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Abstract Several new methods are proposed that can diagnose the interscale transfer (or spectral flux) of kinetic energy (KE) and other properties in oceanic and broader geophysical systems, using integrals of advective structure functions and Bessel functions (herein “Bessel methods”). The utility of the Bessel methods is evaluated using simulations of anisotropic flow within two-dimensional (2D), surface quasigeostrophic (SQG), and two-layer QG systems. The Bessel methods diagnose various spectral fluxes within all of these systems, even under strong anisotropy and complex dynamics (e.g., multiple cascaded variables, coincident and opposing spectral fluxes, and nonstationary systems). In 2D turbulence, the Bessel methods capture the inverse KE cascade at large scales and the downscale enstrophy cascade (and associated downscale energy flux) at small scales. In SQG turbulence, the Bessel methods capture the downscale buoyancy variance cascade and the coincident upscale wavenumber-dependent KE flux. In QG turbulence, the Bessel methods capture the upscale kinetic energy flux. It is shown that these Bessel methods can be applied to data with limited extent or resolution, provided the scales of interest are captured by the range of separation distances. The Bessel methods are shown to have several advantages over other flux-estimation methods, including the ability to diagnose downscale energy cascades and to identify sharp transition scales. Analogous Bessel methods are also discussed for third-order structure functions, along with some caveats due to boundary terms. Significance StatementBig ocean eddies play an important role in Earth’s energy cycle by moving energy to both larger and smaller scales, but it is difficult to measure these “eddy energy fluxes” from oceanic observations. We develop a new method to estimate eddy energy fluxes that utilizes spatial differences between pairs of points and can be applied to various ocean data. This new method accurately diagnoses key eddy energy flux properties, as we demonstrate using idealized numerical simulations of various large-scale ocean systems. 

Abstract Parameterization of mesoscale eddies in coarse resolution ocean models is necessary to include the effect of eddies on the large‐scale oceanic circulation. We propose to use a multiple‐scale Quasi‐Geostrophic (MSQG) model to capture the eddy dynamics that develop in response to a prescribed large‐scale flow. The MSQG model consists in extending the traditional quasi geostrophic (QG) dynamics to include the effects of a variable Coriolis parameter and variable background stratification. Solutions to this MSQG equation are computed numerically and compared to a full primitive equation model. The large‐scale flow field permits baroclinically unstable QG waves to grow. These instabilities saturate due to non‐linearities and a filtering method is applied to remove large‐scale structures that develop due to the upscale cascade. The resulting eddy field represents a dynamically consistent response to the prescribed background flow, and can be used to rectify the large‐scale dynamics. Comparisons between Gent‐McWilliams eddy parameterization and the present solutions show large regions of agreement, while also indicating areas where the eddies feed back onto the large scale in a manner that the Gent‐McWilliams parameterization cannot capture. Also of interest is the time variability of the eddy feedback which can be used to build stochastic eddy parameterizations. 

Abstract. Interactions between wind and trees control energy exchanges between theatmosphere and forest canopies. This energy exchange can lead to thewidespread damage of trees, and wind is a key disturbance agent in many ofthe world's forests. However, most research on this topic has focused onconifer plantations, where risk management is economically important, ratherthan broadleaf forests, which dominate the forest carbon cycle. This studybrings together tree motion time-series data to systematically evaluate thefactors influencing tree responses to wind loading, including data from bothbroadleaf and coniferous trees in forests and open environments. We found that the two most descriptive features of tree motion were (a) the fundamental frequency, which is a measure of the speed at which a treesways and is strongly related to tree height, and (b) the slope of the powerspectrum, which is related to the efficiency of energy transfer from wind totrees. Intriguingly, the slope of the power spectrum was found to remainconstant from medium to high wind speeds for all trees in this study. Thissuggests that, contrary to some predictions, damping or amplificationmechanisms do not change dramatically at high wind speeds, and therefore winddamage risk is related, relatively simply, to wind speed. Conifers from forests were distinct from broadleaves in terms of theirresponse to wind loading. Specifically, the fundamental frequency of forestconifers was related to their size according to the cantilever beam model(i.e. vertically distributed mass), whereas broadleaves were betterapproximated by the simple pendulum model (i.e. dominated by the crown).Forest conifers also had a steeper slope of the power spectrum. We interpretthese finding as being strongly related to tree architecture; i.e. conifersgenerally have a simple shape due to their apical dominance, whereasbroadleaves exhibit a much wider range of architectures with more dominantcrowns.