Tidal interactions of a Maclaurin spheroid. I: Properties of free oscillation modes

We review the work of Bryan (1889) on the normal modes of a Maclaurin spheroid, carrying out numerical calculations of the frequencies and spatial forms of these modes that have not been previously published. We study all modes of degree $l \le 4$, which includes both inertial modes and surface gravity modes, with the aim of better understanding the effect of rapid rotation on tidal interactions. The inclusion of these higher degree modes greatly increases the number of frequencies at which tidal resonances may occur. We derive an expression for the decay rates of these modes to first order in viscosity and explicitly plot these for modes. We see that the equatorial bulge of the spheroid has a significant effect on the decay rates (changing some of these by a factor of 2 between an eccentricity of $e=0$ and $0.5$), and a more modest effect on the mode frequencies. This suggests that models of tidal interaction between rapidly rotating stars and giant planets that model the Coriolis force while neglecting the centrifugal distortion of the body may be in error by an order unity factor. In a subsequent paper we shall examine the case of a forced flow in this spheroid, and complete the model by considering how the tides raised by the orbiting companion change the orbital elements.Comment: 27 pages, 39 figures, 1 table, accepted for publication in MNRA

Take A Number From One To Ten

Photographs of male cast members of College Rhythm playing stringed instruments with Hellen Mack standing in middlehttps://scholarsjunction.msstate.edu/cht-sheet-music/11520/thumbnail.jp

I\u27ve Got A Date With A Dream

https://digitalcommons.library.umaine.edu/mmb-vp-copyright/8216/thumbnail.jp

Persistence of chlorpropham (CIPC) in the concrete flooring of potato stores

The loss of the sprout suppressant, chlorpropham (CIPC), to the fabric of potato stores is currently of concern due to the risk of potential cross contamination of other crops subsequently housed in these stores. HPLC UV/VIS and GCMS methods were successfully employed to detect CIPC in the concrete flooring of research and commercial potato stores with histories of between 1 and 26 years of use. The concentrations in identical research stores, with different numbers of applications, were in the range 0.58–5.7 and 3.4–112 μg g−1, suggesting the magnitude of contamination was influenced by the number of applications. Commercial store A, with a history of 18 seasons of applications (estimate of total CIPC applied 2040 kg), had concentrations varying between 6 and 48 μg g−1 in the top three centimetres, with more than 92% within the top centimetre. In contrast, commercial store B, with a history of less than five seasons of applications (estimate of total CIPC applied 319 kg), had concentrations varying between 0.58 and 304 μg g−1 in the top four centimetres, with less than 47% within the top centimetre. The difference in depth distributions between A and B may be due to the structural integrity of the concrete, which was much poorer in B. CIPC was persistent in all stores irrespective of the total quantities of CIPC applied and date of the final application

Short-Run Economic Impacts of Hurricane Katrina (and Rita)

Sturm; Erdölförderung; Offshore-Industrie; Makroökonomischer Einfluss; USA

Simulation evaluation of a low-altitude helicopter flight guidance system adapted for a helmet-mounted display

A computer aiding concept for low-altitude helicopter flight was developed and evaluated in a real-time piloted simulation. The concept included an optimal control trajectory-generation algorithm based upon dynamic programming and a helmet-mounted display (HMD) presentation of a pathway-in-the-sky, a phantom aircraft, and flight-path vector/predictor guidance symbology. The trajectory-generation algorithm uses knowledge of the global mission requirements, a digital terrain map, aircraft performance capabilities, and advanced navigation information to determine a trajectory between mission way points that seeks valleys to minimize threat exposure. The pilot evaluation was conducted at NASA ARC moving base Vertical Motion Simulator (VMS) by pilots representing NASA, the U.S. Army, the Air Force, and the helicopter industry. The pilots manually tracked the trajectory generated by the algorithm utilizing the HMD symbology. The pilots were able to satisfactorily perform the tracking tasks while maintaining a high degree of awareness of the outside world