This is the 2D companion to the 3D Oyster Reef Filtration Engine. The 3D model treats the whole water column above the reef as one perfectly-mixed volume (a "CSTR": one turbidity number, drops uniformly everywhere at once). Real reefs don't work that way — oysters are benthic, sitting right on the bed, and the water immediately above them gets cleared faster than water higher in the column unless turbulence mixes the two together. This sim solves the real 2D field instead, along the direction of flow (x) and depth (z):
∂C/∂t = −u(z)·∂C/∂x + ∂/∂z( Kz·∂C/∂z ) − k(x,z)·C
u(z) = Umax·(z/H)^(1/7) (log-law current profile, 0 at bed)
k(x,z) = N_cell·CR(T) / V_cell (filtration sink, benthic band only)
CR(T) = CR_max·exp(−(T−T_opt)²/2σ²) (same thermal curve as the 3D model)
Water enters at the upstream edge at the loading concentration and is only ever removed by the thin near-bed band where the oysters actually sit — not by the whole column at once. That creates a genuine benthic depletion boundary layer: a real, well-documented mechanism in suspension-feeder ecology (mass-transfer-limited feeding, after Wildish & Kristmanson) where a dense reef can locally starve itself, clearing the water right at the bed while the water higher up stays comparatively turbid, unless the current is strong enough to mix the column. Watch the gradient shrink as you raise current speed — more turbulence keeps re-supplying the bed with turbid water from above, which paradoxically can raise the reef's total intake even though each animal's own clearance rate hasn't changed.
- Oyster density — sets the strength of the near-bed sink; a denser reef depletes its own boundary layer faster and more severely.
- Water temperature — same Gaussian thermal-performance curve as the 3D model; feeding nearly stops far from ~22 °C.
- Current / flushing speed — drives both the along-reef advection speed and the vertical turbulent mixing (Kz) that erodes the depletion layer.
- Sediment / algae loading — the upstream boundary condition; the reef can only pull local clarity below this, never below zero.
Real-world relevance: this is the flow-dependent feeding limitation restoration ecologists design around when spacing oyster reef structures — pack them too dense in slow water and the animals nearest the bed effectively starve the ones behind them of food, even though the reef as a whole looks abundant.