New Scaling Parameter For Turbulent BoundaryLayer With Large Roughness

Abstract

Nikuradse uses the equivalent sand-grain roughness to characterize the effect of roughness. While this approach works when the roughness is contained in the inner layer, it does not apply in recent studies with a larger roughness. Various techniques have been applied in the past to scale the mean velocity and the Reynolds stress profiles for a zero pressure gradient boundary layer, the classical scaling using the friction velocity u* to normalize the velocity profiles. However none of these techniques holds universally. This study attempts to improve the understanding that we have of the way roughness affects the inner layer behaviour and aims to find an alternative scaling parameter for cases where roughness is large compared to the inner layer. Measured mean and turbulent velocity profiles on a large regular roughness show a non-zero wall normal pressure is caused which contributes to the velocity deficit in the near wall rough boundary layer velocity profile. The normal turbulent stresses are also increased. Hence a pressure gradient velocity rather than the friction velocity is defined to capture the pressure effects induced by roughness. The power law seems to give a better representation of the velocity profiles than the log law in this case.