Evaluating the power mean method to determine an equivalent sandgrain roughness parameter over streamwise-heterogeneous roughness

Abstract Weighted and unweighted power mean methods are compared against the accuracy of the simple arithmetic average to estimate an equivalent sandgrain roughness parameter ( $k_{s}$ ) for streamwise-heterogeneous rough surfaces. Specifically, these methods are conceptually and iteratively tested on roughness plates with surface characteristics following beta ( $\beta$ ), uniform or Gaussian distributions. The sandgrain roughness computed using these averaging methods, $k_{s_{eq}}$ , is then compared with true parameters, $k_{s_{eff}}$ , estimated from the fully rough asymptote model and a modified momentum integral method that accounts for the streamwise variation of skin friction over the heterogeneous surface. The weighted power mean offers significant advantages, particularly for roughness in $\beta$ distribution, which is attributed to the distribution bias towards smaller magnitudes of $k_s$ . While the advantage of using the weighted power mean over the unweighted power mean is less significant for the other surface distributions, the weighted method consistently yields the lowest discrepancy in effective drag estimates, independent of roughness configuration, and is therefore the recommended method for estimating the effective sandgrain roughness across heterogeneous surfaces.