Is secondary flow of Prandtl's second kind due to intense Reynolds-stress events?

We investigate intense Reynolds-stress structures in the turbulent flow through ducts square and rectangular cross-sections, with the aim of clarifying their relation with the secondary flow of Prandtl’s second kind. The intense Reynolds-stress structures are defined as connected regions of the domain that fulfil the condition $|uv|>H u' v'$, where $u$ and $v$ are the fluctuations of the streamwise and vertical component of the velocity, respectively, $u'$ and $v'$ are their root-mean-square, and $H$ is a scalar threshold. In particular, we focus on the fractional contribution of these events to the mean vertical velocity, $V$. The comparison between duct and channel flows unveils that: 1) in the core of the duct, the fractional contribution is in very good agreement with that in the channel, despite the presence of the secondary flow in the duct; 2) in the corner of the duct, the fractional contribution is in good agreement with the channel only in a small region below the corner bisector. Both in the core and in corner of the duct, the behaviour of the fractional contribution as a function of the wall distance is significantly different from that of $V$. According to our results, the secondary flow of Prandtl’s second kind is not due to intense Reynolds-stress events.