On the Taylor hypothesis corrections for measured energy spectra of turbulence

The acceleration terms of the Navier-Stokes equations are taken into account to obtain the corrections for the measured longitudinal spectrum of homogeneous isotropic turbulence. The viscous term correction gives approximately uniform relative deviation of the sign such as the Lumely correction for intertial subrange with no influence on the slope of the spectrum but can be significantly increased for scales less than the Kolmogorov one. The deviations for small wave numbers are also estimated. In addition, the different forms of the corrections in the case of advection velocity fluctuations are discussed and some simple one-dimensional models are presented.