Optimal trajectory generation in ocean flows

In this paper it is shown that Lagrangian Coherent Structures (LCS) are useful in determining near optimal trajectories for autonomous underwater gliders in a dynamic ocean environment. This opens the opportunity for optimal path planning of autonomous underwater vehicles by studying the global flow geometry via dynamical systems methods. Optimal glider paths were computed for a 2-dimensional kinematic model of an end-point glider problem. Numerical solutions to the optimal control problem were obtained using Nonlinear Trajectory Generation (NTG) software. The resulting solution is compared to corresponding results on LCS obtained using the Direct Lyapunov Exponent method. The velocity data used for these computations was obtained from measurements taken in August, 2000, by HF-Radar stations located around Monterey Bay, CA

Lagrangian coherent structures in n-dimensional systems

Numerical simulations and experimental observations reveal that unsteady fluid systems can be divided into regions of qualitatively different dynamics. The key to understanding transport and stirring is to identify the dynamic boundaries between these almost-invariant regions. Recently, ridges in finite-time Lyapunov exponent fields have been used to define such hyperbolic, almost material, Lagrangian coherent structures in two-dimensional systems. The objective of this paper is to develop and apply a similar theory in higher dimensional spaces. While the separatrix nature of these structures is their most important property, a necessary condition is their almost material nature. This property is addressed in this paper. These results are applied to a model of Rayleigh-Bénard convection based on a three-dimensional extension of the model of Solomon and Gollub

Design and evaluation of an experimental helical vegetable harvester

This study was conducted to evaluate a basic and new principle for vegetable harvesting. A tractor mounted machine, using an auxiliary engine as the power source, was designed and constructed primarily for harvesting snap beans with limited tests on bell peppers. It incorporated a cylindrical helix and a cylindrical brush as the picking mechanism. Both laboratory and field tests were conducted to determine picking efficiency and plant and fruit damage in relation to the forward speed of the machine, the angular velocity of the helix, and the ratio of the angular velocity of the helix to that of the brush. The average picking efficiency for peppers was 71 percent with a high of 89 percent for one trial. Statistical analysis of the results from laboratory tests and field tests on snap beans showed that all three variables significantly affected both picking efficiency and plant damage. Results from laboratory tests showed that as the speed of the helix increased and the forward speed of the machine decreased, the picking efficiency increased and plant damage decreased for the range of values tested. Results from field tests showed that a 1;1|.5 ratio of angular velocity of the helix to that of the brush resulted in the best picking efficiency and the greatest plant damage for each level of angular velocity of the helix. The highest picking efficiency in the laboratory for snap beans was 97 percent and in the field was 8? percent. Damage to both picked peppers and snap beans was severe; however, it was concluded that the major damage was due to inadequate means for the fruit to exit from the harvester

Lagrangian analysis of fluid transport in empirical vortex ring flows

In this paper we apply dynamical systems analyses and computational tools to fluid transport in empirically measured vortex ring flows. Measurements of quasisteadily propagating vortex rings generated by a mechanical piston-cylinder apparatus reveal lobe dynamics during entrainment and detrainment that are consistent with previous theoretical and numerical studies. In addition, the vortex ring wake of a free-swimming Aurelia aurita jellyfish is measured and analyzed in the framework of dynamical systems to elucidate similar lobe dynamics in a naturally occurring biological flow. For the mechanically generated rings, a comparison of the net entrainment rate based on the present methods with a previous Eulerian analysis shows good correspondence. However, the current Lagrangian framework is more effective than previous analyses in capturing the transport geometry, especially when the flow becomes more unsteady, as in the case of the free-swimming jellyfish. Extensions of these results to more complex flow geometries is suggested