The VIScous Vorticity Equation (VISVE) method has previously been applied to the laminar oscillatory flow around a circular cylinder (Li and Kinnas (2017); Wu and Kinnas (2021a)). In this work, the VISVE method is applied to the oscillatory turbulent flow around a cylinder. To handle the flow within the turbulent regime, the k-w SST turbulence model is employed for calculating the turbulent viscosity. The VISVE and the k-w SST 2-equation turbulence model are both discretized based on the Finite Volume Method (FVM), with Quadratic Upstream Interpolation for Convective Kinematics (QUICK) method dealing with the convective terms, and the Alternating Direction Implicit (ADI) method calculating the unsteady terms. The method is applied to various Reynolds and Keulegan-Carpenter numbers, and the results, including vorticities and velocities are compared with those from a Reynolds-Averaged Navier-Stokes (RANS) solver. The results of turbulent VISVE agree well with those from RANS for KC =2, but deviate from RANS at a higher KC number.

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