Turbulent Friction Velocity Calculated from the Reynolds Stress Tensor

Abstract

AbstractTo eliminate the need to correct for instrument tilt, a process that can be problematic in complex terrain, a new way to calculate the turbulent friction velocity is derived based on invariants of the Reynolds stress tensor. In utilizing Reynolds stress tensor invariants, this new method eliminates the need for tilt correction. The friction velocity is calculated without any reference to the wall normal or other terrain features making this method a candidate for future use with data from complex environments. Since this new method is derived from a different theoretical basis than the well-established methods, it is evaluated using data from flat terrain to compare the new method to the standard calculation method, treated here as a baseline truth. For neutral thermal stratification the values calculated using the new method nearly identically match the control values calculated using the standard method. Although for nonneutral stratification the values calculated using the new method do not closely match the values calculated using the standard method, the new friction velocity produces the same dimensionless shear versus dimensionless height Monin?Obukhov scaling relationship over the full range of stabilities as does the standard friction velocity.