Reply by the Authors to P. J. Sherman

What is it about?

This note tries to bridge the gap between turbulence shaping filters associated with two forms of power spectral densities and clarify the use of them for simulation. The single-sided power spectral densities in power per rad/s are demonstrated as correct for real-world turbulence, and the associated shaping filters have been widely used for engineering simulation. However, the correct shaping filters are those derived from the two-sided power spectral densities in power per Hz to be mathematically consistent with the Laplace transform, and only they are applicable to researches involving s-domain analysis. It is demonstrated that both two forms of shaping filters produce desired turbulence samples as long as the variances of white noise inputs are correctly defined according to the spectrum functions forming the shaping filters. Finally, as a guide to the use of the shaping filters, it is shown that a long simulation time is desired to obtain turbulence samples with accurate statistical properties. The power loss due to simulation results in the bias of the turbulence sample root mean square which along with the mean error of simulation contributes to the bias of the standard deviation.

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