Cascades and Dissipative Anomalies in Compressible Fluid Turbulence

We investigate dissipative anomalies in a turbulent fluid governed by the compressible Navier-Stokes equation. We follow an exact approach pioneered by Onsager, which we explain as a non-perturbative application of the principle of renormalization-group invariance. In the limit of high Reynolds and P\'eclet numbers, the flow realizations are found to be described as distributional or "coarse-grained" solutions of the compressible Euler equations, with standard conservation laws broken by turbulent anomalies. The anomalous dissipation of kinetic energy is shown to be due not only to local cascade, but also to a distinct mechanism called pressure-work defect. Irreversible heating in stationary, planar shocks with an ideal-gas equation of state exemplifies the second mechanism. Entropy conservation anomalies are also found to occur by two mechanisms: an anomalous input of negative entropy (negentropy) by pressure-work and a cascade of negentropy to small scales. We derive "4/5th-law"-type expressions for the anomalies, which allow us to characterize the singularities (structure-function scaling exponents) required to sustain the cascades. We compare our approach with alternative theories and empirical evidence. It is argued that the "Big Power-Law in the Sky" observed in electron density scintillations in the interstellar medium is a manifestation of a forward negentropy cascade, or an inverse cascade of usual thermodynamic entropy

THE EFFECT OF COOPERATIVES ON PRODUCT INNOVATION IN THE AGRI-FOOD SYSTEM

This paper develops a game-theoretic model of heterogeneous consumers to analyze the effect of cooperative involvement on quality-enhancing product innovation activity, the pricing of food products, and the welfare of the groups involved in the context of a mixed duopoly where an openmembership consumer co-op competes with an IOF. Analytical results show that the involvement of the member welfare-maximizing co-op in R&D can be quality and welfare enhancing by increasing the arrival rate of product innovations and reducing the prices of food products. The effectiveness of the coop is shown to depend on the nature of product differentiation and the relative quality of its products, the degree of consumer heterogeneity, and the size of innovation costs.cooperatives, product innovation, mixed oligopoly, retained earnings, Agribusiness,

Turbulent Cascade Direction and Lagrangian Time-Asymmetry

We establish Lagrangian formulae for energy conservation anomalies involving the discrepancy between short-time two-particle dispersion forward and backward in time. These results are facilitated by a rigorous version of the Ott-Mann-Gaw\c{e}dzki relation, sometimes described as a "Lagrangian analogue of the 4/5ths law". In particular, we prove that for any space-time $L^3$ weak solution of the Euler equations, the Lagrangian forward/backward dispersion measure matches on to the energy defect in the sense of distributions. For strong limits of $d\geq3$ dimensional Navier-Stokes solutions the defect distribution coincides with the viscous dissipation anomaly. The Lagrangian formula shows that particles released into a $3d$ turbulent flow will initially disperse faster backward-in-time than forward, in agreement with recent theoretical predictions of Jucha et. al (2014). In two dimensions, we consider strong limits of solutions of the forced Euler equations with increasingly high-wavenumber forcing as a model of an ideal inverse cascade regime. We show that the same Lagrangian dispersion measure matches onto the anomalous input from the infinite-frequency force. As forcing typically acts as an energy source, this leads to the prediction that particles in $2d$ typically disperse faster forward in time than backward, which is opposite to what occurs in $3d$. Time-asymmetry of the Lagrangian dispersion is thereby closely tied to the direction of the turbulent cascade, downscale in $d\geq 3$ and upscale in $d=2$. These conclusions lend support to the conjecture of Eyink & Drivas (2015) that a similar connection holds for time-asymmetry of Richardson two-particle dispersion and cascade direction, albeit at longer times.Comment: 16 pages. Some claims in the proof of Theorem 1 are rigorously justified. Accepted to J. Nonlinear Scienc

THE EFFECT OF MARKETING COOPERATIVES ON COST-REDUCING PROCESS INNOVATION ACTIVITY

This paper examines the market and welfare effects of cooperative involvement in cost-reducing process innovation activity in the context of a mixed oligopsony where an open-membership marketing co-op competes with an IOF. The presence of the marketing co-op is shown to result in increased producer prices and welfare gains for all farmers, members and non-members of the co-op. The effect of the marketing co-op on process innovation activity depends on the relative quality of its final products, the degree of producer heterogeneity, and the size of innovation costs.Agribusiness,