Wall-attached structures over a traveling wavy boundary: Scalar transport

Abstract

The wall-attached structures of scalar fluctuations over a traveling wavy boundary are investigated using large eddy simulations (LESs) at a moderate Reynolds number (Reτ≈1000) and various Prandtl numbers (Pr=0.2, 0.7, 1, and 2). The wave slope is ak=0.1, where a is the wave amplitude and k is the wavenumber. The prescribed wave age is c/u*=2, where c is the wave phase speed and u* is the friction velocity. For comparison, the results of an LES over a smooth wall are also discussed. The results provide evidence for the presence of self-similar wall-attached structures of scalar fluctuations in both turbulent flow over a traveling wavy boundary and that over a smooth wall. In particular, the population density of the attached structures exhibits an inverse power-law distribution, reminiscent of a hierarchy of attached structures. The conditionally averaged scalar variance reconstructed from the superposition of attached structures has a near-wall peak and a logarithmic variation in the log region. The magnitude of this peak varies logarithmically with the hierarchical length scale, and the variation slope decreases with increase in the Prandtl number. In addition, the correlations between the attached structures and vertical scalar transport are examined by direct observation of instantaneous snapshots. The ejection event of the fluid leads the negative wall-attached structures to contribute positive vertical scalar flux and the positive wall-attached structures to contribute negative vertical scalar flux.