*2.4. Simulation Details and Cases*

Three cases have been simulated in the present work, including the straight model, as listed in Table 1. The two wavy models have the same wavelength, *λ*/*D* = 0.375, and undulation amplitudes of 3% and 11%. In all simulations, the initial 100 *D*/*U*∞ time units were considered as numerical transient, in which the turbulent wake was left to accommodate across the domain. This time span corresponds to approximately 20 vortex shedding cycles and also allows for a number of large vortices to first leave the domain through the outlet boundary. The cases were then further simulated in order for the flow statistics to be collected, up to a total of 290 *D*/*U*∞ time units for a good statistical convergence.

**Table 1.** Geometry parameters for the models simulated.


We note that, according to Lam and Lin [16], who performed LES of several wavy configurations, cases with smaller wavelengths end up requiring less time for statistics' convergence, provided *λ*/*D* < 1, due to the spanwise periodicity imparted on the wake structures (modulating the spanwise length of the largest wake structures). Therefore, the time required for the convergence of the wavy cases' statistics is expected to be less than that of the straight cylinder case.

To remind the reader, by keeping the same common position on the trailing-edge line, the cross section of the wavy cylinder is always a circle, and its diameter at any position along span (*z* coordinate) is given by:

$$D(z) = D\_m + A \sin\left(\frac{2\pi z}{\lambda}\right) \,\,\,\,\,\tag{12}$$

Therefore, it is trivial to conclude that the mean diameter of the wavy cylinder is equal to *Dm*, which is unitary by construction. This mean diameter is used as characteristic length in the calculation of flow parameters such as the Reynolds number. Also, it is important to name two special cross sections that will serve as references for comparisons with the straight cylinder, and between the wavy ones: first, the smallest cross section diameter as "Valley", and second, the largest one as "Peak".

Table 2 presents the computational costs exclusively referring to the simulation of each case, without considering preliminary simulations to evaluate the domain and mesh resolution.



After the simulation results are generated by Nektar++, mean flow fields and instantaneous force values are mainly processed using both post-processing tools already available in Nektar++ and some in-house scripts written for MATLAB®. The in-house scripts assist in processing and plotting the spatial flow field averages over consecutive spanwise wavelengths (given the spatial flow periodicity in this direction), the power spectral density, the graph generation of temporal forces distributions, and coefficients distributions around circumferential positions. Visit, an open-source CFD viewer, is used to visualize the iso-surfaces of the mean streamwise velocity and flow streamlines.
