Ambidextrous light transforms for celestial amplitudes

Low multiplicity celestial amplitudes of gluons and gravitons tend to be distributional in the celestial coordinates z,$$ \overline{z} $$ z ¯ . We provide a new systematic remedy to this situation by studying celestial amplitudes in a basis of light transformed boost eigenstates. Motivated by a novel equivalence between light transforms and Witten’s half-Fourier transforms to twistor space, we light transform every positive helicity state in the coordinate z and every negative helicity state in $$ \overline{z} $$ z ¯ . With examples, we show that this “ambidextrous” prescription beautifully recasts two- and three-point celestial amplitudes in terms of standard conformally covariant structures. These are used to extract examples of celestial OPE for light transformed operators. We also study such amplitudes at higher multiplicity by constructing the Grassmannian representation of tree-level gluon celestial amplitudes as well as their light transforms. The formulae for n-point Nk−2MHV amplitudes take the form of Euler-type integrals over regions in Gr(k, n) cut out by positive energy constraints.

A new Wilson line-based action for gluodynamics

We perform a canonical transformation of fields that brings the Yang-Mills action in the light-cone gauge to a new classical action, which does not involve any triple-gluon vertices. The lowest order vertex is the four-point MHV vertex. Higher point vertices include the MHV and $$ \overline{\mathrm{MHV}} $$ MHV ¯ vertices, that reduce to the corresponding amplitudes in the on-shell limit. In general, any n-leg vertex has 2 ≤ m ≤ n − 2 negative helicity legs. The canonical transformation of fields can be compactly expressed in terms of path-ordered exponentials of fields and their functional derivative. We apply the new action to compute several tree-level amplitudes, up to 8-point NNMHV amplitude, and find agreement with the standard methods. The absence of triple-gluon vertices results in fewer diagrams required to compute amplitudes, when compared to the CSW method and, obviously, considerably fewer than in the standard Yang-Mills action.

Evaluating EYM amplitudes in four dimensions by refined graphic expansion

The recursive expansion of tree level multitrace Einstein-Yang-Mills (EYM) amplitudes induces a refined graphic expansion, by which any tree-level EYM amplitude can be expressed as a summation over all possible refined graphs. Each graph contributes a unique coefficient as well as a proper combination of color-ordered Yang-Mills (YM) amplitudes. This expansion allows one to evaluate EYM amplitudes through YM amplitudes, the latter have much simpler structures in four dimensions than the former. In this paper, we classify the refined graphs for the expansion of EYM amplitudes into N k MHV sectors. Amplitudes in four dimensions, which involve k + 2 negative-helicity particles, at most get non-vanishing contribution from graphs in N k′ (k′ ≤ k) MHV sectors. By the help of this classification, we evaluate the non-vanishing amplitudes with two negative-helicity particles in four dimensions. We establish a correspondence between the refined graphs for single-trace amplitudes with $$ \left({g}_i^{-},{g}_j^{-}\right) $$ g i − g j − or $$ \left({h}_i^{-},{g}_j^{-}\right) $$ h i − g j − configuration and the spanning forests of the known Hodges determinant form. Inspired by this correspondence, we further propose a symmetric formula of double-trace amplitudes with $$ \left({g}_i^{-},{g}_j^{-}\right) $$ g i − g j − configuration. By analyzing the cancellation between refined graphs in four dimensions, we prove that any other tree amplitude with two negative-helicity particles has to vanish.

Palatial twistor theory and the twistor googly problem

A key obstruction to the twistor programme has been its so-called ‘googly problem’, unresolved for nearly 40 years, which asks for a twistor description of right -handed interacting massless fields (positive helicity), using the same twistor conventions that give rise to left -handed fields (negative helicity) in the standard ‘nonlinear graviton’ and Ward constructions. An explicit proposal for resolving this obstruction— palatial twistor theory —is put forward (illustrated in the case of gravitation). This incorporates the concept of a non-commutative holomorphic quantized twistor ‘Heisenberg algebra’, extending the sheaves of holomorphic functions of conventional twistor theory to include the operators of twistor differentiation.

Environmental Helicity and Its Effects on Development and Intensification of Tropical Cyclones

Much attention has been given to the impact of environmental wind shear in the 850–200-hPa layer on tropical cyclones (TCs). However, even with the same magnitude of shear, helicity in this layer can vary significantly. A new parameter is presented, the tropical cyclone–relative environmental helicity (TCREH). Positive TCREH leads to a tilted storm that enhances local storm-scale helicity in regions of convection within the TC. This enhanced local-scale helicity potentially allows for more robust and longer-lasting convection, which is more effective at generating latent heat and subsequent TC intensification. TC vertical tilt is often attributed to wind shear. Different values of helicity modulate this tilt and certain tilt configurations are more favorable for development or intensification than others, suggesting that mean positive environmental helicity is more favorable for development and intensification than mean negative helicity. Idealized modeling simulations demonstrate the impact of environmental helicity on TC development and intensification. Results show that wind profiles with the same 850–200-hPa wind shear but different values of helicity lead to different rates of development. TCREH also is computed from the Interim ECMWF Re-Analysis (1979–2011) and Global Forecast System analyses (2004–11) to determine if a significant signal exists between TCREH and TC intensification. Mean annular helicity is averaged over various time periods and correlated with the TC intensity change during those periods. Results suggest a weak but statistically significant correlation between environmental helicity and TC intensity change with positive helicity being more favorable for intensification.

Evolution of a turbulent cloud under rotation

Localized patches of turbulence frequently occur in geophysics, such as in the atmosphere and oceans. The effect of rotation, $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}\boldsymbol{\Omega}$, on such a region (a ‘turbulent cloud’) is governed by inhomogeneous dynamics. In contrast, most investigations of rotating turbulence deal with the homogeneous case, although inhomogeneous turbulence is more common in practice. In this paper, we describe the results of $512^3$ direct numerical simulations (DNS) of a turbulent cloud under rotation at three Rossby numbers ($\mathit{Ro}$), namely 0.1, 0.3 and 0.5. Using a spatial filter, fully developed homogeneous turbulence is vertically confined to the centre of a periodic box before the rotation is turned on. Energy isosurfaces show that columnar structures emerge from the cloud and grow into the adjacent quiescent fluid. Helicity is used as a diagnostic and confirms that these structures are formed by inertial waves. In particular, it is observed that structures growing parallel to the rotation axis (upwards) have negative helicity and those moving antiparallel (downwards) to the axis have positive helicity, a characteristic typical of inertial waves. Two-dimensional energy spectra of horizontal wavenumbers, $k_{\perp }$, versus dimensionless time, $2 \varOmega t$, confirm that these columnar structures are wavepackets which travel at the group velocities of inertial waves. The kinetic energy transferred from the turbulent cloud to the waves is estimated using Lagrangian particle tracking to distinguish between turbulent and ‘wave-only’ regions of space. The amount of energy transferred to waves is 40 % of the initial at $\mathit{Ro}=0.1$, while it is 16 % at $\mathit{Ro}=0.5$. In both cases the bulk of the energy eventually resides in the waves. It is evident from this observation that inertial waves can carry a significant portion of the energy away from a localized turbulent source and are therefore an efficient mechanism of energy dispersion.

Split energy–helicity cascades in three-dimensional homogeneous and isotropic turbulence

We investigate the transfer properties of energy and helicity fluctuations in fully developed homogeneous and isotropic turbulence by changing the nature of the nonlinear Navier–Stokes terms. We perform a surgery of all possible interactions, by keeping only those triads that have sign-definite helicity content. In order to do this, we apply an exact decomposition of the velocity field in a helical Fourier basis, as first proposed by Constantin & Majda (Commun. Math. Phys, vol. 115, 1988, p. 435) and exploited in great detail by Waleffe (Phys. Fluids A, vol. 4, 1992, p. 350), and we evolve the Navier–Stokes dynamics keeping only those velocity components carrying a well-defined (positive or negative) helicity. The resulting dynamics preserves translational and rotational symmetries but not mirror invariance. We give clear evidence that this three-dimensional homogeneous and isotropic chiral turbulence is characterized by a stationary inverse energy cascade with a spectrum ${E}_{back} (k)\sim {k}^{- 5/ 3} $ and by a direct helicity cascade with a spectrum ${E}_{forw} (k)\sim {k}^{- 7/ 3} $. Our results are important to highlight the dynamics and statistics of those subsets of all possible Navier–Stokes interactions responsible for reversal events in the energy-flux properties, and demonstrate that the presence of an inverse energy cascade is not necessarily connected to a two-dimensionalization of the flow. We further comment on the possible relevance of such findings to flows of geophysical interest under rotations and in thin layers. Finally we propose other innovative numerical experiments that can be achieved by using a similar decimation of degrees of freedom.

Magnetic Helicity in Sigmoids, Coronal Mass Ejections and Magnetic Clouds

Sigmoids, coronal mass ejections (CMEs) and magnetic clouds (MCs) all show signatures of twisted and writhing magnetic fields. CMEs are often associated with MCs, whose fields are regularly mapped with sensitive magnetometers. These measurements reveal that MC fields are helical, and each MC carries magnetic helicity away from the sun. It is more difficult to determine the magnetic helicity of the corresponding features on the sun. This presentation surveys recent work on helicity in solar features, focusing especially on the interpretation of sigmoids, which are S-shaped, bright features seen in images from the Yohkoh soft X-ray telescope. Several lines of evidence indicate that sigmoids are twisted and writhing flux ropes that erupt as components of CMEs. CMEs may be initiated by MHD-instable flux ropes. The fact that the ejected flux ropes carry off a large amount of positive helicity from the south and negative helicity from the north each solar cycle implies an equal, compensating flow of helicity through the sun’s equatorial plane.

Self-Organization in Three-Dimensional Hydrodynamic Turbulence Self-Organization in Three-Dimensional Hydrodynamic Turbulence

The three-dimensional incompressible Euler equations are expanded in eigenflows of the curl operator, which represent positive and negative helicity flows in a particularly simple and convenient way. Four different basic types of interactions between eigenflows are found. Two represent an "inverse cascade", the interaction familiar from the two-dimensional Euler equations, in which only modes of the same sign of the helicity interact. The other two interactions mix positive and negative helicity modes. Only these interactions can transport all of the available energy to higher wave numbers. Initial conditions, which lead to the appearance of structures and self-organization, are discussed.