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In this paper, we introduce a new way to estimate the scaling parameter of aself-similar process by considering the maximum probability density function(pdf) of tis increments. We prove this for $H$-self-similar processes ingeneral and experimentally investigate it for turbulent velocity andtemperature increments. We consider turbulent velocity database from anexperimental homogeneous and nearly isotropic turbulent channel flow, andtemperature data set obtained near the sidewall of a Rayleigh-B\'{e}nardconvection cell, where the turbulent flow is driven by buoyancy. For the formerdatabase, it is found that the maximum value of increment pdf $p_{\max}(\tau)$is in a good agreement with lognormal distribution. We also obtain a scalingexponent $\alpha\simeq 0.37$, which is consistent with the scaling exponent forthe first-order structure function reported in other studies. For the latterone, we obtain a scaling exponent $\alpha_{\theta}\simeq0.33$. This index valueis consistent with the Kolmogorov-Obukhov-Corrsin scaling for passive scalarturbulence, but different from the scaling exponent of the first-orderstructure function that is found to be $\zeta_{\theta}(1)\simeq 0.19$, which isin favor of Bolgiano-Obukhov scaling. A possible explanation for these resultsis also given.

Scaling of maximum probability density functions of velocity and temperature increments in turbulent systems