ALBERT

Description: American political campaigns have become a multi-billion dollar industry. Rather than assume that only political factors affect the campaigns that voters see, scholars must assess the importance of the business incentives associated with political consulting. Economic competition does not match political competition; firms compete for clients within the two major parties, against their political allies. I argue that the supply of firms in each party, the revenue models in the industry, the diversification of client types, and the cooperative structure in each party all may affect political campaigns. The way the industry operates and the different patterns of behavior within each party create incentives and practices that may alter campaigns in response to economic factors having little to do with optimal political strategy. Using two original surveys and a network analysis, I analyze how the industry is changing and how consultants in each party cooperate and compete.

Description: Recent work on single-bubble sonoluminescence (SBSL) has shown that many features of this phenomenon, especially the dependence of SBSL intensity and stability on experimental parameters, can be explained within a hydrodynamic approach. More specifically, many important properties can be derived from an analysis of bubble wall dynamics. This dynamics is conveniently described by the Rayleigh-Plesset (RP) equation. Here we derive analytical approximations for RP dynamics and subsequent analytical laws for parameter dependences. These results include (i) an expression for the onset threshold of SL, (ii) an analytical explanation of the transition from diffusively unstable to stable equilibria for the bubble ambient radius (unstable and stable sonoluminescence), and (iii) a detailed understanding of the resonance structure of the RP equation. It is found that the threshold for SL emission is shifted to larger bubble radii and larger driving pressures if surface tension is increased, whereas even a considerable change in liquid viscosity leaves this threshold virtually unaltered. As an enhanced viscosity stabilizes the bubbles to surface oscillations, we conclude that the ideal liquid for violently collapsing, surface-stable SL bubbles should have small surface tension and large viscosity, although too large viscosity (ηl ≳ 40ηwater) will again preclude collapses.

Description: A systematic theory for the scaling of the Nusselt number Nu and of the Reynolds number Re in strong Rayleigh-Benard convection is suggested and shown to be compatible with recent experiments. It assumes a coherent large-scale convection roll ('wind of turbulence') and is based on the dynamical equations both in the bulk and in the boundary layers. Several regimes are identified in the Rayleigh number Ra versus Prandtl number Pr phase space, defined by whether the boundary layer or the bulk dominates the global kinetic and thermal dissipation, respectively, and by whether the thermal or the kinetic boundary layer is thicker. The crossover between the regimes is calculated. In the regime which has most frequently been studied in experiment (Ra ≤ 1011) the leading terms are Nu ~ Ra(1/4) Pr(1/8), Re ~ Ra(1/2) Pr(-3/4) for Pr ≤ 1 and Nu ~ Ra(1/4) Pr(-1/12), Re ~ Ra(1/2) Pr(-5/6) for Pr ≥ 1. In most measurements these laws are modified by additive corrections from the neighbouring regimes so that the impression of a slightly larger (effective) Nu vs. Ra scaling exponent can arise. The most important of the neighbouring regimes towards large Ra are a regime with scaling Nu ~ Ra(1/2) Pr(1/2), Re ~ Ra(1/2) Pr(-1/2) for medium Pr ('Kraichnan regime'), a regime with scaling Nu ~ Ra(1/5) Pr(1/5), Re ~ Ra(2/5) Pr(-3/5) for small Pr, a regime with Nu ~ Ra(1/3), Re ~ Ra(4/9) Pr(-2/3) for larger Pr, and a regime with scaling Nu ~ Ra(3/7) Pr(-1/7), Re ~ Ra(4/7) Pr(-6/7) for even larger Pr. In particular, a linear combination of the 1/4 and the (1/3) power laws for Nu with Ra, Nu = 0.27Ra(1/4) + 0.038Ra(1/3) (the prefactors follow from experiment), mimics a (2/7) power-law exponent in a regime as large as ten decades. For very large Ra the laminar shear boundary layer is speculated to break down through the non-normal-nonlinear transition to turbulence and another regime emerges. The theory presented is best summarized in the phase diagram figure 2 and in table 2.

Description: Turbulent Taylor - Couette flow with arbitrary rotation frequencies ω1, ω2 of the two coaxial cylinders with radii r1 lt; r2 is analysed theoretically. The current Jω of the angular velocity ω(x, t) = uψ(r, ψ, z, t)/r across the cylinder gap and and the excess energy dissipation rate εω due to the turbulent, convective fluctuations (the 'wind') are derived and their dependence on the control parameters analysed. The very close correspondence of Taylor - Couette flow with thermal Rayleigh - Bénard convection is elaborated, using these basic quantities and the exact relations among them to calculate the torque as a function of the rotation frequencies and the radius ratio η = r1/ r2 or the gap width d = r2 - r1 between the cylinders. A quantity σ corresponding to the Prandtl number in Rayleigh - Bénard flow can be introduced, σ = ((1 + η)/2)/√ η)4. In Taylor - Couette fow it characterizes the geometry, instead of material properties of the liquid as in Rayleigh - Bénard flow. The analogue of the Rayleigh number is the Taylor number, de.ned as T α ∞ (ω1 - ω2)2 times a specific geometrical factor. The experimental data show no pure power law, but the exponent a of the torque versus the rotation frequency ω1 depends on the driving frequency ω1. An explanation for the physical origin of the ω1-dependence of the measured local power-law exponents α(ω1) is put forward. Also, the dependence of the torque on the gap width η is discussed and, in particular its strong increase for η → 1. © 2007 Cambridge University Press.

Description: The second-order velocity structure tensor of weakly anisotropic strong turbulence is decomposed into its SO(3) invariant amplitudes dj(r). Their scaling is derived within a scaling approximation of a variable-scale mean-field theory of the Navier-Stokes equation. In the isotropic sector j = O Kolmogorov scaling do(r) α r2/3 is recovered. The scaling of the higher j amplitudes (j even) depends on the type of the external forcing that maintains the turbulent flow. We consider two options: (i) for an analytic forcing and for decreasing energy input into the sectors with increasing j, the scaling of the higher sectors j 〉 O can become as steep as dj(r) α rj+2/3; (ii) for a non-analytic forcing we obtain dj(r) α r4/3 for all non-zero and even j.

Description: Non-Oberbeck-Boussinesq (NOB) effects on the Nusselt number Nu and Reynolds number Re in strongly turbulent Rayleigh-Bénard (RB) convection in liquids were investigated both experimentally and theoretically. In the experiments the heat current, the temperature difference, and the temperature at the horizontal midplane were measured. Three cells of different heights L, all filled with water and all with aspect ratio Γ close to 1, were used. For each L, about 1.5 decades in Ra were covered, together spanning the range 108 ≤ Ra ≤ 1011. For the largest temperature difference between the bottom and top plates, Δ = 40 K, the kinematic viscosity and the thermal expansion coefficient, owing to their temperature dependence, varied by more than a factor of 2. The Oberbeck-Boussinesq (OB) approximation of temperature-independent material parameters thus was no longer valid. The ratio χ of the temperature drops across the bottom and top thermal boundary layers became as small as χ = 0.83, which may be compared with the ratio χ = 1 in the OB case. Nevertheless, the Nusselt number Nu was found to be only slightly smaller (by at most 1.4%) than in the next larger cell with the same Rayleigh number, where the material parameters were still nearly height independent. The Reynolds numbers in the OB and NOB case agreed with each other within the experimental resolution of about 2%, showing that NOB effects for this parameter were small as well. Thus Nu and Re are rather insensitive against even significant deviations from OB conditions. Theoretically, we first account for the robustness of Nu with respect to NOB corrections: the NOB effects in the top boundary layer cancel those which arise in the bottom boundary layer as long as they are linear in the temperature difference Δ. The net effects on Nu are proportional to Δ2 and thus increase only slowly and still remain minor despite drastic material-parameter changes. We then extend the Prandtl-Blasius boundary-layer theory to NOB Rayleigh-Bénard flow with temperature-dependent viscosity and thermal diffusivity. This allows calculation of the shift in the bulk temperature, the temperature drops across the boundary layers, and the ratio χ without the introduction of any fitting parameter. The calculated quantities are in very good agreement with experiment. When in addition we use the experimental finding that for water the sum of the top and bottom thermal boundary-layer widths (based on the slopes of the temperature profiles at the plates) remains unchanged under NOB effects within the experimental resolution, the theory also gives the measured small Nusselt-number reduction for the NOB case. In addition, it predicts an increase by about 0.5% of the Reynolds number, which is also consistent with the experimental data. By studying theoretically hypothetical liquids for which only one of the material parameters is temperature dependent, we are able to shed further light on the origin of NOB corrections in water: while the NOB deviation of χ from its OB value χ = 1 mainly originates from the temperature dependence of the viscosity, the NOB correction of the Nusselt number primarily originates from the temperature dependence of the thermal diffusivity. Finally, we give predictions from our theory for the NOB corrections if glycerol were used as the operating liquid. © 2006 Cambridge University Press.

Description: Non-OberbeckBoussinesq (NOB) effects on the flow organization in two-dimensional Rayleigh-Bénard turbulence are numerically analysed. The working fluid is water. We focus on the temperature profiles, the centre temperature, the Nusselt number and on the analysis of the velocity field. Several velocity amplitudes (or Reynolds numbers) and several kinetic profiles are introduced and studied; these together describe the various features of the rather complex flow organization. The results are presented both as functions of the Rayleigh number Ra (with Ra up to 108) for fixed temperature difference δ between top and bottom plates and as functions of δ(non-OberbeckBoussinesqness) for fixed Ra with δ up to 60K. All results are consistent with the available experimental NOB data for the centre temperature Tc and the Nusselt number ratio NuNOB/NuOB (the label OB meaning that the OberbeckBoussinesq conditions are valid). For the temperature profiles we find due to plume emission from the boundary layers increasing deviations from the extended PrandtlBlasius boundary layer theory presented in Ahlers et al. (J. Fluid Mech., vol. 569, 2006, p. 409) with increasing Ra, while the centre temperature itself is surprisingly well predicted by that theory. For given non-OberbeckBoussinesqness, both the centre temperature Tc and the Nusselt number ratio NuNOB/NuOB only weakly depend on Ra in the Ra range considered here. Beyond Ra 106 the flow consists of a large diagonal centre convection roll and two smaller rolls in the upper and lower corners, respectively (corner flows). Also in the NOB case the centre convection roll is still characterized by only one velocity scale. In contrast, the top and bottom corner flows are then of different strengths, the bottom one being a factor 1.3 faster (for δ = 40K) than the top one, due to the lower viscosity in the hotter bottom boundary layer. Under NOB conditions the enhanced lower corner flow as well as the enhanced centre roll lead to an enhancement of the volume averaged energy based Reynolds number ReE= 1/221/2L/v of about 4% to 5% for δ = 60K. Moreover, we find ReE NOBReEOB≈ (β (Tc)/beta (Tm))1/2, with the thermal expansion coefficient and Tm the arithmetic mean temperature between top and bottom plate temperatures. This corresponds to the ratio of the free fall velocities at the respective temperatures. By artificially switching off the temperature dependence of in the numerics, the NOB modifications of ReE is less than 1% even at = 60K, revealing the temperature dependence of the thermal expansion coefficient as the main origin of the NOB effects on the global Reynolds number in water. © 2009 Copyright Cambridge University Press.

Description: Various recent experiments hint at a geometry dependence of scaling relations in Rayleigh-Bénard convection. Aspect ratio and shape dependences have been found. In this paper a mechanism is suggested which can account for such dependences, based on Prandtl's theory for laminar boundary layers and on the conservation of volume flux of the large-scale wind. The mechanism implies the possibility of different thickness of the kinetic boundary layers at the sidewalls and at the top/bottom plates, as found experimentally, and also different Ra-scaling of the wind over the plates and at the sidewalls. A scaling argument for the velocity and temperature fluctuations in the bulk is also developed.

Description: We present a numerical strategy that allows us to explore the full scope of the Doering-Constantin variational principle for computing rigorous upper bounds on energy dissipation in turbulent shear flow. The key is the reformulation of this principle's spectral constraint as a boundary value problem that can be solved efficiently for all Reynolds numbers of practical interest. We state results obtained for the plane Couette flow, and investigate in detail a simplified model problem that can serve as a definite guide for the application of the variational principle to other flows. The most notable findings are a bifurcation of the minimizing wavenumber and a pronounced minimum of the bound at intermediate Reynolds numbers, and a distinct asymptotic scaling of the optimized variational parameters.