Turbulent Friction in Canonical Flows: State of the Science and Future Outlook

Quantifying turbulent friction holds significant importance, not only for understanding the fundamental flow physics but also for enriching system performance across a wide range of engineering applications. This vision article presents the state of the science of the turbulent friction in canonical flows, shedding light on its current status through a combination of theoretical developments and experimental observations. First, the article discusses the law of the wall, including the scaling behavior, the possible origin of the logarithmic law, and the effects of wall roughness. Then, it provides an overview of roughness height and its connection with the wall topography. The scaling behaviors of the logarithmic and power laws of turbulent friction are thoroughly appraised, offering insights into their implications. Additionally, the phenomenological models of turbulent friction based on the spectral and co-spectral budget theories are furnished. The behavior of turbulent friction for extremely large Reynolds number flows is examined, based on theoretical models and experimental data. The semiempirical finite Reynolds number model for turbulent friction is reviewed, emphasizing the pertinent scaling laws in various forms. The scaling laws of turbulent friction in curved-pipe and axisymmetric boundary layer flows are discussed. Finally, future research directions are outlined, highlighting the key challenges to be addressed.