Gravity or density currents constitute a wide class of flows that are generated and maintained due to the density difference between two or even more fluids. The density difference between two fluids, usually arises from corresponding differences in temperature or salinity. However, this density difference can also arise by the presence of suspended sediment particles. Such particle-laden flows, in the case of sediment-laden water that enters a water basin, are classified into three major categories according to their density difference with the ambient fluid: (a) hypopycnal currents, when the density of the sediment-laden water is lower than that of the receiving water basin, (b) homopycnal currents, when the density of the sediment-laden water is almost equal to the density of the receiving water basin and (c) hyperpycnal currents, when the density of the sediment-laden water is greater than that of the receiving water basin. The most common example of such particulate currents, is a type of currents that are usually formed at river outflows into the sea, lakes or reservoirs. During floods, the suspended sediment concentration of river waters rises to a great extent. Therefore, when the sediment-laden river discharges into the water of a receiving basin, it plunges underneath the free surface forming a hyperpycnal plume that continuous to flow along the bottom of the basin. This hyperpycnal plume is also known as turbidity current. Turbidity currents can travel remarkable distances along the bottom of the sea, lakes or reservoirs, transferring, eroding and depositing large amounts of suspended sediment particles. Therefore, the study and understanding of such complex and rare phenomena is of great importance, as they constitute one of the major mechanisms for suspended sediment transport from rivers into the ocean or into lakes and reservoirs. Turbidity currents are very difficult to be observed and studied in the field, due to their rare and unexpected occurrence nature as they are usually formed during flood river discharges. Therefore, field investigations are usually limited to the study of the deposits originating from turbidity currents, aiming to identify various depositional and erosional elements such as lobes, levees and subaqueous channels. Scaled laboratory experiments constitute a widely used alternative method for simulating and studying the dynamics as well as the erosional and depositional characteristics of turbidity currents, providing valuable and detailed results. However, laboratory experiments are usually limited in the study of small-scale turbidity currents. Moreover, the installation, maintenance and operation of the required experimental set-ups, demands a lot of time and money. On the other hand, mathematical and numerical models when properly designed and tested against field or laboratory data, can constitute a quite promising tool for understanding and predicting the hydrodynamics of three-dimensional turbidity currents as well as their erosional and depositional characteristics. This chapter aims to the simulation and study of the hydrodynamic characteristics of turbidity currents that are usually formed at river outflows, both in fundamental research level, conducting parametric analysis through various series of laboratory scale numerical experiments, and in pilot application level, studying the formation and the dispersal of turbidity currents that are formed at River Evros outflow during flood discharges, using CFD (Computational Fluid Dynamics) methods that are offered by the commercial code FLUENT. More specifically, an "uncommon" three-dimensional numerical approach is used, which is based in a multiphase modification of the Reynolds Averaged Navier-Stokes Equations (RANS). Turbulence closure is achieved through the application of the RNG (Renormalization-Group) k-ε turbulence model. Most of the previous CFD investigations, treat turbidity current flows using a quasi single-phase approach, in which a single set of continuity and momentum equations is solved for the ambient water, while the suspended sediment transport is calculated indirectly through an advection-diffusion equation for sediment concentration. On the contrary, the novel multiphase numerical approach that is presented and used in the applications of the present chapter, assumes that the sediment-laden flow of a turbidity current, consists of separate solid (various suspended sediment classes) and fluid (ambient water of receiving basin and inflow/carrier water) phases that are treated as interpenetrating continua. The main advantages of the proposed multiphase numerical approach in relation to previous quasi single-phase approaches are the following: Separate velocity fields are calculated for each phase (ambient water, inflow/carrier water and various classes of suspended sediment), since the laws for the conservation of mass and momentum are accordingly modified, in order to be satisfied by each phase individually. The use of the RNG k-ε turbulence model, significantly increases the applicability of the proposed numerical approach, as it can also account for turbidity current flows with low Reynolds numbers. The total number of flow phases that can be simulated is only limited by the available memory of the computational resources. Hence, it can also be used for the simulation of polydisperse turbidity currents that contain many classes of suspended sediment particles, which are more close to natural turbidity current flows. It can handle a wide range of particulate loading, and therefore is capable for the simulation of both dilute and dense turbidity current flows. It is based on the finite volume method, and therefore it can be applied in situations with complex geometries, like in the case of turbidity currents that are formed at natural, water basin beds (sea, lakes, reservoirs), where morphological anomalies are usually present. Prior to the laboratory-scale and field-scale applications that are presented in the present chapter, the proposed numerical approach is validated through numerical reproduction of laboratory experiments that are available in the literature, and the degree of convergence of the numerical results with the corresponding experimental data is checked. The comparison of the numerical results with the corresponding experimental data indicates that the numerical predictions are realistic and reliable. In the first application of the present chapter, the proposed numerical approach is applied in laboratory scale numerical experiments of continuous, high density turbidity currents. The turbidity currents are produced by the steady discharge of fresh water – suspended sediment mixtures, into an inclined channel which is connected at its downstream end to a wide horizontal tank. Both, channel and tank are initially filled with fresh water. This configuration serves as a simplified experimental analog of natural, hyperpycnal turbidity currents that are formed at river outflows in the sea, lakes or reservoirs which usually travel within subaqueous canyon-fan complexes. The main aim is to investigate the exact qualitative and quantitative effect of fundamental, flow controlling parameters in the hydrodynamic and depositional characteristics of continuous, high density turbidity currents. The results indicate that each one of the examined flow controlling parameters affects differently the main flow characteristics of turbidity currents, such as the flow front advance with respect to time, the main expansion angle in the unconstrained part of the flow and the deposit density distribution at the bottom boundary. The main expansion angle of the generated turbidity currents at the expansion tank, when their flow has reached a quasi-steady state, is found to decrease exponentially with the increase of the densimetric Froude number, at the downstream boundary of the inclined channel. From the comparison of the relative percentage effect of all the examined controlling parameters in the maximum flow front advance velocity, in the main expansion angle of the current and in the maximum value of the deposit density, it can be concluded that the greater effect in each case is caused from the variation of the initial suspended sediment concentration as well as from the variation of the suspended sediment grain diameter. The variation of the bed roughness has in each case a minor effect, while the variation of the channel bed slope has an intermediate effect. In the second application of the present chapter, the proposed numerical approach is applied in a field scale scenario, aiming to simulate the hydrodynamic behaviour, structure and flow characteristics of turbidity currents that are potentially formed in Evros River mouth, in Greece, during flood discharges. It should be mentioned that the effects of the bed morphology and the Coriolis force are taken into account, during the numerical simulation. The simulation results indicate, that during the inflow of the fresh water – suspended sediment mixture from Evros River into the saline water of the North Aegean Sea, a turbidity current is formed, plunging to the bottom of the receiving basin. It is found that the travel and dispersal of the proposed turbidity current, is highly influenced from the bottom topography, as well as from the Coriolis force. Moreover, a characteristic differentiation in the response of the different suspended sediment classes in the flow field is observed. Summarizing, in the present chapter, an “uncommon”, multiphase numerical approach is presented, as a useful tool for the simulation of the hydrodynamic behavior of turbidity currents, since the simulations results prove that the proposed investigation methodology provides realistic forecasts, constituting thus an attractive alternative solution in laboratory experiments of turbidity currents, which usually require a lot of time and money as well as in field investigation that are very difficult to be performed. The use of proposed numerical approach, in laboratory scale applications, offers the following important advantages: It allows the determination and the continuous observation of a much wider range of parameters on turbidity current flows, at any point of the flow field and at any time, with high precision. It allows the determination of the response and the relative importance of separate flow parameters, in relation to the variation of the initial conditions. It can be easily applied to experimental setups of any geometry and scale. It provides a detailed presentation and estimation of the hydrodynamic characteristics, to the entire flow field of turbidity currents, at any time of their flow, which are difficult to be observed and determined in laboratory experiments. Finally, the use of the proposed numerical model in field scale numerical applications can considerably contribute in a more complete understanding of the mechanisms of river suspended sediment transport and deposition, in the sea bed as well as in the bed of lakes and reservoirs.