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A reason has been given for the inverse energy cascade in thetwo-dimensionalised rapidly rotating 3D incompressible turbulence. For suchsystem, literature shows a possibility of the exponent of wavenumber in theenergy spectrum's relation to lie between -2 and -3. We argue the existence ofa more strict range of -2 to -7/3 for the exponent in the case of rapidlyrotating turbulence which is in accordance with the recent experiments. Also, arigorous derivation for the two point third order structure function has beenprovided helping one to argue that even with slow rotation one gets, thoughdominated, a spectrum with the exponent -2.87, thereby hinting at theinitiation of the two-dimensionalisation effect with rotation.Comment: An extended and typos-corrected version of the earlier submissio

Signatures of two-dimensionalisation of 3D turbulence in the presence of rotation