The standard Proper Orthogonal Decomposition (POD) is an optimal tool to extract the energy-containing structures from a turbulent flow field. Some POD applications involve more than the structure identification process, and use the resulting eigenfunctions as a subspace onto which the flow state equations are projected, thus creating a low-dimensional model for the system under study. For these more elaborate applications, an increasing number of which are in the field of flow control, this low-dimensional plant is expected to represent the flow dynamics as accurately as possible. In this work, which ultimately intends to control the flow separation over an airfoil using a dynamical model of the flow, we introduce a variation to the POD formulation that we will refer to as the convection POD or cPOD. This formulation is developed using the non-linear convection terms of the Navier-Stokes equations to build a new kernel, thus producing a subspace knowledgeable about the dynamical realizations in the flow. We show that the convection POD succeeds in capturing the dynamical features of the flow more effectively than the standard formulation. It is found that the eigenfunctions now reveal physical structures in the flow field as opposed to patterns of highest energy concentration. Possible improvements in flow control applications and potential difficulties associated with this method are also discussed.