Trkalian fields and Radon transformation

We write the spherical curl transformation for Trkalian fields using differential forms. Then we consider Radon transform of these fields. The Radon transform of a Trkalian field satisfies a corresponding eigenvalue equation on a sphere in transform space. The field can be reconstructed using knowledge of the Radon transform on a canonical hemisphere. We consider relation of the Radon transformation with Biot-Savart integral operator and discuss its transform introducing Radon-Biot- Savart operator. The Radon transform of a Trkalian field is an eigenvector of this operator. We also present an Ampere law type relation for these fields. We apply these to Lundquist solution. We present a Chandrasekhar-Kendall type solution of the corresponding equation in the transform space. Lastly, we focus on the Euclidean topologically massive Abelian gauge theory. The Radon transform of an anti-self-dual field is related by antipodal map on this sphere to the transform of the self-dual field obtained by inverting space coordinates. The Lundquist solution provides an example of quantization of topological mass in this context.Comment: 23 page

Guiding of Rydberg atoms in a high-gradient magnetic guide

We study the guiding of $^{87}$Rb 59D$_{5/2}$ Rydberg atoms in a linear, high-gradient, two-wire magnetic guide. Time delayed microwave ionization and ion detection are used to probe the Rydberg atom motion. We observe guiding of Rydberg atoms over a period of 5 ms following excitation. The decay time of the guided atom signal is about five times that of the initial state. We attribute the lifetime increase to an initial phase of $l$-changing collisions and thermally induced Rydberg-Rydberg transitions. Detailed simulations of Rydberg atom guiding reproduce most experimental observations and offer insight into the internal-state evolution

Possible geopotential improvement from satellite altimetry

Possible geopotential improvement from satellite altimetr

Plasma Relaxation and Topological Aspects in Hall Magnetohydrodynamics

Parker's formulation of isotopological plasma relaxation process in magnetohydrodynamics (MHD) is extended to Hall MHD. The torsion coefficient alpha in the Hall MHD Beltrami condition turns out now to be proportional to the "potential vorticity." The Hall MHD Beltrami condition becomes equivalent to the "potential vorticity" conservation equation in two-dimensional (2D) hydrodynamics if the Hall MHD Lagrange multiplier beta is taken to be proportional to the "potential vorticity" as well. The winding pattern of the magnetic field lines in Hall MHD then appears to evolve in the same way as "potential vorticity" lines in 2D hydrodynamics

Evaluation of the wind farm parameterization in the Weather Research and Forecasting model (version 3.8.1) with meteorological and turbine power data

Abstract. Forecasts of wind power production are necessary to facilitate the integration of wind energy into power grids, and these forecasts should incorporate the impact of wind turbine wakes. This paper focuses on a case study of four diurnal cycles with significant power production, and assesses the skill of the wind farm parameterization (WFP) distributed with the Weather Research and Forecasting (WRF) model version 3.8.1, as well as its sensitivity to model configuration. After validating the simulated ambient flow with observations, we quantify the value of the WFP as it accounts for wake impacts on power production of downwind turbines. We also illustrate that a vertical grid with nominally 12-m vertical resolution is necessary for reproducing the observed power production, with statistical significance. Further, the WFP overestimates wake effects and hence underestimates downwind power production during high wind speed and low turbulence conditions. We also find the WFP performance is independent of atmospheric stability, the number of wind turbines per model grid cell, and the upwind-downwind position of turbines. Rather, the ability of the WFP to predict power production is most dependent on the skill of the WRF model in simulating the ambient wind speed. </jats:p

US East Coast lidar measurements show offshore wind turbines will encounter very low atmospheric turbulence

© The Author(s), 2019. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Bodini, N., Lundquist, J. K., & Kirincich, A. US East Coast lidar measurements show offshore wind turbines will encounter very low atmospheric turbulence. Geophysical Research Letters, 46(10), (2019):5582-5591, doi:10.1029/2019GL082636.The rapid growth of offshore wind energy requires accurate modeling of the wind resource, which can be depleted by wind farm wakes. Turbulence dissipation rate (ϵ) governs the accuracy of model predictions of hub‐height wind speed and the development and erosion of wakes. Here we assess the variability of turbulence kinetic energy and ϵ using 13 months of observations from a profiling lidar deployed on a platform off the Massachusetts coast. Offshore, ϵ is 2 orders of magnitude smaller than onshore, with a subtle diurnal cycle. Wind direction influences the annual cycle of turbulence, with larger values in winter when the wind flows from the land, and smaller values in summer, when the wind flows from open ocean. Because of the weak turbulence, wind plant wakes will be stronger and persist farther downwind in summer.Collection of the wind data was funded by the Massachusetts Clean Energy Center through agreements with WHOI and AWS Truepower. The authors appreciate the efforts of the MVCO/ASIT technicians and AWS staff who collected the data. This analysis was supported by the National Science Foundation CAREER Award (AGS‐1554055) to J. K. L. and N. B., and by internal funds from WHOI for A. K. This work was authored (in part) by the National Renewable Energy Laboratory, operated by Alliance for Sustainable Energy, LLC, for the U.S. Department of Energy (DOE) under Contract DE‐AC36‐08GO28308. Funding was provided by the U.S. Department of Energy Office of Energy Efficiency and Renewable Energy Wind Energy Technologies Office. The views expressed in the article do not necessarily represent the views of the DOE or the U.S. Government. The U.S. Government retains and the publisher, by accepting the article for publication, acknowledges that the U.S. Government retains a nonexclusive, paid‐up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for U.S. Government purposes. The lidar observations used here are described at https://www.masscec.com/masscec-metocean-data-initiative, and available at https://doi.org/10.26025/1912/24050. The postprocessed data and the scripts used for the Figures of the present paper can be found at https://github.com/nicolabodini/GRL_OffshoreTurbulence.2019-11-0

On the jets, kinks, and spheromaks formed by a planar magnetized coaxial gun

Measurements of the various plasma configurations produced by a planar magnetized coaxial gun provide insight into the magnetic topology evolution resulting from magnetic helicity injection. Important features of the experiments are a very simple coaxial gun design so that all observed geometrical complexity is due to the intrinsic physical dynamics rather than the source shape and use of a fast multiple-frame digital camera which provides direct imaging of topologically complex shapes and dynamics. Three key experimental findings were obtained: (1) formation of an axial collimated jet [Hsu and Bellan, Mon. Not. R. Astron. Soc. 334, 257 (2002)] that is consistent with a magnetohydrodynamic description of astrophysical jets, (2) identification of the kink instability when this jet satisfies the Kruskal-Shafranov limit, and (3) the nonlinear properties of the kink instability providing a conversion of toroidal to poloidal flux as required for spheromak formation by a coaxial magnetized source [Hsu and Bellan, Phys. Rev. Lett. 90, 215002 (2003)]. A new interpretation is proposed for how the n=1 central column instability provides flux amplification during spheromak formation and sustainment, and it is shown that jet collimation can occur within one rotation of the background poloidal field.Comment: Physics of Plasmas (accepted

Estimation of turbulence dissipation rate and its variability from sonic anemometer and wind Doppler lidar during the XPIA field campaign

Despite turbulence being a fundamental transport process in the boundary layer, the capability of current numerical models to represent it is undermined by the limits of the adopted assumptions, notably that of local equilibrium. Here we leverage the potential of extensive observations in determining the variability in turbulence dissipation rate (ϵ). These observations can provide insights towards the understanding of the scales at which the major assumption of local equilibrium between generation and dissipation of turbulence is invalid. Typically, observations of ϵ require time- and labor-intensive measurements from sonic and/or hot-wire anemometers. We explore the capability of wind Doppler lidars to provide measurements of ϵ. We refine and extend an existing method to accommodate different atmospheric stability conditions. To validate our approach, we estimate ϵ from four wind Doppler lidars during the 3-month XPIA campaign at the Boulder Atmospheric Observatory (Colorado), and we assess the uncertainty of the proposed method by data intercomparison with sonic anemometer measurements of ϵ. Our analysis of this extensive dataset provides understanding of the climatology of turbulence dissipation over the course of the campaign. Further, the variability in ϵ with atmospheric stability, height, and wind speed is also assessed. Finally, we present how ϵ increases as nocturnal turbulence is generated during low-level jet events.</p

An LES-based airborne Doppler lidar simulator and its application to wind profiling in inhomogeneous flow conditions

Wind profiling by Doppler lidar is common practice and highly useful in a wide range of applications. Airborne Doppler lidar can provide additional insights relative to ground-based systems by allowing for spatially distributed and targeted measurements. Providing a link between theory and measurement, a first large eddy simulation (LES)-based airborne Doppler lidar simulator (ADLS) has been developed. Simulated measurements are conducted based on LES wind fields, considering the coordinate and geometric transformations applicable to real-world measurements. The ADLS provides added value as the input truth used to create the measurements is known exactly, which is nearly impossible in real-world situations. Thus, valuable insight can be gained into measurement system characteristics as well as retrieval strategies. As an example application, airborne Doppler lidar wind profiling is investigated using the ADLS. For commonly used airborne velocity azimuth display (AVAD) techniques, flow homogeneity is assumed throughout the retrieval volume, a condition which is violated in turbulent boundary layer flow. Assuming an ideal measurement system, the ADLS allows to isolate and evaluate the error in wind profiling which occurs due to the violation of the flow homogeneity assumption. Overall, the ADLS demonstrates that wind profiling is possible in turbulent wind field conditions with reasonable errors (root mean squared error of 0.36 m s−1 for wind speed when using a commonly used system setup and retrieval strategy for the conditions investigated). Nevertheless, flow inhomogeneity, e.g., due to boundary layer turbulence, can cause an important contribution to wind profiling error and is non-negligible. Results suggest that airborne Doppler lidar wind profiling at low wind speeds (<5ms −1) can be biased, if conducted in regions of inhomogeneous flow conditions