Abstract
Consider a body of marine sediment, which an organism burrows into. Advective transport of water induced by the organism‘s activity is referred to as bioirrigation here. One consequence is that the spatial distribution of oxygen in the sediment can be disturbed. To better understand these effects, further research into estimating flows induced by bioirrigation is conducted given images depicting spatio- temporal distributions of tracers that are carried with flows induced by the organism Arenicola marina in aquaria which are “narrow” in depth [1–3]. The multi- resolution Horn- Schunck method is employed here because it can cope with the sometimes fictitious “large” displacements that fluid deformation seems to produce [2]. But some of the recovered divergences here have unrealistically “large” magnitudes (relative to those near the injection location) where they ought to be comparatively “small” [2]. Quantifying error in flow fields is difficult when the true solution is unknown. One can subjectively define uncertainty in their components, and observations, to follow Gaussian distributions which are updated using Kalman filtering [2]. Given a pair of synthetic images, posterior variances seem to get reduced most where angular errors are comparatively “small” [2]. So posterior variances are used to infer errors when the true solution is unknown here because they are independent of it [2]. Unrealistic “large” divergence magnitudes (relative to those near injection locations) still appear where they ought to be comparatively “small” [2]. In line with previous research, one tries modelling flows induced by bioirrigating Arenicola marina as two- dimensional incompressible point sources. Only three parameters, namely the source strength, x- and y- coordinates, need estimating rather than flow components at each grid cell. A Markov chain Monte- Carlo method is employed for this task, instead of the Kalman filter, because the state being estimated is no longer proportional to observations. Although comparatively “large” divergence magnitudes now only appear near locations of fluid injection, this approach seems computationally expensive on one‘s Dell Optiplex 7010 computer. Outflow appears to be induced at the sediment- water interface by a two- dimensional incompressible point source beneath it. One questions whether there should be a little inflow as well because when an organism burrows forwards, the volume that it previously occupied ought to refill with surrounding fluid. This could be accounted for here by considering an additional two- dimensional incompressible flow at the sediment- water interface, as well as a point source at the injection location. But more parameters would need estimating. In an attempt to reduce computation times, the simulations involving the Markov chain Monte- Carlo method are rerun using two iterative ensemble Kalman filters (respectively).