  The objective of the present study is to provide a numerical database of
thermal boundary layers and to contribute to the understanding of the dynamics
of passive scalars at different Prandtl numbers. In this regard, a direct
numerical simulation (DNS) of an incompressible zero-pressure-gradient
turbulent boundary layer is performed with the Reynolds number based on
momentum thickness $Re_{\theta}$ up to $1080$. Four passive scalars,
characterized by the Prandtl numbers $Pr = 1,2,4,6$ are simulated with constant
Dirichlet boundary conditions, using the pseudo-spectral code SIMSON (Chevalier
et al. 2007). To the best of our knowledge, the present direct numerical
simulation provides the thermal boundary layer with the highest Prandtl number
available in the literature. It corresponds to that of water at
$\sim$24$^{o}C$, when the fluid temperature is considered as a passive scalar.
Turbulence statistics for the flow and thermal fields are computed and compared
with available numerical simulations at similar Reynolds numbers. The mean flow
and temperature profiles, root-mean squared (RMS) velocity and temperature
fluctuations, turbulent heat flux, turbulent Prandtl number and higher-order
statistics agree well with the numerical data reported in the literature.
Furthermore, the pre-multiplied two-dimensional spectra of the velocity and of
the passive scalars are computed, providing a quantitative description of the
energy distribution at the different lengthscales for various wall-normal
locations. The energy distribution of the heat flux fields at the wall is
concentrated on longer temporal structures and exhibits different footprint at
the wall, with increasing Prandtl number.
