Statistical behavior of wall-attached motions in open- and closed-channel flows via direct numerical simulation

Abstract

Direct numerical simulations at two friction Reynolds numbers (550 and 1000) have been performed to explore the statistical behaviors of wall-attached motions (WAMs) in open- and closed-channel flows (OCFs and CCFs). To fully capture the largest energetic WAMs, superlarge domain sizes are employed (24–48 π h along streamwise direction with h being the height of OCFs). Based on the analysis of linear coherence spectrum, both geometric and kinematic characteristics of WAMs are investigated. Results revealed that obvious peaks could be found in spanwise coherence spectra of u (streamwise velocity) and w (spanwise velocity) at a wavelength close to 2h. Both the coherence and energy spectra density value of OCFs are greater than those of CCFs at large wavelengths, indicating that OCFs are more wall-attached. Within y/h = 0.2–0.7, the diagnosed streamwise and spanwise wavelengths of WAMs increase roughly linearly with increasing vertical position y. In the upper region ( y / h > 0.7), the diagnosed wavelengths in OCFs are smaller than those in CCFs. In addition, the inclination angle of u fluctuates around 14° within y / h = 0.4–0.6, and angles of CCFs are slightly larger than those in OCFs when y / h > 0.6. Regarding kinematic behavior, contribution fractions of WAMs to total turbulent intensity in OCFs are always larger than those in CCFs. Additionally, the wall-attached behaviors of u were found to be more sensitive to Reynolds number than w.