Validation of Simplified Mathematical Model for Turbidity Currents
Authors: Bitton Luiz F. , Martha Luiz F. , Waltham David , Keevil Gareth , Peakall Jeff 
Published: June 2014

Abstract
Computer models have improved dramatically the mathematical understanding of gravity currents; however, these models cannot replace the analysis by experimental work. The use of scaled analogue models, or physical models, proved to be essential in validating depth average velocity equation for turbidity currents. In order to reduce the level of complexity to solve this equation numerically and to create an efficient computer model to simulate these currents, some mathematical approximations were applied during the development of the velocity equation (Waltham & Davison, 2001). Therefore, willing to prove that these approximations would not compromise the numerical results, many experiments were performed to acquire a spatio-temporal velocity evolution database for both unconfined particle free and particulate turbidity flows. Comparing the results from the numerical and physical simulations, it was concluded that, unfortunately, the approximations have influenced the numerical results. Nevertheless, the data and visual comparisons between the simulations also revealed some encouraging results, which will stimulate some future research to improve the model accuracy.

Introduction
Particulate gravity currents have been discussed in many scientific studies, especially in sedimentary geology. Their importance is due to the fact that these currents have a substantial influence on deep-water depositional systems. However, these currents can occur not only in submarine but also in subaerial environments, for example, hot clouds of volcanic ash going down slope after an eruption. In a submarine environment, turbidity currents are generally triggered by slope failures (Partson et al., 2000). These failures provide a large volume of sediment and water mixture, which has normally a greater density than the surrounding water. The difference in density between these two fluids is the ignition of the current. A difference of only a few percent is enough to raise the fluid pressure force that together with the fluid weight component, if on a slope, induce the current to propagate (Waltham, 2004).
Many studies have been published about turbidity currents behavior and how to reproduce them in fluid mechanics laboratory. Some of these studies concern simple time series measurements of flow parameters (Kneller et al., 1997; Best et al., 2001), while others concern spatio-temporal evolution of flow parameters (McCafrey et al., 2003 & 2005). Although such studies may yield valuable knowledge to this research, none of them provide information about the spatio-temporal evolution of velocity, or any other parameter, for unconfined turbidity currents. In other words, it is not possible to analyze how velocity varys over time at different points in these currents.
Since an empirical methodology is being used to validate a numerical simulation, a database about the spatio-temporal evolution of velocity for unconfined turbidity currents became essential to achieve the foremost objective of this work. Thus, a physical model was created in order to run experiments simulating turbidity currents and measuring their velocities to finally get the required database. Meanwhile, the numerical simulation was created by developing a computer program, using finite difference to solve the partial diferential equations applied to model the phenomenon. Once both the numerical model and the database are ready, they will be compared against each other to check how precise the applied equations are.