commit af525100cd9f8cfd4d69b5aa9b166cd4d1f1e465 parent c78988bad9f22c2d6ea8a76eac920b6f8488e1b7 Author: Anders Damsgaard <anders@adamsgaard.dk> Date: Thu, 21 Nov 2019 15:45:31 +0100 Update results with flux Diffstat:
16 files changed, 16 insertions(+), 4 deletions(-)
diff --git a/continuum-granular-manuscript1.tex b/continuum-granular-manuscript1.tex @@ -291,7 +291,7 @@ In rate-\emph{limited} experiments, the iterative procedure is only performed fo Parameter values and their references are listed in Table~\ref{tab:params}. For the first experiment with variable water pressure, we apply a water-pressure forcing amplitude of 50 kPa that modulates effective stress at the top around 100 kPa (Fig.~\ref{fig:stick_slip}). Many simulations are performed under both stress- and rate-controlled shear, which both idealize the driving glacier physics. -Real glacier settings likely fall somewhere in between, depending on how important basal friction is to the overall stress balance. +Real glacier settings fall somewhere in between, depending on how important basal friction is to the overall stress balance. Stress-controlled conditions approximate a setting where ice flow directly responds to changes in subglacial strain rates. Whillans Ice Plain, West Antarctica is an example of this setting, where a low surface slope and low driving stress results in stick-slip movement \citep[e.g.][]{Bindschadler2003}. A rate-controlled setup is the opposite end member, where changes in bed friction do not influence ice flow velocity. @@ -424,6 +424,14 @@ There is a significant strengthening when the bed thickness $L_z$ begins to cons Next we vary the top water pressure and observe the shear dynamics over a simulation time of seven days Figure~\ref{fig:stick_slip}. We perform tests under both stress and rate-controlled configurations. The response during the first cycle ($t<1$ d) is slightly different from later cycles ($t>1$ d) since the model is initialized with a hydrostatic water-pressure distribution. +Under stress-controlled conditions (Fig.~\ref{fig:stick_slip}a), the system shows stick-slip behavior where velocities range from 0 to $\sim$9 km/d. +The depth of maximum deformation moves into the bed as effective normal stress at the top boundary increases. +However, under stress-controlled conditions the till flux is only significant when the bed is rapidly slipping. +The sediment advective flux is not significant during deep deformation events, as the overall shear velocity is low. + +In the rate-controlled configuration (Fig.~\ref{fig:stick_slip}b), the shear stress varies as effective normal stress oscillates, as expected from a Mohr-Coulomb material. +As in the stress-controlled configuration, deformation propagates into the bed as effective normal stress increases at the top. +Contrary to the stress-controlled setup, the till flux is under rate-controlled shear largest during deep deformation events. \begin{figure}[htbp] \begin{center} @@ -437,9 +445,13 @@ The response during the first cycle ($t<1$ d) is slightly different from later c \end{center} \end{figure} -Under both stress and rate-controlled conditions, the grain/fluid system displays strong hysteresis in shear velocity and strain distribution (Fig.~\ref{fig:hysteresis}). -The granular deformation primarily occurs where the effective normal stress is the lowest value. +Figure~\ref{fig:hysteresis}) demonstrates that the grain/fluid system displays strong hysteresis in shear velocity, strain distribution, and till flux under both stress and rate-controlled conditions. +The sediment flux has opposite trends, according to the driving mode. +Stress-controlled shear produces a large sediment flux in a thin deforming layer close to the boundary during slip events when effective pressure is at its lowest value (Fig.~\ref{fig:hysteresis}a). +On the other hand, under rate-controlled conditions the majority of sediment flux occurs as a plug-like flow where deformation occurs deep in the bed during maxima in effective normal stress at the ice-bed interface (Fig.~\ref{fig:hysteresis}b). + When water pressure drops at the ice-bed interface, there is a remnant of high fluid-pressure diffusing downwards (Fig.~\ref{fig:stick_slip_depth}). +The granular deformation primarily occurs where the effective normal stress is at its lowest value. The depth of maximum shear-strain rate corresponds to the depth of minimum in effective normal stress, as long as the shear zone width can be accommodated. \begin{figure*}[htbp] @@ -533,7 +545,7 @@ Similarly, sudden water-pressure pulses are powerful drivers for single events o \section*{Acknowledgements}% -A.D. benefited from conversations with Dongzhuo Li, Indraneel Kasmalkar, Jason Amundson, Martin Truffer, and Lucas Zoet during model development. +A.D. benefited from conversations with Dongzhuo Li, Indraneel Kasmalkar, Jason Amundson, Martin Truffer, Dougal Hansen, and Lucas Zoet during model development. Analysis and visualization of model output was performed with Gnuplot. \section*{Appendix}% diff --git a/experiments/fig-hysteresis_rate.pdf b/experiments/fig-hysteresis_rate.pdf Binary files differ. diff --git a/experiments/fig-hysteresis_stress.pdf b/experiments/fig-hysteresis_stress.pdf Binary files differ. diff --git a/experiments/fig-mohr_coulomb.pdf b/experiments/fig-mohr_coulomb.pdf Binary files differ. diff --git a/experiments/fig-parameter_test.pdf b/experiments/fig-parameter_test.pdf Binary files differ. diff --git a/experiments/fig-pulse_square.pdf b/experiments/fig-pulse_square.pdf Binary files differ. diff --git a/experiments/fig-pulse_triangle.pdf b/experiments/fig-pulse_triangle.pdf Binary files differ. diff --git a/experiments/fig-rate_dependence.pdf b/experiments/fig-rate_dependence.pdf Binary files differ. diff --git a/experiments/fig-skin_depth.pdf b/experiments/fig-skin_depth.pdf Binary files differ. diff --git a/experiments/fig-stick_slip_rate.pdf b/experiments/fig-stick_slip_rate.pdf Binary files differ. diff --git a/experiments/fig-stick_slip_rate_depth.pdf b/experiments/fig-stick_slip_rate_depth.pdf Binary files differ. diff --git a/experiments/fig-stick_slip_stress.pdf b/experiments/fig-stick_slip_stress.pdf Binary files differ. diff --git a/experiments/fig-strain_distribution.pdf b/experiments/fig-strain_distribution.pdf Binary files differ. diff --git a/experiments/p_f_analytical.pdf b/experiments/p_f_analytical.pdf Binary files differ. diff --git a/experiments/pulse-square-fig4b.pdf b/experiments/pulse-square-fig4b.pdf Binary files differ. diff --git a/experiments/pulse-triangle-fig4b.pdf b/experiments/pulse-triangle-fig4b.pdf Binary files differ.