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The initial development of the two dimensional viscous, incompressible flow induced by an impulsively started circular cylinder which performs time dependent sinusoidal rotational oscillations about its axis is investigated numerically. The investigation is based on the solutions of stream function-vorticity formulation of Navier-Stokes equations on non-uniform polar grids using higher order compact formulation. The numerical method is validated by comparing the computed results with existing experimental and numerical results for Reynolds numbers Re = 150 and 500. The effects of forced oscillation frequency f and peak rotation rate αm on the early development of the flow structure in the near wake region are discussed. Results are given for the initial development with time of the flow structure at the rear of the cylinder at Re = 200. The details of the formation, movement, closure points, and strengths of the vortices behind the cylinder are presented. The velocity profiles at different locations and vorticity profiles at the surface of the cylinder are also shown. The effect of increase in αm on the timing of the formation of the vortices, the closed wake length, and the thickness of the boundary layer is investigated.

This study investigates the risk from oil spills along the main shipping lane in the Red Sea based upon oil spill model trajectories forced by the outputs of validated high resolution regional met-ocean data. Following the intra-annual variations in the met-ocean conditions, the results are presented by classifying the basin into three regions: northern, central and southern Red Sea. The maximum distance traveled by the slick is presented for 1, 2, 5, 10, 14 and 20 days after the commencement of a spill. Different measures of hazard assessment in terms of the concentration of beached oil alongside the corresponding probability maps are also analyzed. The volume fractions of beached, dispersed and evaporated oil, 20 days after the commencement of a spill are quantified. The Red Sea general circulation is characterized by rich mesoscale eddies, which appear to be the most prevailing dynamics in oil transport in the basin. Two case events are analyzed to closely examine the effects of the mesoscale circulations on the fate of spilled oil. The results of this study provide a comprehensive assessment of oil spill hazards in the Red Sea, stemming its main shipping lane and identifies the areas at high risk that require timely mitigation strategies.

Summary In this paper, we propose a new methodology for numerically solving elliptic and parabolic equations with discontinuous coefficients and singular source terms. This new scheme is obtained by clubbing a recently developed higher‐order compact methodology with special interface treatment for the points just next to the points of discontinuity. The overall order of accuracy of the scheme is at least second. We first formulate the scheme for one‐dimensional (1D) problems, and then extend it directly to two‐dimensional (2D) problems in polar coordinates. In the process, we also perform convergence and related analysis for both the cases. Finally, we show a new direction of implementing the methodology to 2D problems in cartesian coordinates. We then conduct numerous numerical studies on a number of problems, both for 1D and 2D cases, including the flow past circular cylinder governed by the incompressible Navier–Stokes equations. We compare our results with existing numerical and experimental results. In all the cases, our formulation is found to produce better results on coarser grids. For the circular cylinder problem, the scheme used is seen to capture all the flow characteristics including the famous von Kármán vortex street. Copyright © 2016 John Wiley & Sons, Ltd.

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