Vidal A, Nagib HM, Schlatter P, Vinuesa R (2018)

**Publication Type:** Journal article

**Publication year:** 2018

**Book Volume:** 851

**Pages Range:** 288-316

**DOI:** 10.1017/jfm.2018.498

Direct numerical simulations (DNSs) are performed to analyse the secondary flow of Prandtl's second kind in fully developed spanwise-periodic channels with in-plane sinusoidal walls. The secondary flow is characterized for different combinations of wave parameters defining the wall geometry at and 5000, where is the half-height of the channel. The total cross-flow rate in the channel is defined along with a theoretical model to predict its behaviour. Interaction between the secondary flows from opposite walls is observed if, where and are the amplitude and wavelength of the sinusoidal function defining the wall geometry. As the outer-scaled wavelength is reduced, the secondary vortices become smaller and faster, increasing the total cross-flow rate per wall. However, if the inner-scaled wavelength is below 130 viscous units, the cross-flow decays for smaller wavelengths. By analysing cases in which the wavelength of the wall is much smaller than the half-height of the channel, we show that the cross-flow distribution depends almost entirely on the separation between the scales of the instantaneous vortices, where the upper and lower bounds are determined by and, respectively. Therefore, the distribution of the secondary flow relative to the size of the wave at a given can be replicated at higher by decreasing and keeping constant. The mechanisms that contribute to the mean cross-flow are analysed in terms of the Reynolds stresses and using quadrant analysis to evaluate the probability density function of the bursting events. These events are further classified with respect to the sign of their instantaneous spanwise velocities. Sweeping events and ejections are preferentially located in the valleys and peaks of the wall, respectively. The sweeps direct the instantaneous cross-flow from the core of the channel towards the wall, turning in the wall-tangent direction towards the peaks. The ejections drive the instantaneous cross-flow from the near-wall region towards the core. This preferential behaviour is identified as one of the main contributors to the secondary flow.

Indian Institute of Technology (IIT) Gandhinagar
India (IN)
Royal Institute of Technology / Kungliga Tekniska Högskolan (KTH)
Sweden (SE)

**APA:**

Vidal, A., Nagib, H.M., Schlatter, P., & Vinuesa, R. (2018). Secondary flow in spanwise-periodic in-phase sinusoidal channels. *Journal of Fluid Mechanics*, *851*, 288-316. https://doi.org/10.1017/jfm.2018.498

**MLA:**

Vidal, A., et al. "Secondary flow in spanwise-periodic in-phase sinusoidal channels." *Journal of Fluid Mechanics* 851 (2018): 288-316.

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