Gerardo Ruiz-Chavarría

Experiments on generation of surface waves by an underwater moving bottom

We report laboratory experiments on surface waves generated in a uniform fluid layer whose bottom undergoes an upward motion. Simultaneous measurements of the free-surface deformation and the fluid velocity field are focused on the role of the bottom kinematics (i.e. its spatio-temporal features) in wave generation. We observe that the fluid layer transfers bottom motion to the free surface as a temporal high-pass filter coupled with a spatial low-pass filter. Both filter effects are often neglected in tsunami warning systems, particularly in real-time forecast. Our results display good agreement with a prevailing linear theory without any parameter fitting. Based on our experimental findings, we provide a simple theoretical approach for modelling the rapid kinematics limit that is applicable even for initially non-flat bottoms: this may be a key step for more realistic varying bathymetry in tsunami scenarios.

Transport of Particles in a Periodically Forced Flow

In oceanography particle transport is a constant: the ocean currents carry the plankton from one place to another. In shallow water trawling and sand deposition can affect positively or negatively certain human activities. For example, sandbars formed by the deposition in areas of low pressure may affect navigation near the coast, but at the same time they can reduce the intensity of a tsunami when approaching a populated coast. In this work we present a numerical solution of particle transport in a flow occurring in a system formed by the channel and an open domain and that is subject to a periodic forcing. For this purpose the equations of motion in the formulation vorticity- stream function are solved with a pseudo spectral method. After the velocity field is calculated, the trajectory of particles is obtained through the solution of a differential equation deduced from first principles. The goal is to model the transport of particles in a tide induced flow. The results we obtain are consistent with some experimental and observational data reported in previous works.

Numerical Study of Water Flow in a Channel Output with Periodic Forcing

In this work a numerical solution for the flow in a system of two basins connected by a channel is presented. The flow rate is assumed to be time dependent. With this assumption we intend to model the effect of tides in coastal systems. Our results show the formation of a vortex dipole at the channel outlet. Evolution of dipole depends strongly on the period of flow rate, as already noted by previous works. Using the velocity field obtained with the numerical method we calculate trajectories of fluid particles and show that dipole has an effect of suction in the region it pass. On the other hand the process of vortex formation and further evolution are well described.

The Cooling of a Granular Material in a Rotating Horizontal Cylinder

In this chapter we investigate the cooling of the lateritic ore moving inside a rotating horizontal cylinder. The mineral, which has been previously milled, forms a granular bed. Due to rotation, the granular material undergoes discrete avalanching, whose characteristics depends either upon the angular velocity and the filling degree. The ore enters into the cooler at a temperature of approximately \({750\;^{\circ }}\)C and after moving along the cylinder its temperature decreases. The goal is to reduce the ore temperature to a value around \({170\;^{\circ }}\)C, so its metallic properties are preserved. To model this process a system of two differential equations and an algebraic equation depending only on the axial coordinate is solved. Otherwise we present data of the cooling in a cylinder 30 m long, a diameter \(\text{ d } = 3\) m and rotating with an angular velocity of 6.24 rpm. We show that numerical solution exhibits a partial agreement with experimental data.