Joana Prat

ROBUST HETEROCLINIC CYCLES IN TWO-DIMENSIONAL RAYLEIGH–BÉNARD CONVECTION WITHOUT BOUSSINESQ SYMMETRY

The onset of convection in systems that are heated via current dissipation in the lower boundary or that lose heat from the top boundary via Newton’s law of cooling is formulated as a bifurcation problem. The Rayleigh number as usually dened is shown to be inappropriate as a bifurcation parameter since the temperature dierence across the layer depends on the amplitude of convection and hence changes as convection evolves at xed external parameter values. A modied Rayleigh number is introduced that does remain constant even when the system is evolving, and solutions obtained with the standard formulation are compared with those obtained via the new one. Near the 1 : 2 spatial resonance in low Prandtl number fluids these eects open up intervals of Rayleigh number with no stable solutions in the form of steady convection or steadily traveling waves. Direct numerical simulations in two dimensions show that in such intervals the dynamics typically take the form of a nearly heteroclinic modulated traveling wave. This wave may be quasiperiodic or chaotic.

Development of a low-cost autonomous oceanographic observation vehicle

This work proposes the development of a low-cost ocean observation vehicle. This vehicle, a hybrid between Autonomous Underwater Vehicles (AUV) and Autonomous Surface Vehicles (ASV) moves on the surface of the sea and makes vertical immersions to obtain profiles of a water column according to a pre-established plan. Its design means production costs are low and efficiency is increased. Also, the vehicle is able to make high resolution space and time measurements simultaneously. GPS navigation allows the platform to move along the surface of the water while a radio-modem provides direct communication links and telemetry. The vehicle measures 1885mm by 320mm wide. It weighs 76kg. It navigates at a speed of 1.5m/s at 80% at full propulsion power and reaches a maximum depth of 20m. It is a vehicle of electrical propulsion with an autonomy of 3–5 hours. This work outlines the mechanical and electronic design of the vehicle, as well as considerations for navigational and immersion experiments.

THE 1:2 MODE INTERACTION IN RAYLEIGH–BÉNARD CONVECTION WITH WEAKLY BROKEN MIDPLANE SYMMETRY

The effects of weak breaking of the midplane reflection symmetry on the 1:2 steady state mode interaction in Rayleigh–Benard convection are discussed in a PDE setting. Effects of this type arise from the inclusion of non-Boussinesq terms or due to small differences in the boundary conditions at the top and bottom of the convecting layer. The latter provides the simplest realization, and captures all qualitative effects of such symmetry breaking. The analysis is performed for two Prandtl numbers, σ=10 and σ=0.1, representing behavior typical of large and low Prandtl numbers, respectively.

THE 1:2 MODE INTERACTION IN RAYLEIGH–BÉNARD CONVECTION WITH AND WITHOUT BOUSSINESQ SYMMETRY

Nonlinear two-dimensional Rayleigh–Benard convection with periodic boundary conditions in the horizontal is studied for spatial periods near the 1:2 steady state mode interaction. The boundary conditions at the bottom are no-slip, and convection is driven by a fixed imposed temperature difference across the layer. Homotopic continuation is used to continue the boundary conditions at the top from no-slip (β=0) to stress-free (β=1). When β=0 and non-Boussinesq effects are absent the system has midplane reflection symmetry and the 1:2 resonance is weak. When β=1 this symmetry is strongly broken and the resonance is strong. The transition between these two cases is explored for two Prandtl numbers, σ=10 and σ=0.1, representing behavior typical of large and low Prandtl numbers, respectively.

Design of obstacle detection and avoidance system for Guanay II AUV

This paper presents the design of an obstacle avoidance algorithm for Guanay II AUV. The obstacle detection system disposes a SONAR and its use guarantees the safety in navigation of AUV. Obstacle avoidance is performed based on a fuzzy reactive architecture for different forward speeds of the vehicle. The simulation results obtained through the implementation of the algorithms designed in Matlab validate the designs.

Rayleigh-Bénard Convection with Experimental Boundary Conditions

The onset of convection in systems that are heated via current dissipation in the lower boundary or that lose heat from the top boundary via Newton’s law of cooling is formulated as a bifurcation problem. The Rayleigh number as usually defined is shown to be inappropriate as a bifurcation parameter since the temperature across the layer depends on the amplitude of convection and hence changes as convection evolves at fixed external parameter values. Moreover, the final state of the system is also different since it depends on the details of the applied boundary conditions. A modified Rayleigh number is introduced that does remain constant even when the system is evolving, and solutions obtained with the standard formulation are compared with those obtained via the new one.

Real-Time Seismic Data from the Bottom Sea

An anchored marine seismometer, acquiring real-time seismic data, has been built and tested. The system consists of an underwater seismometer, a surface buoy, and a mooring line that connects them. Inductive communication through the mooring line provides an inexpensive, reliable, and flexible solution. Prior to the deployment the dynamics of the system have been simulated numerically in order to find optimal materials, cables, buoys, and connections under critical marine conditions. The seismometer used is a high sensitivity triaxial broadband geophone able to measure low vibrational signals produced by the underwater seismic events. The power to operate the surface buoy is provided by solar panels. Additional batteries are needed for the underwater unit. In this paper we also present the first results and an earthquake detection of a prototype system that demonstrates the feasibility of this concept. The seismometer transmits continuous data at a rate of 1000 bps to a controller equipped with a radio link in the surface buoy. A GPS receiver on the surface buoy has been configured to perform accurate timestamps on the seismic data, which makes it possible to integrate the seismic data from these marine seismometers into the existing seismic network.

Design a vectorial propulsion system for Guanay II AW

The autonomous underwater vehicle (AUV) Guanay II was designed to navigate on the surface of the sea, and to realize a vertical immersion in specific points. This vehicle has three thrusters located on stern, oriented to provide propulsion and yaw control on the horizontal plane. On the other hand, the immersion system used in the Guanay II is based in the change of the buoyancy of the vehicle, by using a piston system. Therefore, the vehicle does not have the ability to navigate in immersion, due to its design, which the inclination of the vehicle (pitch angle) cannot be controlled. In this work, we show the design a vector propulsion system for the vehicle Guanay II, which will allow to control the pitch of the AUV in immersion. For this purpose, we have provided to the two laterals thruster the possibility of varying their propulsion angle on the vertical plane, using two servomotors. Next, we will show the design and the results obtained.

Simulations and design of a sea moored buoy with a real time data undersea seismometer

In this paper we present numerical simulations performed prior to the deployment of a real-time seismic buoy in the Alboran Sea (Western Mediterranean), in an active seismic area at 250–300m depth. Due to the inherent difficulties in underwater communications there are not many real time data available and the implementation of seabed seismic real time networks has been neglected for years. Our system mainly consists of a seabed unit (containing the seismometer), an intermediate buoy and a surface buoy (containing the offshore communication system). Physical connection between seabed and surface buoy allows communications and real time data sending through the mooring cable. Two different mooring possibilities using a steel cable and a combination of a steel cable plus an elastomer were analyzed. Numerical simulations were performed for a specific marine buoy taking into account different sea parameters (waves, winds and currents) under usual and extreme conditions.