  Growth in static and controlled environments such as a Petri dish can be used
to study the spatial population dynamics of microorganisms. However, natural
populations such as marine microbes experience fluid advection and often grow
up in heterogeneous environments. We investigate a generalized
Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation describing single species
population subject to a constant flow field and quenched random spatially
inhomogeneous growth rates with a fertile overall growth condition. We
analytically and numerically demonstrate that the non-equilibrium steady-state
population density develops a flow-driven striation pattern. The striations are
highly asymmetric with a longitudinal correlation length that diverges linearly
with the flow speed and a transverse correlation length that approaches a
finite velocity-independent value. Linear response theory is developed to study
the statistics of the steady states. Theoretical predictions show excellent
agreement with the numerical steady states of the generalized FKPP equation
obtained from Lattice Boltzmann simulations. These findings suggest that,
although the growth disorder can be spatially uncorrelated, correlated
population structures with striations emerge naturally at sufficiently strong
advection.
