Corrections for underresolved scalar measurements in turbulent flows using a DNS database

We estimate the effect of finite spatial resolution of a probe for scalar measurements, using a database from direct numerical simulations (DNS). These are for homogeneous isotropic turbulence in temporal decay, Schmidt number unity, and low Taylor-microscale Reynolds number (27-42). The probe could be a cold wire for measuring temperature in a turbulent flow. Correction factors for the scalar variance, scalar dissipation rate, and mixed velocity-scalar derivative skewness are estimated, for a sensor length up to 15 times the Batchelor length scale. It is shown that the lack of resolution yields the largest attenuation on the dissipation rate, followed by the scalar variance. On the contrary, the mixed skewness, which is affected the least, is overestimated. Further, it is shown that if one estimates the mixed skewness via the scalar variance dynamical equation and neglects the term involving the time derivative of the scalar energy spectrum, large errors in the correction factor of the mixed skewness are introduced. Finally, it is found that correction factors obtained assuming Kraichnan scalar model spectrum and following Wyngaard (in Phys Fluids 14:2052-2054, 1971) approach are close to those from the DNS.