Figure 1.

50% and 95% probability contours of the joint probability density function of (a) $\overline{u}{|}_w$ and $\partial \overline{u}/\partial y{|}_w$, (b) $\overline{v}{|}_w$ and $\partial \overline{v}/\partial y{|}_w$, and (c) $\overline{w}{|}_w$ and $\partial \overline{w}/\partial y{|}_w$ for box-filtered DNS of turbulent channel flow for Δ = 0 (blue solid line), 0.01δ (red dashed line), 0.02δ (yellow dotted line), and 0.03δ (purple dot-dash line) with Re_τ = 950; (d) $\overline{u}{|}_w$ with $\partial \overline{u}/\partial y{|}_w$ for filter size Δ = 0.01δ, Re_τ = 950 (blue solid line), 2000 (red dashed line), and 4200 (yellow dotted line).