Abstract
The role of turbulent large-scale streaks or large-scale motions in forming subaqueous sediment ridges on an initially flat sediment bed is investigated with the aid of particle resolved direct numerical simulations of open channel flow at bulk Reynolds numbers up to 9500. The regular arrangement of quasi-streamwise ridges and troughs at a characteristic spanwise spacing between 1 and 1.5 times the mean fluid height is found to be a consequence of the spanwise organisation of turbulence in large-scale streamwise velocity streaks. Ridges predominantly appear in regions of weaker erosion below large-scale low-speed streaks and vice versa for troughs. The interaction between the dynamics of the large-scale streaks in the bulk flow and the evolution of sediment ridges on the sediment bed is best described as ‘top-down’ process, as the arrangement of the sediment bedforms is seen to adapt to changes in the outer flow with a time delay of several bulk time units. The observed ‘top-down’ interaction between the outer flow and the bed agrees fairly well with the conceptual model on causality in canonical channel flows proposed by Jiménez (J. Fluid Mech., vol. 842, 2018, P1, § 5.6). Mean secondary currents of Prandtl's second kind of comparable intensity and lateral spacing are found over developed sediment ridges and in single-phase smooth-wall channels alike in averages over ${O}(10)$ bulk time units. This indicates that the secondary flow commonly observed together with sediment ridges is the statistical footprint of the regularly organised large-scale streaks.
Highlights
Secondary currents have been studied in flows with non-circular cross-section featuring smooth walls (Nikuradse 1926; Prandtl 1926), where they are generated in the 930 A11-1M
Perhaps even more important is the fact that these observations confirm for the first time that sediment ridges can form due to mechanisms that are completely independent of sidewall-induced secondary currents (Ikeda 1981; Colombini 1993)
We have investigated the role of turbulent large-scale velocity streaks in the formation cycle of sediment ridges in open channels and their connection to mean secondary currents
Summary
Secondary currents have been studied in flows with non-circular cross-section featuring smooth walls (Nikuradse 1926; Prandtl 1926), where they are generated in the 930 A11-1M. Secondary currents have been studied in flows with non-circular cross-section featuring smooth walls (Nikuradse 1926; Prandtl 1926), where they are generated in the 930 A11-1. It was Prandtl who proposed the nowadays standard classification of secondary flows into two categories: secondary flows of Prandtl’s first kind are due to the skewness of the mean flow axis as in meandering rivers or curved pipes, while secondary flows of the second kind are a pure turbulent phenomenon and originate in anisotropy and non-homogeneity of Reynolds stresses across the flow domain (Bradshaw 1987). Our current study focusses on the second family of turbulence-induced secondary currents exclusively and in the remainder of the text, we will always refer to this type when using the term secondary flow
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