Calculates Advective Velocities of the Pore Water and Solid Phase in a Water Saturated Sediment assuming Steady State Compaction

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Description

This function calculates the advective velocities of the pore water and the solid phase in a sediment based on the assumption of steady state compaction.

The velocities of the pore water (u) and the solid phase (v) are calculated in the middle (mid) of the grid cells and the interfaces (int).

One needs to specify the porosity at the interface (por.0), the porosity at infinite depth (por.inf), the porosity profile (por.grid) encoded as a 1D grid property (see setup.prop.1D, as well as the advective velocity of the solid phase at one particular depth (either at the sediment water interface (v.0) or at infinite depth (v.inf)).

Usage

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setup.compaction.1D(v.0 = NULL, v.inf = NULL, por.0, por.inf,
                    por.grid)

Arguments

v.0

advective velocity of the solid phase at the sediment-water interface (also referred to as the sedimentation velocity); if NULL then v.inf must not be NULL [L/T]

v.inf

advective velocity of the solid phase at infinite depth (also referred to as the burial velocity); if NULL then v.0 must not be NULL [L/T]

por.0

porosity at the sediment-water interface

por.inf

porosity at infinite depth

por.grid

porosity profile specified as a 1D grid property (see setup.prop.1D for details on the structure of this list)

Value

A list containing:

u

list with pore water advective velocities at the middle of the grid cells (mid) and at the grid cell interfaces (int).

v

list with solid phase advective velocities at the middle of the grid cells (mid) and at the grid cell interfaces (int).

Author(s)

Filip Meysman <filip.meysman@nioz.nl>, Karline Soetaert <karline.soetaert@nioz.nl>

References

Meysman, F. J. R., Boudreau, B. P., Middelburg, J. J. (2005) Modeling Reactive Transport in Sediments Subject to Bioturbation and Compaction. Geochimica Et Cosmochimica Acta 69, 3601-3617

Examples

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# setup of the 1D grid

L <-10
grid <- setup.grid.1D(x.up = 0, L = L, N = 20)

# attaching an exponential porosity profile to the 1D grid
# this uses the "p.exp" profile function

por.grid <- setup.prop.1D(func = p.exp, grid = grid, 
                          y.0 = 0.9, y.inf = 0.5, x.att = 3)

# calculate the advective velocities

dummy <- setup.compaction.1D(v.0 = 1, por.0 = 0.9, por.inf = 0.5, 
                             por.grid = por.grid)
u.grid <- dummy$u
v.grid <- dummy$v

# plotting the results

par(mfrow = c(2, 1), cex.main = 1.2, cex.lab = 1.2)

plot(por.grid$int, grid$x.int, pch = 19, ylim = c(L,0), xlim = c(0,1),
     xlab = "", ylab = "depth [cm]", main = expression("porosity"),
     axes = FALSE)
abline(h = 0)
axis(pos = 0, side = 2)
axis(pos = 0, side = 3)

plot(u.grid$int, grid$x.int, type = "l", lwd = 2, col = "blue",
     ylim = c(L, 0), xlim = c(0, max(u.grid$int,v.grid$int)),
     xlab = "", ylab = "depth [cm]",
     main = "advective velocity [cm yr-1]", axes = FALSE)
abline(h = 0)
axis(pos = 0, side = 2)
axis(pos = 0, side = 3)

lines(v.grid$int, grid$x.int, lwd = 2, col = "red")

legend(x = "bottomright", legend = c("pore water","solid phase"),
       col = c("blue", "red"), lwd = 2)