Gravity wave focusing on the Antarctic polar vortex using Gaussian-beam approximation in horizontally non-uniform flows

Ray path theory is an asymptotic approximation to the wave equations. It represents efficiently gravity wave propagation in non-uniform background flows so that it is useful to develop schemes of gravity wave effects in general circulation models. One of the main limitations of ray path theory to be applied in realistic flows is in caustics where rays intersect and the ray solution has a singularity. Gaussian beam approximation is a higher-order asymptotic ray path approximation which considers neighboring rays to the central one and thus it is free of the singularities produced by caustics. A previous implementation of the Gaussian beam approximation assumes a horizontally uniform flow. In this work, we extend the Gaussian beam approximation to include horizontally nonuniform flows. Under these conditions the wave packet can undergo horizontal wave refraction producing changes in the horizontal wavenumber, which affects the ray path as well as the ray tube cross-sectional area and so the wave amplitude via wave action conservation. As an evaluation of the Gaussian beam approximation in horizontally nonuniform flows a series of proof-of-concept experiments is conducted comparing the approximation with the linear wave solution given by the WRF model. A very good agreement in the wave field is found. An evaluation is conducted with conditions that mimic the Antarctic polar vortex and the orography of the Southern flank of South America. The Gaussian beam approximation nicely reproduces the expected asymmetry of the wave field. A much stronger disturbance propagates towards higher latitudes (polar vortex) compared to lower latitudes.

An architectural understanding of natural sway frequencies in trees

The relationship between form and function in trees is the subject of a longstanding debate in forest ecology and provides the basis for theories concerning forest ecosystem structure and metabolism. Trees interact with the wind in a dynamic manner and exhibit natural sway frequencies and damping processes that are important in understanding wind damage. Tree-wind dynamics are related to tree architecture, but this relationship is not well understood. We present a comprehensive view of natural sway frequencies in trees by compiling a dataset of field measurement spanning conifers and broadleaves, tropical and temperate forests. The field data show that a cantilever beam approximation adequately predicts the fundamental frequency of conifers, but not that of broadleaf trees. We also use structurally detailed tree dynamics simulations to test fundamental assumptions underpinning models of natural frequencies in trees. We model the dynamic properties of greater than 1000 trees using a finite-element approach based on accurate three-dimensional model trees derived from terrestrial laser scanning data. We show that (1) residual variation, the variation not explained by the cantilever beam approximation, in fundamental frequencies of broadleaf trees is driven by their architecture; (2) slender trees behave like a simple pendulum, with a single natural frequency dominating their motion, which makes them vulnerable to wind damage and (3) the presence of leaves decreases both the fundamental frequency and the damping ratio. These findings demonstrate the value of new three-dimensional measurements for understanding wind impacts on trees and suggest new directions for improving our understanding of tree dynamics from conifer plantations to natural forests.

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals

The real part of the dispersion surface in X-ray dynamical diffraction in the Laue case for perfect crystals is analysed using a Riemann surface. In the conventional two-beam approximation, each branch or wing of the dispersion surface is specified by one sheet of the Riemann surface. The characteristic features of the dispersion surface are analytically revealed using four parameters, which are the real and imaginary parts of two quantities that specify the degree of departure from the exact Bragg condition and the reflection strength. The present analytical method is generally applicable, irrespective of the magnitudes of the parameters with no approximation. Characteristic features of the dispersion surface are also revealed by geometrical considerations with respect to the Riemann surface.