# Changeset 2874

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Timestamp:
May 16, 2006, 1:32:39 PM (17 years ago)
Message:

updates to smf document

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1 edited

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Unmodified
 r2871 (http://www.ga.gov.au/urban/projects/risk/index.jsp). Due to recent events, we are investigating the tsunami risk to Australia. To understand events and Australia's apparent vulnerabiliy to tsunami hazards, we are investigating the tsunami risk to Australia. To understand impact ashore, we have developed in conjunction with the Australian National University, a hydrodynamic model called A recent tsunami inundation study called for the tsunami source to be a slump and as such, we implemented the surface elevation function as described in Watts et al 2005, [3]. We found this a useful function as described in Watts et al 2005, [2]. We found this a very useful way to incorporate another tsunami-genic event to our understanding of tsunami risk. In trying to implement this function however, we had some questions. {\bf Question 1:}   Is there a physical explanation to why the total volume to implement this function however, we had some questions; \begin{itemize} \item Is there a physical explanation to why the total volume of the surface elevation function should not be zero? {\bf Question 2:}   Is the substitution of $x_g$ into the elevation function realistic? \item Should $\eta_{\rm min}$ used in the surface elevation function be | ${\eta_{\rm min}}$ | instead? \item Is the substitution of $x_g$ into the elevation function realistic? \end{itemize} Investigating the long term behaviour of the the depressed volume was greater than the volume displaced above the water surface with approximately 2-3 \% loss. You can see from Figure 2 of [3] that the Figure 2 of [2] that the surface elevation function $\eta(x,y)$ indicates that the total volume is not conserved. However, we can alleviate this issue by finding the appropriate set of parameters which will conserve volume. Setting the integral of the elevation function to zero and solving for $\kappa'$ yields the result, However, we can alleviate this issue by finding the appropriate set of parameters which will conserve volume. Setting the integral of the elevation function to zero and solving for $\kappa'$ yields the result, $$\kappa' = [ {\rm erf} ( \frac{x - x_0 } {\sqrt \lambda_0 } ) / (a parameter used in [2]). We've reproduced Figure 2 in [3] We've reproduced Figure 2 in [2] for appropriate values of \kappa' and \Delta x to ensure volume conservation within the system. Using the above formulation, the values of interest shown in Figure 2 of [3] would formulation, the values of interest shown in Figure 2 in [2] would be (\kappa', \Delta x) = (1,2), (1,4), (1.2, 13.48) and shown in Figure \ref{fig:eta_vary}. Note, this has not been scaled by \eta_{\rm min}. \begin{figure} \centerline{ \includegraphics[width=100mm, height=75mm]{volume_conservation.png}} \centerline{ \includegraphics[width=75mm, height=50mm]{volume_conservation.png}} \caption{Relationship between \kappa' and \Delta x to ensure volume conservation.} \begin{figure}[hbt] \centerline{ \includegraphics[width=100mm, height=75mm]{redo_figure.png}} \centerline{ \includegraphics[width=75mm, height=50mm]{redo_figure.png}} \caption{Surface elevation functions for For our particular test case, changing the surface elevation function in this way increases the inundation depth ashore by a factor greater than the water loss. the initial water loss of 2-3 \%. Turning to our question regarding the scaling of the surface elevation function formulation, we see that \eta_{\rm min} is always negative and hence - \eta_{O,3D} / \eta_{\rm min} would be always positive. This would change the form of \eta(x,y) and place the depressed volume behind the submarine mass failure. Should then \eta_{\rm min} be replaced by |\eta_{\rm min}|? Our next question is whether it was appropriate to substitute (x_g is formulated as x_g = d/\tan \theta + T/ \sin \theta (described as a gauge located above the SMF initial submergence location in [4]).) In this located above the submarine mass failure initial submergence location in [3]).) In this way, \kappa' as described above would not be dependent on \Delta x;$$\kappa'  \approx {\rm erf} ( \frac{x - x_0}{\sqrt\lambda_0} ) / {\rm erf} ( \frac{x - 2 x_0 - x_g}{\sqrt \lambda_0 } ) be dependent on $\Delta x$, nor the subsequent surface elevation function. We are continuing to seek out validation data sets to improve the accuracy of our model. We recently had success in validating the model against the Benchmark Problem #2  Tsunami Run-up the model against the Benchmark Problem $\#$2 Tsunami Run-up onto a complex 3-dimensional beach, as provided to the 3rd International Workshop on Long Wave Run-up in 2004, see [1]. cases described there for experimental or numerical work. Your model has been compared with the laboratory experiments in 2003 [5] and again in 2005 [4] with fairly good agreement. Given again in 2005 [3] with fairly good agreement. Given the numerical model you implemented was the boundary element method, we would be very interested in comparing our finite volume model using the \parindent 0pt We look forward to your response. Thanks for your time and we look forward to your response. Yours sincerely, Risk Research Group, Geoscience Australia. \newpage {\bf References} [4] Watts, P., Imamura, F. and Grilli, S. (2000) Comparting Model Simulations of Three Benchmark Tsunami Generation, Comparing Model Simulations of Three Benchmark Tsunami Generation, Science of Tsunami Hazards, 18, 2, 107-123. [5] Enet, F., Grilli, S.T. and Watts, P. (2003), Laboratory Experiments for Tsunamis Generated by Underwater Landslides: Comparison with Numerical Modeling, Tsunamis Generated by Underwater Landslides: Comparison with Numerical Modeling, Proceedings of the Thirteenth (2003) International Offshore and Polar Engineering Conference. The International Society of Offshore and