commit c0e737bebc44f7e6eaa7c5f158b5ef00e5890fe2
parent 40a695841eb4faf45eede393bc84c51843e49a15
Author: Anders Damsgaard <anders@adamsgaard.dk>
Date: Thu, 4 Jul 2019 12:38:08 +0200
Add caption to hysteresis figure, update figures
Diffstat:
3 files changed, 2 insertions(+), 1 deletion(-)
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex
@@ -129,7 +129,7 @@ We apply fixed-value (Dirichlet) boundary conditions for the fluidity field ($g(
This condition causes the velocity field transition towards a constant value at the domain edges.
Neumann boundary conditions, which are not used here, create a velocity profile resembling a free surface flow.
-The pore-pressure solution (Eq.~\ref{eq:p_f}) is constrained by a zero pressure gradient at the bottom ($dp_\text{f}/dz (z=0) = 0$), and a sinusoidal pressure forcing at the top ($p_\text{f}(z = L_z) = A \sin(2\pi f t) + p_{\text{f},0}$).
+The pore-pressure solution (Eq.~\ref{eq:p_f}) is constrained by a hydrostatic pressure gradient at the bottom ($dp_\text{f}/dz (z=0) = \rho_\text{f}G$), and a sinusoidal pressure forcing at the top ($p_\text{f}(z = L_z) = A \sin(2\pi f t) + p_{\text{f},0}$).
Here, $A$ is the forcing amplitude [Pa], $f$ is the forcing frequency [1/s], and $p_{\text{f},0}$ is the mean pore pressure over time [Pa].
As for the granular flow solution, we also use operator splitting and finite differences to solve the equation for pore-pressure diffusion (Eq.~\ref{eq:p_f}):
\begin{equation}
@@ -190,6 +190,7 @@ For the first experiment with variable water pressure, we apply a water-pressure
\begin{center}
\includegraphics[width=7.5cm]{experiments/fig3.pdf}
\caption{\label{fig:hysteresis}%
+ Hysteresis between stress and velocity under diurnal forcing (Fig.~\ref{fig:stick_slip}).
}
\end{center}
\end{figure}
diff --git a/experiments/fig2.pdf b/experiments/fig2.pdf
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diff --git a/experiments/fig3.pdf b/experiments/fig3.pdf
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