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This paper examines the Reynolds number (
) dependence of a zero-pressure-gradient (ZPG) turbulent boundary layer (TBL) which develops over a two-dimensional rough wall with a view to ascertaining whether this type of boundary layer can become independent of
. Measurements are made using hot-wire anemometry over a rough wall that consists of a periodic arrangement of cylindrical rods with a streamwise spacing of eight times the rod diameter. The present results, together with those obtained over a sand-grain roughness at high Reynolds number, indicate that a
-independent state can be achieved at a moderate
. However, it is also found that the mean velocity distributions over different roughness geometries do not collapse when normalised by appropriate velocity and length scales. This lack of collapse is attributed to the difference in the drag coefficient between these geometries. We also show that the collapse of the
-normalised mean velocity defect profiles may not necessarily reflect
-independence. A better indicator of the asymptotic state of
is the mean velocity defect profile normalised by the free-stream velocity and plotted as a function of
is the vertical distance from the wall and
is the boundary layer thickness. This is well supported by the measurements.
A fundamental understanding of the filament thinning of viscoelastic fluids is important in practical applications such as spraying and printing of complex materials. Here, we present direct numerical simulations of the two-phase axisymmetric momentum equations using the volume-of-fluid technique for interface tracking and the log-conformation transformation to solve the viscoelastic constitutive equation. The numerical results for the filament thinning are in excellent agreement with the theoretical description developed with a slender body approximation. We show that the off-diagonal stress component of the polymeric stress tensor is important and should not be neglected when investigating the later stages of filament thinning. This demonstrates that such numerical methods can be used to study details not captured by the one-dimensional slender body approximation, and pave the way for numerical studies of viscoelastic fluid flows.