Figure 7.

(a) Continuum of uniform steady-state solutions, for (Eqs.(1), blue line). The purple line indicates the zero-flux condition which determines M^U. (b,c) Real and imaginary parts (respectively) of the dispersion relation about M^U. The most unstable mode q_max is denoted in (b), while the advection velocity v_b is denoted by the dashed line in (c). (d) Space-time plot of the fluctuation amplitude after an initial perturbation located at z = 30 μm, where corresponds to the M^U state. (e) Exponential decay of the fluctuation in time at the initiation site (in addition to a shift of the overall background due to the spreading of the initial perturbation). Parameters used are: v_w = 0.6 μm/sec, v_b = 0.03 μm/sec, D = 0.1 μm²/sec, D_b = 0.0005 μm²/sec, sec⁻¹, sec⁻¹, sec⁻¹, sec⁻¹, sec⁻¹, sec⁻¹, and k_bw = 2 μm².