Complementary file for the linked data Written 15-12-2015 by Angeliki Laskari General Comments All the data attached refer to the figures presented in the paper. For details on how these data were acquired, the reader is referred the corresponding sections in the paper. Section 3 - Uncertainty Estimates Following the uncertainty propagation analysis outlined in the section, the total uncertainty on pressure estimation using the three approaches is presented in figure 1. The uncertainty in pressure - for an initial uncertainty on the total velocity field ranging from 0 to 4% - shown in figure 1a, for all three methods can be found in the attached txt file Fig1a.txt. In figure 1b the uncertainty in pressure for TH, assuming increasing levels of uncertainty for the mean and convection velocity, can be found in the attached txt file Fig1b.txt. Section 4 - Numerical assessment Using the data from the John's Hopkins University channel database ([1], [2], [3]), synthetic PIV images have been created following the procedure outlined in the section and the dependence of the methods on time-step, convection velocity, noise, and resolution are presented in figures 2 - 5 respectively. The correlation coefficient values between the DNS and estimated pressure volumes using both EU and pLA for time-steps ranging from 0.32 to 2.56, presented in figure 2 can be found in the attached txt file Fig2.txt. The correlation coefficient values between the DNS and estimated pressure volumes using EU for the same time-steps as above but for three different noise levels (0 - 2%) shown in figure 3, can be found in the attached txt file Fig3.txt for the three noise levels respectively. The correlation coefficient values between the DNS and estimated pressure volumes using all methods, for noise levels ranging from 0 to 4%, which are presented in figure 4, can be found in the attached txt file Fig4.txt for each method respectively. The correlation coefficient values between the DNS and estimated pressure volumes using all methods, for resolutions ranging from 12 to 48 wall units, which are presented in figure 5, can be found in the attached txt file Fig5.txt for each method respectively. Section 5 - Experimental assessment The inner normalised mean velocity values shown in figure 7 along with the corresponding y+ values can be found in the attached txt Fig7.txt, while the U+ and y+ values from Spalding's law of the wall can be found in the attached txt Fig7Spalding.txt. For a single velocity snapshot from the experimental setup, the estimated pressure fields using all three methods (including a single time-step for EU and three time-steps for pLA), shown in figure 8, can be found in the attached txt files Fig8_EU.txt, Fig8_pLA_0.38dt.txt, Fig8_pLA_11.4dt.txt, Fig8_pLA_dt19.txt, Fig8_TH. The root-mean-squared values of the estimated pressures using EU, for different time-steps are presented in figure 9a and the corresponding values can be found in the attached txt file Fig9a.txt. For figure 9b, the corrected root-mean-squared values of the estimated pressures using EU, for different time-steps are presented and the corresponding values can be found in the attached txt file Fig9b.txt. The root-mean-squared values of the estimated pressures using pLA, for different time-steps are presented in figure 10a and the corresponding values can be found in the attached txt files Fig10a_7.6dt.txt, Fig10a_11.4dt.txt, Fig10a_15.2dt.txt, Fig10a_19dt.txt, and Fig10a_22.8dt.txt for each of the tested time-steps respectively. For figure 10b, the corrected root-mean-squared values of the estimated pressures using pLA, for different time-steps are presented and the corresponding values can be found in the attached txt files Fig10b_7.6dt.txt, Fig10b_11.4dt.txt, Fig10b_15.2dt.txt, Fig10b_19dt.txt, and Fig10b_22.8dt.txt for each of the tested time-steps respectively. For figure 11, the corrected root-mean-squared values of the estimated pressures using TH can be found in the attached txt file Fig11.txt. For figure 12, the normalised root-mean-squared errors between the pressure distributions of the previous figures and the DNS data ([4], [5], [6], [7]) can be found in the attached txt files Fig12EU.txt, Fig12pLA.txt, and Fig12TH.txt for each of the methods respectively. For figure 13, the corrected root-mean-squared values of the estimated pressures using the best time-separations for EU and pLA, as selected in the corresponding section of the paper, can be found in the attached txt files Fig13EU.txt, Fig13pLA.txt, and Fig13TH.txt for each of the methods respectively. References [1] Y. Li, E. Perlman, M. Wan, Y. Yang, C. Meneveau, R. Burns, S. Chen, A. Szalay and G. Eyink (2008) A public turbulence database cluster and applications to study Lagrangian evolution of velocity increments in turbulence. Journal of Turbulence 9(31):1-29. [2] E. Perlman, R. Burns, Y. Li and C. Meneveau (2007) Data exploration of turbulence simulations using a database clusteng. Proceedings of the 2007 ACM/IEEE Conference on Supercomputing No 23:1-11. [3] J. Graham, M. Lee, R. Moser, G. Eyink, C. Meneveau, K. Kanov, R. Burns and A. Szalay (2013) Turbulent channel flow data set available at http://turbulence.pha.jhu.edu/docs/README- CHANNEL.pdf. [4] G. Borrell, J. A. Sillero and J. Jim�nez (2013) A code for direct numerical simulation of turbulent boundary layers at high Reynolds numbers in BG/P supercomputers. Computers & Fluids 80:37- 43. [5] J. A. Sillero, J. Jim�nez and R. D. Moser (2013) One-point statistics for turbulent wall-bounded flows at Reynolds numbers up to d+�2000. Physics of Fluids 25(10):105102. [6] J. A. Sillero, J. Jim�nez and R. D. Moser (2014) Two-point statistics for turbulent boundary layers and channels at Reynolds numbers up to d+�2000. Physics of Fluids 26(10):105109. [7] M. P. Simens, J. Jim�nez, S. Hoyas and Y. Mizuno (2009) A High-resolution Code for Turbulent Boundary Layers. Journal of Compuational Physics 228(11):4218-4231.