Reynolds stresses and mean fields generated by pure waves: applications to shear flows and convection in a rotating shell

A general reformulation of the Reynolds stresses created by two-dimensional waves breaking a translational or a rotational invariance is described. This reformulation emphasizes the importance of a geometrical factor: the slope of the separatrices of the wave flow. Its physical relevance is illustrated by two model systems: waves destabilizing open shear flows; and thermal Rossby waves in spherical shell convection with rotation. In the case of shear-flow waves, a new expression of the Reynolds–Orr amplification mechanism is obtained, and a good understanding of the form of the mean pressure and velocity fields created by weakly nonlinear waves is gained. In the case of thermal Rossby waves, results of a three-dimensional code using no-slip boundary conditions are presented in the nonlinear regime, and compared with those of a two-dimensional quasi-geostrophic model. A semi-quantitative agreement is obtained on the flow amplitudes, but discrepancies are observed concerning the nonlinear frequency shifts. With the quasi-geostrophic model we also revisit a geometrical formula proposed by Zhang to interpret the form of the zonal flow created by the waves, and explore the very low Ekman-number regime. A change in the nature of the wave bifurcation, from supercritical to subcritical, is found

Inertial convection in rotating fluid spheres

The onset of convection in the form of inertial waves in a rotating fluid sphere is studied through a perturbation analysis in an extension of earlier work by Zhang (1994). Explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived and new results for the case of a nearly thermally insulating boundary are obtained

Prandtl-number dependence of convection-driven dynamos in rotating spherical fluid shells

The value of the Prandtl number P exerts a strong influence on convection-driven dynamos in rotating spherical shells filled with electrically conducting fluids. Low Prandtl numbers promote dynamo action through the shear provided by differential rotation, while the generation of magnetic fields is more difficult to sustain in high-Prandtl-number fluids where higher values of the magnetic Prandtl number Pm are required. The magnetostrophic approximation often used in dynamo theory appears to be valid only for relatively high values of P and Pm. Dynamos with a minimum value of Pm seem to be most readily realizable in the presence of convection columns at moderately low values of P. The structure of the magnetic field varies strongly with P in that dynamos with a strong axial dipole field are found for high values of P while the energy of this component is exceeded by that of the axisymmetric toroidal field and by that of the non-axisymmetric components at low values of P. Some conclusions are discussed in relation to the problem of the generation of planetary magnetic fields by motions in their electrically conducting liquid cores

Mobile Aerobee launch facility

Mobile Aerobee Launch Facilit

Bistability and hysteresis of dipolar dynamos generated by turbulent convection in rotating spherical shells

Bistability and hysteresis of magnetohydrodynamic dipolar dynamos generated by turbulent convection in rotating spherical fluid shells is demonstrated. Hysteresis appears as a transition between two distinct regimes of dipolar dynamos with rather different properties including a pronounced difference in the amplitude of the axisymmetric poloidal field component and in the form of the differential rotation. The bistability occurs from the onset of dynamo action up to about 9 times the critical value of the Rayleigh number for onset of convection and over a wide range of values of the ordinary and the magnetic Prandtl numbers including the value unity

Magneto-inertial convection in rotating fluid spheres

The onset of convection in the form of magneto-inertial waves in a rotating fluid sphere permeated by a constant axial electric current is studied through a perturbation analysis. Explicit expressions for the dependence of the Rayleigh number on the azimuthal wavenumber are derived in the limit of high thermal diffusivity. Results for the cases of thermally infinitely conducting and of nearly thermally insulating boundaries are obtained.Comment: 10 pages, 5 figures, to be submitted for publicatio

Who Wins the Olympic Games: Economic Development and Medal Totals

This paper examines determinants of Olympic success at the country level. Does the U.S. win its fair share of Olympic medals? Why does China win 6% of the medals even though it has 1/5 of the world's population? We consider the role of population and economic development in determining medal totals from 1960-1996. We also provide out of sample predictions for the 2000 Olympics in Sydney.

Aerobee 150 structural and aerodynamic pitch coupling

Aerobee 150 structural and aerodynamic pitch coupling failure analysis based on flight performance data reductio

"The Best Price You'll Ever Get" The 2005 Employee Discount Pricing Promotions in the U.S. Automobile Industry

During the summer of 2005, the Big Three U.S. automobile manufacturers offered a customer promotion that allowed customers to buy new cars at the discounted price formerly offered only to employees. The initial months of the promotion were record sales months for each of the Big Three firms, suggesting that customers thought that the prices offered during the promotions were particularly attractive. In fact, such large rebates had been available before the employee discount promotion that many customers paid higher prices following the introduction of the promotions than they would have in the weeks just before. We hypothesize that the complex nature of auto prices, the fact that prices are negotiated rather than posted, and the fact that buyers do not participate frequently in the market leads customers to rely on "price cues" in evaluating how good current prices are. We argue that the employee discount pricing promotions were price cues, and that customers responded to the promotions as a signal that prices were discounted.