Changeset 2874
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- May 16, 2006, 1:32:39 PM (19 years ago)
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documentation/experimentation/smf.tex (modified) (12 diffs)
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documentation/experimentation/smf.tex
r2871 r2874 57 57 (http://www.ga.gov.au/urban/projects/risk/index.jsp). 58 58 Due to recent 59 events, we are investigating the tsunami risk to Australia. To understand 59 events and Australia's apparent vulnerabiliy to tsunami hazards, 60 we are investigating the tsunami risk to Australia. To understand 60 61 impact ashore, we have developed in conjunction 61 62 with the Australian National University, a hydrodynamic model called … … 64 65 A recent tsunami inundation study called for the tsunami source to 65 66 be a slump and as such, we implemented the surface elevation 66 function as described in Watts et al 2005, [ 3]. We found this auseful67 function as described in Watts et al 2005, [2]. We found this a very useful 67 68 way to incorporate another tsunami-genic event to our understanding 68 69 of tsunami risk. In trying 69 to implement this function however, we had some questions. 70 71 {\bf Question 1:} Is there a physical explanation to why the total volume 70 to implement this function however, we had some questions; 71 72 \begin{itemize} 73 \item 74 Is there a physical explanation to why the total volume 72 75 of the surface elevation function should not be zero? 73 74 {\bf Question 2:} Is the substitution of $x_g$ into the elevation function realistic? 76 \item 77 Should $\eta_{\rm min}$ used in the surface elevation function 78 be | ${\eta_{\rm min}}$ | instead? 79 \item 80 Is the substitution of $x_g$ into the elevation 81 function realistic? 82 \end{itemize} 75 83 76 84 Investigating the long term behaviour of the … … 79 87 the depressed volume was greater than the volume displaced above the 80 88 water surface with approximately 2-3 \% loss. You can see from 81 Figure 2 of [ 3] that the89 Figure 2 of [2] that the 82 90 surface elevation function $\eta(x,y)$ indicates that 83 91 the total volume is not conserved. 84 92 85 However, we can alleviate this issue by finding the appropriate set of parameters which86 will conserve volume. Setting the integral of the elevation function to zero and 87 solving for $\kappa'$ yields the result, 88 93 However, we can alleviate this issue by finding the appropriate set of 94 parameters which 95 will conserve volume. Setting the integral of the elevation function to zero 96 and solving for $\kappa'$ yields the result, 89 97 $$\kappa' = [ 90 98 {\rm erf} ( \frac{x - x_0 } {\sqrt \lambda_0 } ) / … … 99 107 (a parameter used in [2]). 100 108 101 We've reproduced Figure 2 in [ 3]109 We've reproduced Figure 2 in [2] 102 110 for appropriate values of $\kappa'$ and $\Delta x$ to 103 111 ensure volume conservation within the system. Using the above 104 formulation, the values of interest shown in Figure 2 of [3] would112 formulation, the values of interest shown in Figure 2 in [2] would 105 113 be ($\kappa', \Delta x) = (1,2), (1,4), (1.2, 13.48)$ and shown in 106 114 Figure \ref{fig:eta_vary}. Note, this has not been scaled by $\eta_{\rm min}$. … … 109 117 \begin{figure} 110 118 111 \centerline{ \includegraphics[width= 100mm, height=75mm]{volume_conservation.png}}119 \centerline{ \includegraphics[width=75mm, height=50mm]{volume_conservation.png}} 112 120 113 121 \caption{Relationship between $\kappa'$ and $\Delta x$ to ensure volume conservation.} … … 117 125 \begin{figure}[hbt] 118 126 119 \centerline{ \includegraphics[width= 100mm, height=75mm]{redo_figure.png}}127 \centerline{ \includegraphics[width=75mm, height=50mm]{redo_figure.png}} 120 128 121 129 \caption{Surface elevation functions for … … 126 134 For our particular test case, changing the surface elevation function 127 135 in this way increases the inundation depth ashore by a factor greater than 128 the water loss. 136 the initial water loss of 2-3 \%. 137 138 Turning to our question regarding the scaling of the surface elevation 139 function formulation, we see that $\eta_{\rm min}$ is always negative 140 and hence 141 $- \eta_{O,3D} / \eta_{\rm min}$ would be always positive. This 142 would change the form of $\eta(x,y)$ and place the depressed volume behind 143 the submarine mass failure. Should then $\eta_{\rm min}$ be replaced 144 by |$\eta_{\rm min}$|? 129 145 130 146 Our next question is whether it was appropriate to substitute … … 133 149 ($x_g$ is formulated 134 150 as $x_g = d/\tan \theta + T/ \sin \theta$ (described as a gauge 135 located above the SMF initial submergence location in [4]).)136 In this151 located above the submarine mass failure 152 initial submergence location in [3]).) In this 137 153 way, $\kappa'$ as described above would not 138 be dependent on $\Delta x$; 139 140 $$\kappa' \approx {\rm erf} ( \frac{x - x_0}{\sqrt\lambda_0} ) / 141 {\rm erf} ( \frac{x - 2 x_0 142 - x_g}{\sqrt \lambda_0 } )$$ 154 be dependent on $\Delta x$, nor the subsequent surface elevation function. 143 155 144 156 145 157 We are continuing to seek out validation data sets to improve the 146 158 accuracy of our model. We recently had success in validating 147 the model against the Benchmark Problem #2 Tsunami Run-up159 the model against the Benchmark Problem $\#$2 Tsunami Run-up 148 160 onto a complex 3-dimensional beach, as provided to the 3rd 149 161 International Workshop on Long Wave Run-up in 2004, see [1]. … … 151 163 cases described there for experimental or numerical work. 152 164 Your model has been compared with the laboratory experiments in 2003 [5] and 153 again in 2005 [ 4] with fairly good agreement. Given165 again in 2005 [3] with fairly good agreement. Given 154 166 the numerical model you implemented was the boundary element method, we would 155 167 be very interested in comparing our finite volume model using the … … 160 172 \parindent 0pt 161 173 162 We look forward to your response.174 Thanks for your time and we look forward to your response. 163 175 164 176 Yours sincerely, … … 168 180 Risk Research Group, Geoscience Australia. 169 181 182 \newpage 170 183 {\bf References} 171 184 … … 187 200 188 201 [4] Watts, P., Imamura, F. and Grilli, S. (2000) 189 Compar ting Model Simulations of Three Benchmark Tsunami Generation,202 Comparing Model Simulations of Three Benchmark Tsunami Generation, 190 203 Science of Tsunami Hazards, 18, 2, 107-123. 191 204 192 205 [5] Enet, F., Grilli, S.T. and Watts, P. (2003), Laboratory Experiments for 193 Tsunamis Generated by Underwater Landslides: Comparison with Numerical Modeling, 206 Tsunamis Generated by Underwater Landslides: 207 Comparison with Numerical Modeling, 194 208 Proceedings of the Thirteenth (2003) International Offshore and 195 209 Polar Engineering Conference. The International Society of Offshore and
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