Flows past a circular cylinder develop in a variety of practical situations in engineering and in nature. One can properly focus on the study of beneficial cases and specifically attempt to harness this renewable clean energy resource to generate electrical power to help decrease air pollution and global warming. In addition, we need studies on stress and deformation of a circular cylinder due to the passing flow vortex in order to reduce the destructive effects, for example, on offshore structures. In this paper, we implement a two-dimensional numerical simulation with no-slip walls to monitor in detail how vortices are formed around a stationary circular cylinder when a shear current flows past a bluff body, namely a fixed circular cylinder. The Computational Fluid Dynamics (CFD) part of COMSOL Multiphysics was used to implement the continuity and Navier-Stokes equations that are based on the velocity field, pressure, and other preliminary variables. In the research reported here, various mathematical techniques such as various selected wavelet transforms over the space domain are applied to the exported data. A comprehensive wavelet numerical investigation is carried out on the vorticity and pressure field by using MATLAB software. Various Daubechies wavelets, Haar, Morlet, Paul and the m-th order derivative of Gaussian wavelets were tested to find the best wavelet transform to accurately analyze flow past a fixed cylinder. Numerical simulation results are compared with experimental data from the literature. An extensive comparative analysis is performed and discussed in detail in order to suggest improvements and expansions for the developed model.