The robustness of the orbital angular momentum (OAM) of light beams propagating in a turbulent medium, e.g., atmosphere, is critical for many applications such as OAM-based free-space optical communications and remote sensing. However, the total OAM of a beam interacting with the turbulent medium inevitably changes. Here, we demonstrate a practical algorithm to control the total OAM of a beam transmitted through a time-evolving, turbulent medium by dynamically modulating the weights of two coherently superimposed OAM modes, which served as the input beam. A cross-OAM matrix is introduced, and applied for checking whether the desired total OAM in the output plane can be achieved. Furthermore, analytical relations between the weights of two input modes and the output total OAM, as well as its modulation range, are established. As a numerical example, we study the behavior of total OAM of the two-mode beam after passing through a thermal convection occurring in an aqueous medium and suggest a possible application of our strategy.