*Appendix A.2. Results*

The Strouhal number is the dimensionless frequency defined by *St* = *f D*/*U*, with *f* the frequency at which the vortices are shed in the wake of the cylinder. A fast Fourier transform was performed on the velocity signal, and the result is presented in Figure A2. For each simulation, the velocity signal showed one peak value. However, the peak value was not the same for the two turbulence models. Periodic structures were shed in the wake of the cylinder for both simulations, but the frequency differed depending on the turbulence model.

**Figure A2.** Spectrum of the velocity signal.

A typical value of the Strouhal number for cylinder at Reynolds number *Re* = 4.35 × 10<sup>4</sup> is 0.2 [32]. This value corresponded to the peak value found for the *k* − *ω*2006 turbulence model. The oscillatory behavior of the flow downstream of the pipeline was consistent with the results from the literature. On the contrary, the Strouhal number found with the *k* − *ε* model was largely underestimated. The unsteady turbulent wake behind the cylinder was not properly captured. In conclusion, the *k* − *ω*2006 turbulence model was more suitable to reproduce the lee-wake erosion stage of scour.
