On the scaling of large-scale structures in smooth-bed turbulent open-channel flows

Abstract

This paper investigates the existence and scaling of the so-called large-scale and very-large-scale motions (LSMs and VLSMs) in non-uniform turbulent open-channel flows developing over a smooth bed in a laboratory flume. A laser Doppler anemometry system was employed to measure vertical profiles of longitudinal and bed-normal velocity statistics over a wide range of hydraulic conditions. Pre-multiplied spectra of the longitudinal velocity fluctuations revealed the existence of two peaks occurring at wavelengths consistent with those associated with LSMs and VLSMs as detected in the past literature pertaining to wall turbulence. However, contrary to so-called canonical wall flows (i.e. flat-plate boundary layers, pipe and closed-channel flows), the LSM and VLSM peaks observed in the open-channel flows investigated herein are detectable over a much larger extent of the wall-normal coordinate. Furthermore, the VLSM peak appears at von Karman numbers $Re_{\unicode[STIX]{x1D70F}}$ as low as 725, whereas in other wall flows much higher values are normally required. Finally, as conjectured by a recent study on uniform rough-bed open-channel flows, the present paper confirms that LSM wavelengths scale nicely with the flow depth, whereas the channel aspect ratio (i.e. the ratio between channel width and flow depth) is the non-dimensional parameter controlling the scaling of VLSM wavelengths. The intensity and wavelengths of the VLSM peaks were also observed to depend on the spanwise coordinate. This result suggests that VLSMs might be dynamically linked to secondary currents, as these are also known to vary in strength and size across the channel width.