence produced in the rotating plasma. The temperature spectrum is also obtained in the pre-equilibrium stage. The spectrum is different from what would be expected for isotropic turbulence. All of them seem to suggest that, for relativistic heavy-ion collisions, the large-scale momentum anisotropy exists in the smaller length scales.