Direct numerical simulations (DNS) are used to assess the similarity, in rough-wall turbulent flow, between the time-averaged transport of mechanical energy (i.e. the sum of kienetic energy and pressure work) and of the squared passive-scalar field, theta^2/2.

The database comprises three simulations: 1) k00re180, smooth wall at a friction Reynolds number Re_tau=180; 2) k15re180, rough wall at a friction Reynolds number Re_tau=180 and roughness Reynolds number k^+=15 (k^+=k u_tau/nu, k is the roughness characteristics size, u_tau is the friction velocity, and nu is the kinematic viscosity); 3) k90re540, rough-wall at a friction Reynolds number Re_tau=540 and roughness Reynolds number k^+=90.

The roughness topography is taken from: 'Thakkar, M. (2017) Investigation of turbulent flow over irregular rough surfaces using direct numerical simulations (PhD Thesis), University of Southampton, Southampton, UK'. The DNS are performed using the spectral element flow solver Nek5000 (Version 19.0. 2019, Argonne National Laboratory, Illinois. https://nek5000.mcs.anl.gov).

The dataset contains the following files: 1) Mean wall-normal profiles (ascii), - k00re180.dat - k15re180.dat - k90re540.dat 2) Volume-averaged quantities (i.e. volume integrated quantities per unit volume) (ascii) - BULK_k00re180.dat - BULK_k15re180.dat - BULK_k90re540.dat 3) Time-averaged dispersive fluctuations distributions on the plane y/delta=1.2 (y is the spanwise coordinate and delta is the half channel height) (binary) - sfA_y120_k15re180.vtk - sfA_y120_k90re540.vtk

In each file, the variables are made dimensionless using the friction velocity u_tau and the channel half-height delta. For all the cases, a unit Prandtl number is used. Therefore, the friction Peclet number is equal to the friction Reynolds number, Pe_tau=Re_tau. Furthermore, the flow is always considered incompressible. In the following, Ui indicates the i-velocity component; C indicates the scalar field; P indicates the pressure; K=UiUi/2 is the kinetic energy; G=C^2/2 is the squared scalar field; ,i denotes differentiation in the i-direction; Oi indicates the i-vorticity component; Sij indicates the (i,j)-component of the strain-rate tensor; t indicates a time-averaged quantity; ts indicates a space- and time-averaged quantity; a prime superscript, (.)', indicates temporal fluctuations; a double prime superscript, (.)'', indicates dispersive fluctuations of the time-averaged field induced by the roughness. Note that the coordinate directions are: Streamwise, x, i=1; Spanwise, y, i=2; Wall-normal, z, i=3.

The dataset files contain: 1) kXXreXXX.dat z ts tsts/Pe_tau /Pe_tau tsts/Re_tau /Re_tau 2tsts/Re_tau 2ts/Re_tau ts ts ts/Re_tau ts/Re_tau ts ts ts/Pe_tau

2) BULK_kXXreXXX.dat tt t t''t'' tsts tts tst'' tt t t''t'' tsts tts tst'' AER[tt] AER[t] AER[t''t''] AER[tsts] AERtts AER[tst'' AER[tt] AER[t] AER[t''t''] AER[tsts] AER[tts] AER[tst''] WMR[tt] WMR[t] WMR[t''t''] WMR[tsts ] WMR[tts] WMR[tst''] WMR[tt] WMR[t] WMR[t''t''] WMR[tsts] WMR[tts] WMR[tst'']

  Note: AER[  ] and WMR[  ] indicate conditional integration over "attached, exposed" and "well-mixed" region. Further information is provided in the header of each file.

3) sfA_y120_kXXreXXX.vtk VTK NAME: corresponding quantity p: t s00: t s01: t'' s02: t'' s03: t'' s04: t'' s05: t'' s06: t''t'' s07: t''t'' s08: t''t'' s09: t''t'' s10: t''t'' s11: t''t'' s12: t'' s13: t'' s14: t'' s15: t'' s16: t'' s17: t'' s18: t s19: ts s20: t s21: ts s22: ts s23: ts vx: t vy: t vz: t zwb: wall-height of the bottom rough wall as a function of x.