Application of Porous Media Theories in Marine Biological Modeling - Porous Media: Applications in Biological Systems and Biotechnology - page 379

(a) (b)

FIGURE 10.7
Computational analysis of the path of two particles traveling through a porous
medium. Gravity vector parallel to the x axis (a) and rotated by 20 ◦ (b).

few times higher than that of molecular diffusivity. The oxygen concentration
in the middle of this DBL oscillated in time with a magnitude of more than
10% of its mean value and at the frequency of the prevalent surface grav-
ity wave. Gundersen and Jørgensen (1990) attributed the oscillations to the
“numerous eddies which approach the sediment surface from the bulk of the
following sea water and hit the viscous and diffusive sublayers,” but details of
the physical mechanism involved have yet not been explored.
However, mathematical models for quantifying fluxes across permeable
seabeds in the presence of oscillatory flows are, in comparison, not numerous,
and limited to the studies of Shum (1992a,b; 1995) and Hara et al. (1992).
Although these models provide a good insight into solute distribution below
the sediment-water interface, all of them are based on assuming linearized
potential flows, and hence, of limited applications. To gain a better under-
standing of the solute transport in a wave-induced oscillating ambient flow,
the LBM model was used to account for both advective and diffusive transport,
allowing a clear identification and comparison of fluxes arising from diffusive
as well as advective transport (Liu and Khalili 2010a).
In the study, an oscillatory flow has been generated on the surface of the
water layer to follow U = U 0 sin( ωt ) (Figure 10.8) with ω and t being the
oscillation frequency and time. The interfacial solute exchange depends on a
number of different parameters. The first important parameter is the steep-
ness factor, s =2 a/L , which characterizes the sinusoidal ripple. Next, the
flow intensity is decided by Reynolds number, Re = U 0 L/ν . Furthermore,
the Strouhal number, St = πL/U 0 T ), describes the oscillating intensity while
the Schmidt number, Sc = ν/D , describes the momentum and mass diffu-
sion intensity. In the above relations, 2 a, L, U 0 ,ν,T , and D are, respectively,
the wave amplitude, the wave length, constant velocity, fluid viscosity, the