<p>Differential advective transport between interacting species represents a physically important but theoretically understudied mechanism of spatial pattern formation in aquatic ecological systems. In this work, we investigate a two-dimensional reaction-diffusion-advection model of phytoplankton-zooplankton dynamics incorporating cross-diffusion and a fully anisotropic flow term that permits distinct transport intensities along each spatial direction. Through rigorous linear stability analysis, we derive explicit analytical conditions for the onset of flow-induced instability and identify the critical relative flow strength parameter at which the homogeneous coexistence equilibrium first loses stability. A bifurcation diagram in the parameter plane partitions the dynamics into six qualitatively distinct regimes: stable homogeneous state, pure Turing instability, pure flow-induced instability, flow-Turing instability, flow-Hopf instability, and combined flow-Hopf-Turing instability. We demonstrate that differential flow strength between phytoplankton and zooplankton constitutes an independent destabilizing mechanism, capable of generating sustained spatiotemporal patterns even in parameter regimes where classical Turing conditions are not satisfied. When both species are subject to identical flow intensities, advection does not alter the real part of the eigenvalue spectrum but introduces a nonzero imaginary component, converting stationary Turing patterns into complex chaotic structures. Numerical simulations conducted via a finite difference scheme on a periodic spatial domain reveal a wide variety of emergent pattern morphologies, including vertically oriented stripes, horizontally aligned bands, and chaotic spatiotemporal structures whose geometry depends sensitively on both the magnitude and the sign of the relative flow strength. These findings extend classical reaction-diffusion theory and highlight differential advection as a fundamental organizing mechanism in flowing aquatic environments.</p>