\name{setup.compaction.1D}
\alias{setup.compaction.1D}
\title{
  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 (\code{u}) and the solid phase (\code{v})
  are calculated in the middle (\code{mid}) of the grid cells and the
  interfaces (\code{int}).

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

\usage{
setup.compaction.1D(v.0 = NULL, v.inf = NULL, por.0, por.inf,
                    por.grid)
}

\arguments{
  \item{v.0 }{advective velocity of the solid phase at the sediment-water
    interface (also referred to as the sedimentation velocity); if \code{NULL}
    then \code{v.inf} must not be \code{NULL} [L/T]
  }
  \item{v.inf }{advective velocity of the solid phase at infinite depth
    (also referred to as the burial velocity); if \code{NULL} then
    \code{v.0} must not be \code{NULL} [L/T]
  }
  \item{por.0 }{porosity at the sediment-water interface
  }
  \item{por.inf }{porosity at infinite depth
  }
  \item{por.grid }{porosity profile specified as a 1D grid property
    (see \code{\link{setup.prop.1D}} for details on the structure of this list)
  }
}

\value{
  A list containing:
  \item{u }{list with pore water advective velocities at the middle of the
    grid cells (\code{mid}) and at the grid cell interfaces (\code{int}).
  }
  \item{v }{list with solid phase advective velocities at the middle of the
    grid cells (\code{mid}) and at the grid cell interfaces (\code{int}).
  }
}

\author{
  Filip Meysman <filip.meysman@nioz.nl>,
  Karline Soetaert <karline.soetaert@nioz.nl>
}


\examples{

# 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)

}

\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
}  

\keyword{utilities}