Algorithms, transforms and any alternative representations that render simulation data more compact, separable and in essence amenable to high performance computing, are very desirable tools in the field of scientific computing. A rather less explored such tool is the Discrete Chebyshev Transform (or Discrete Cosine Transform - DCT) which enjoys properties such as: energy compactness, orthogonality, separability etc. The impact of these properties on data compression is explored in length both mathematically and as applied to a large case of approximately half a billion gridpoints, i.e. fully resolved turbulence of a flow past an airplane wing. The data compression algorithm developed here is aimed at data intensive applications such as nonlinear adjoint checkpointing, however is also of benefit to visualizations. To assure flexibility we devised an a priori error estimator allowing the user to decide with what accuracy he or she intends to retrieve the data after compression . We have identified that for data visualizations an error as high as 1e-2 is sufficient, leading to data compression of 90%, however for error sensitive applications it is ideal to demand a threshold consistent with the solver accuracy which leads to lower compression ratios in the range of 30-60%. Furthermore we briefly discuss other potential applications of the Discrete Chebyshev Transform in the field of Reduced Order Models and mesh Sensitivity Analysis.