Horizontal mixing has been found to play a crucial role in the development of spatial plankton structures in the ocean. We study the influence of time and length scales of two different horizontal two-dimensional (2-D) flows on the growth of a single phytoplankton patch. To that end, we use a coupled model consisting of a standard three component ecological NPZ model and a flow model able to mimic the mesoscale structures observed in the ocean. Two hydrodynamic flow models are used: a flow based on Gaussian correlated noise, for which the Eulerian length and time scales can be easily controlled, and a multiscale velocity field derived from altimetry data in the North Atlantic ocean. We find the optimal time and length scales for the Gaussian flow model favouring the plankton spread. These results are used for an analysis of a more realistic altimetry flow. We discuss the findings in terms of the time scale of the NPZ model, the qualitative interaction of the flow with the reaction front and a Finite-Time Lyapunov Exponent analysis.