Abstract: We explore the application of a pseudo-spectral Fourier method to a set of reaction-diffusion equations and compare it with a second-order finite difference method. The prototype cubic autocatalytic reaction-diffusion model as discussed by Gray and Scott [Chem. Eng. Sci. 42, 307 (1987)] with a nonequilibrium constraint is adopted. In a spatial resolution study we find that the phase speeds of one-dimensional finite amplitude waves converge more rapidly for the spectral method than for the finite difference method. Furthermore, in two dimensions the symmetry preserving properties of the spectral method are shown to be superior to those of the finite difference method. In studies of plane/axisymmetric nonlinear waves a symmetry breaking linear instability is shown to occur and is one possible route for the formation of patterns from infinitesimal perturbations to finite amplitude waves in this set of reaction-diffusion equations. (c) 1996 American Institute of Physics.

Abstract: The thermal energy needed for the development of hurricanes and monsoons as well as any prolonged marine weather event comes from layers in the upper oceans, not just from the thin layer represented by sea surface temperature alone. Ocean layers have different modes of thermal energy variability because of the different time scales of ocean–atmosphere interaction. Although many previous studies have focused on the influence of upper ocean heat content (OHC) on tropical cyclones and monsoons, no study thus far—particularly in the North Indian Ocean (NIO)—has specifically concluded the types of dominant modes in different layers of the ocean. In this study, we examined the dominant modes of variability of OHC of seven layers in the NIO during 1998–2014. We conclude that the thermal variability in the top 50 m of the ocean had statistically significant semiannual and annual modes of variability, while the deeper layers had the annual mode alone. Time series of OHC for the top four layers were analyzed separately for the NIO, Arabian Sea, and Bay of Bengal. For the surface to 50 m layer, the lowest and the highest values of OHC were present in January and May every year, respectively, which was mainly caused by the solar radiation cycle.

Abstract: Concurrent measurements by satellite tracked drifters of different hull and drogue configurations and coastal high-frequency radar reveal substantial differences in estimates of the near-surface velocity. These measurements are important for understanding and predicting material transport on the ocean surface as well as the vertical structure of the near-surface currents. These near-surface current observations were obtained during a field experiment in the northern Gulf of Mexico intended to test a new ultra-thin drifter design. During the experiment, thirty small cylindrical drifters with 5 cm height, twenty-eight similar drifters with 10 cm hull height, and fourteen drifters with 91 cm tall drogues centered at 100 cm depth were deployed within the footprint of coastal High-Frequency (HF) radar. Comparison of collocated velocity measurements reveals systematic differences in surface velocity estimates obtained from the different measurement techniques, as well as provides information on properties of the drifter behavior and near-surface shear. Results show that the HF radar velocity estimates had magnitudes significantly lower than the 5 cm and 10 cm drifter velocity of approximately 45% and 35%, respectively. The HF radar velocity magnitudes were similar to the drogued drifter velocity. Analysis of wave directional spectra measurements reveals that surface Stokes drift accounts for much of the velocity difference between the drogued drifters and the thin surface drifters except during times of wave breaking.