Scaling and Linear Response in the GOY Turbulence model

The GOY model is a model for turbulence in which two conserved quantities cascade up and down a linear array of shells. When the viscosity parameter, $\nu$, is small the model has a qualitative behavior which is similar to the Kolmogorov theories of turbulence. Here a static solution to the model is examined, and a linear stability analysis is performed to obtain response eigenvalues and eigenfunctions. Both the static behavior and the linear response show an inertial range with a relatively simple scaling structure. Our main results are: (i) The response frequencies cover a wide range of scales, with ratios which can be understood in terms of the frequency scaling properties of the model. (ii) Even small viscosities play a crucial role in determining the model's eigenvalue spectrum. (iii) As a parameter within the model is varied, it shows a ``phase transition'' in which there is an abrupt change in many eigenvalues from stable to unstable values. (iv) The abrupt change is determined by the model's conservation laws and symmetries. This work is thus intended to add to our knowledge of the linear response of a stiff dynamical systems and at the same time to help illuminate scaling within a class of turbulence models.Comment: 25 pages, figures on reques

Wind Farm Wake: The Horns Rev Photo Case

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Enzyme prodrug therapy achieves site-specific, personalized physiological responses to the locally produced nitric oxide

Nitric oxide (NO) is a highly potent but short-lived endogenous radical with a wide spectrum of physiological activities. In this work, we developed an enzymatic approach to the site-specific synthesis of NO mediated by biocatalytic surface coatings. Multilayered polyelectrolyte films were optimized as host compartments for the immobilized β-galactosidase (β-Gal) enzyme through a screen of eight polycations and eight polyanions. The lead composition was used to achieve localized production of NO through the addition of β-Gal–NONOate, a prodrug that releases NO following enzymatic bioconversion. The resulting coatings afforded physiologically relevant flux of NO matching that of the healthy human endothelium. The antiproliferative effect due to the synthesized NO in cell culture was site-specific: within a multiwell dish with freely shared media and nutrients, a 10-fold inhibition of cell growth was achieved on top of the biocatalytic coatings compared to the immediately adjacent enzyme-free microwells. The physiological effect of NO produced via the enzyme prodrug therapy was validated ex vivo in isolated arteries through the measurement of vasodilation. Biocatalytic coatings were deposited on wires produced using alloys used in clinical practice and successfully mediated a NONOate concentration-dependent vasodilation in the small arteries of rats. The results of this study present an exciting opportunity to manufacture implantable biomaterials with physiological responses controlled to the desired level for personalized treatment

How the viscous subrange determines inertial range properties in turbulence shell models

We calculate static solutions of the 'GOY' shell model of turbulence and do a linear stability analysis. The asymptotic limit of large Reynolds numbers is analyzed. A phase diagram is presented which shows the range of stability of the static solution. We see an unexpected oscillatory dependence of the stability range upon $\lg \nu$, where $\nu$ is the viscosity. This effect depends upon the discrete structure of the shell model and goes to zero as the separation between the shells is brought to zero. These findings show how viscous effects play a role in determining inertial properties of shell models and give some hints for understanding the effects of viscous dissipation upon real turbulence.Comment: Physica D, in pres