Markov properties of velocity increments in turbulent channel flow

It has been established that statistics of turbulent velocity increments can be modelled using Markov processes if the increments are measured over separations greater than the Taylor microscale, and that the PDFs of such increments can be described by a Fokker-Planck equation if the higher-order terms of the Kramers-Moyal (K-M) expansion are small (Renner, Peinke & Friedrich, J. Fluid Mech., 2001). The present work builds on that of Tutkun (Physica D, 2017), who demonstrated that the minimum separation at which a turbulent boundary layer exhibits Markovian properties depends on the wall-normal distance. However, the magnitude of the higher-order terms of the K-M expansion and the ensuing applicability of a Fokker-Planck equation to the modelling of velocity increments in wall-bounded turbulence has yet to be investigated. To this end, the present work examines the dependence of statistics of velocity increments on their wall-normal position by way of hot-wire measurements in a turbulent channel flow. It is i) confirmed that the degree to which the turbulent channel flow can be accurately modelled as Markovian also depends on the distance from the wall, and ii) demonstrated that the higher-order terms become increasingly important as the wall is approached.