Forced Rossby waves in a basin with a meridional barrier and bottom friction

The forced, linear, Rossby wave solution for a barotropic fluid in a square basin on a b plane containing a thin, continuous but pierced meridional barrier is examined. The forcing is zonally localized and vorticity is removed through bottom friction. The forcing is applied east of the barrier and is periodic in time. To the north and south of the barrier there are small gaps of equal width d separating the barrier from the basin walls. The value of the stream function on the walls of the basin is zero while the value of the stream function on the barrier, CI , is a function of time, the forcing structure and the forcing frequency. CI is determined by an application of Kelvin’s theorem on a contour about the barrier and its value gives the flux between the two sub-basins that are formed by the barrier. The variance of the stream function is explored as a function of the forcing frequency for different meridional structures of the forcing. We investigate symmetric, antisymmetric, and asymmetric forcings about the mid-latitude of the basin. Peaks in the variance occur at frequencies where the solution is dominated by a full basin or sub-basin mode. It was found that modes which were antisymmetric about the mid-latitude could not propagate past the barrier, while modes which were symmetric about the mid-latitude always had some propagation past the barrier. For the case of eastern sub-basin modes which are symmetric about the mid-latitude this propagation is minute. The sensitivity of the solutions to bottom friction is also discussed. As friction is increased, the peaks in the variance become broader and begin to merge. At sufficiently high values of bottom friction a combination of modes, rather than one single mode, dominates the solution at a peak frequency

Automated acoustic intensity measurements and the effect of gear tooth profile on noise

Acoustic intensity measurements were made at NASA Lewis Research Center on a spur gear test apparatus. The measurements were obtained with the Robotic Acoustic Intensity Measurement System developed by Cleveland State University. This system provided dense spatial positioning, and was calibrated against a high quality acoustic intensity system. The measured gear noise compared gearsets having two different tooth profiles. The tests evaluated the sound field of the different gears for two speeds and three loads. The experimental results showed that gear tooth profile had a major effect on measured noise. Load and speed were found to have an effect on noise also

An Energy-Minimization Finite-Element Approach for the Frank-Oseen Model of Nematic Liquid Crystals: Continuum and Discrete Analysis

This paper outlines an energy-minimization finite-element approach to the computational modeling of equilibrium configurations for nematic liquid crystals under free elastic effects. The method targets minimization of the system free energy based on the Frank-Oseen free-energy model. Solutions to the intermediate discretized free elastic linearizations are shown to exist generally and are unique under certain assumptions. This requires proving continuity, coercivity, and weak coercivity for the accompanying appropriate bilinear forms within a mixed finite-element framework. Error analysis demonstrates that the method constitutes a convergent scheme. Numerical experiments are performed for problems with a range of physical parameters as well as simple and patterned boundary conditions. The resulting algorithm accurately handles heterogeneous constant coefficients and effectively resolves configurations resulting from complicated boundary conditions relevant in ongoing research.Comment: 31 pages, 3 figures, 3 table