manus_continuum_granular1

commit db692c9ac14855b85ea5bce55fd7f0a62aa686fe
parent 2f01a826e703dc0251dca1eddce1d3aeac8580cb
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date:   Wed, 26 Jun 2019 15:30:29 +0200

Move skin depth to discussion

Diffstat:
M
continuum-granular-manuscript1.tex
 | 
22
+++++++++++-----------

1 file changed, 11 insertions(+), 11 deletions(-)
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex
@@ -147,16 +147,6 @@ The method is unconditionally stable and second-order accurate in time and space
 \section{Results}%
 \label{sec:results}
 
-The water pressure variations vary with the same periodocity as the forcing, but with exponential decay in amplitude and increasing lag at depth.
-The skin depth is defined as the distance where the fluctuation amplitude decreases to $1/e$ of its surface value.
-As long as fluid and diffusion properties are constant,
- an analytical solution to skin depth in our system follows the form \citep[after Eq. 4.90 in][]{Turcotte2002},
-\begin{equation}
-	d_\text{s} = \left( \frac{k}{\phi\mu_\text{f}\beta_\text{f}\pi f} \right)^{1/2}
-	\label{eq:skin_depth}
-\end{equation}
-The above relation implies that the amplitude in water-pressure forcing does not influence the maximum depth of slip.
-
 \begin{figure}[htbp]
 	\begin{center}
 		\includegraphics[width=7.5cm]{experiments/fig1.pdf}
@@ -202,7 +192,7 @@ The above relation implies that the amplitude in water-pressure forcing does not
 	\begin{center}
 		\includegraphics[width=7.5cm]{experiments/fig5.pdf}
 		\caption{\label{fig:skin_depth}%
-			Skin depth of pore-pressure fluctuations (Eq.~\ref{eq:skin_depth}) with forcing frequencies ranging from yearly to hourly.
+			Skin depth of pore-pressure fluctuations (Eq.~\ref{eq:skin_depth}) with forcing frequencies ranging from yearly to hourly periods.
 			The permeability range spans commonly encountered tills \citep{Schwartz2003}.
 		}
 	\end{center}
@@ -212,6 +202,16 @@ The above relation implies that the amplitude in water-pressure forcing does not
 \label{sec:discussion}
 % Our model has a representative grain diameter, but tills are polydisperse
 
+The water pressure variations vary with the same periodocity as the forcing, but with exponential decay in amplitude and increasing lag at depth.
+The skin depth is defined as the distance where the fluctuation amplitude decreases to $1/e$ of its surface value.
+As long as fluid and diffusion properties are constant,
+ an analytical solution to skin depth in our system follows the form \citep[after Eq. 4.90 in][]{Turcotte2002},
+\begin{equation}
+	d_\text{s} = \left( \frac{k}{\phi\mu_\text{f}\beta_\text{f}\pi f} \right)^{1/2}
+	\label{eq:skin_depth}
+\end{equation}
+The above relation implies that the amplitude in water-pressure forcing does not influence the maximum depth of slip.
+
 \section{Conclusion}%
 \label{sec:conclusion}