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

### 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

1 2 | ```
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 |

`v.inf ` |
advective velocity of the solid phase at infinite depth
(also referred to as the burial velocity); if |

`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 |

### Value

A list containing:

`u ` |
list with pore water advective velocities at the middle of the
grid cells ( |

`v ` |
list with solid phase advective velocities at the middle of the
grid cells ( |

### 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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 | ```
# 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)
``` |