Propagation Properties of an Off-Axis Hollow Gaussian-Schell Model Vortex Beam in Anisotropic Oceanic Turbulence

Based on the extended Huygens–Fresnel principle and the power spectrum of anisotropic oceanic turbulence, the analytical expressions of the average intensity and coherence properties of an off-axis hollow Gaussian-Schell model (OAHGSM) vortex beam propagating through anisotropic oceanic turbulence were derived. The effects of turbulent ocean and beam characteristic parameters on the evolution properties of the OAHGSM vortex beam were analyzed in detail. Our numerical simulation results showed that the OAHGSM vortex beam with a larger position factor is more focusable. Meanwhile, the OAHGSM vortex beam eventually evolves into a Gaussian-like beam after propagating through the anisotropic oceanic turbulent channel. The speed of this process can be accelerated by the decrease of the hollow order, topological charge, beam width, and transverse coherence width of the beam. The results also indicated that the normalized average intensity spreads more greatly and the spectral degree of coherence decays more rapidly for the smaller dissipation rate of the kinetic energy per unit mass of fluid, the smaller anisotropic coefficient, the smaller inner scale factor, the larger dissipation rate of the mean-squared temperature, and the higher temperature–salinity contribution ratio.

Fractal-like actuator disc theory for optimal energy extraction

The limit of power extraction by a device which makes use of constructive interference, i.e. local blockage, is investigated theoretically. The device is modelled using actuator disc theory in which we allow the device to be split into arrays and these then into sub-arrays an arbitrary number of times so as to construct an $n$ -level multi-scale device in which the original device undergoes $n-1$ sub-divisions. The alternative physical interpretation of the problem is a planar system of arrayed turbines in which groups of turbines are homogeneously arrayed at the smallest $n\mathrm {th}$ scale, and then these groups are homogeneously spaced relative to each other at the next smallest $n-1\mathrm {th}$ scale, with this pattern repeating at all subsequent larger scales. The scale-separation idea of Nishino & Willden (J. Fluid. Mech., vol. 708, 2012b, pp. 596–606) is employed, which assumes mixing within a sub-array occurs faster than mixing of the by-pass flow around that sub-array, so that in the $n$ -scale device mixing occurs from the inner scale to the outermost scale in that order. We investigate the behaviour of an arbitrary level multi-scale device, and determine the arrangement of actuator discs ( $n\mathrm {th}$ level devices) which maximises the power coefficient (ratio of power extracted to undisturbed kinetic energy flux through the net disc frontal area). We find that this optimal arrangement is close to fractal, and fractal arrangements give similar results. With the device placed in an infinitely wide channel, i.e. zero global blockage, we find that the optimum power coefficient tends to unity as the number of device scales tends to infinity, a 27/16 increase over the Lanchester–Betz limit of $0.593$ . For devices in finite width channels, i.e. non-zero global blockage, similar observations can be made with further uplift in the maximum power coefficient. We discuss the fluid mechanics of this energy extraction process and examine the scale distribution of thrust and wake velocity coefficients. Numerical demonstration of performance uplift due to multi-scale dynamics is also provided. We demonstrate that bypass flow remixing and ensuing energy losses increase the device power coefficient above the limits for single devices, so that although the power coefficient can be made to increase, this is at the expense of the overall efficiency of energy extraction which decreases as wake-scale remixing losses necessarily rise. For multi-scale devices in finite overall blockage two effects act to increase extractable power; an overall streamwise pressure gradient associated with finite blockage, and wake pressure recoveries associated with bypass-scale remixing.

Propagation of a Modified Complex Lorentz–Gaussian-Correlated Beam in a Marine Atmosphere

In this paper, we study the second-order statistics of a modified complex Lorentz–Gaussian-correlated (MCLGC) beam, which is a new type of partially coherent beam capable of producing an Airy-like intensity pattern in the far field, propagation through marine atmospheric turbulence. The propagation formula of spectral density is derived by the extended Huygens–Fresnel integral, which could explicitly indicate the interaction of turbulence on the beams’ spectral density under propagation. The influences of the structure constant of the turbulence, initial coherence width and wavelength on the spectral density are investigated in detail through numerical examples. In addition, analytical expressions for the r.m.s beam width, divergence angle and M2 factor of the MCLGC beam in the marine turbulence are also derived with the help of the Wigner distribution function. The results reveal that the beam spreads much faster, and the M2 factor deteriorates severely with the increase of the structure constant and the decrease of the inner scale size, whereas the outer scale size has little effect on these two quantities.

An observation-based scaling model for climate sensitivity estimates and global projections to 2100

We directly exploit the stochasticity of the internal variability, and the linearity of the forced response to make global temperature projections based on historical data and a Green’s function, or Climate Response Function (CRF). To make the problem tractable, we take advantage of the temporal scaling symmetry to define a scaling CRF characterized by the scaling exponent H, which controls the long-range memory of the climate, i.e. how fast the system tends toward a steady-state, and an inner scale $$\tau \approx 2$$ τ ≈ 2 years below which the higher-frequency response is smoothed out. An aerosol scaling factor and a non-linear volcanic damping exponent were introduced to account for the large uncertainty in these forcings. We estimate the model and forcing parameters by Bayesian inference which allows us to analytically calculate the transient climate response and the equilibrium climate sensitivity as: $$1.7^{+0.3} _{-0.2}$$ 1 . 7 - 0.2 + 0.3 K and $$2.4^{+1.3} _{-0.6}$$ 2 . 4 - 0.6 + 1.3 K respectively (likely range). Projections to 2100 according to the RCP 2.6, 4.5 and 8.5 scenarios yield warmings with respect to 1880–1910 of: $$1.5^{+0.4}_{-0.2}K$$ 1 . 5 - 0.2 + 0.4 K , $$2.3^{+0.7}_{-0.5}$$ 2 . 3 - 0.5 + 0.7 K and $$4.2^{+1.3}_{-0.9}$$ 4 . 2 - 0.9 + 1.3 K. These projection estimates are lower than the ones based on a Coupled Model Intercomparison Project phase 5 multi-model ensemble; more importantly, their uncertainties are smaller and only depend on historical temperature and forcing series. The key uncertainty is due to aerosol forcings; we find a modern (2005) forcing value of $$[-1.0, -0.3]\, \,\,\mathrm{Wm} ^{-2}$$ [ - 1.0 , - 0.3 ] Wm - 2 (90 % confidence interval) with median at $$-0.7 \,\,\mathrm{Wm} ^{-2}$$ - 0.7 Wm - 2 . Projecting to 2100, we find that to keep the warming below 1.5 K, future emissions must undergo cuts similar to RCP 2.6 for which the probability to remain under 1.5 K is 48 %. RCP 4.5 and RCP 8.5-like futures overshoot with very high probability.

Effects of Oceanic Turbulence on Orbital Angular Momenta of Optical Communications

The propagation properties of Laguerre-Gaussian beams in oceanic turbulence are investigated for both single-photon and biphoton cases. For single-photon communication, the channel capacity and trace distance are employed, both of which effectively reveal the communication performance via different viewpoints. For the biphoton case, we consider distributions of quantum resources including entanglement and quantum coherence. Turbulence conditions with a larger inner-scale and anisotropic factors, higher dissipation rate of kinetic energy, lower dissipation rate of the mean-squared temperature, and lower temperature-salinity contribution ratio combined with longer wavelength and an appropriate range of optimal beam width are beneficial to communication performances. Our results provide theoretical significance to improve the orbital-angular-momentum communication via oceanic turbulence.

Palissya – absolutely incomprehensible or surprisingly interpretable: a new morphological model, affiliations and phylogenetic insights

The morphology of the adaxial structures of cones belonging to Palissya Endlicher 1847 emend. nov. are reinterpreted based on exquisitely preserved permineralised material from the Lower Cretaceous of Queensland. Although the material was not found in situ, it likely derives from the Orallo Formation, which is Valanginian in age. The cones have dual vascular bundles in each bract/scale complex, and the different tissue types in the bract and ovule/scale complex support interpretation of the cone as a compound structure. Since the early twentieth century it has been widely accepted that each ovule is surrounded by a cup-shaped structure, but the detailed morphology of the “cup” has hitherto been unclear. These new three-dimensionally preserved specimens with in situ ovules are described as Palissya tillackiorum sp. nov. This study demonstrates that the “cup” is formed from a pair of thin scales that subtend but are not fused to each ovule; each pair of scales comprises a thicker outer and thinner inner scale. The organographic relationships among ovules and scales in Palissya show a high degree of synorganisation. The adaxial surface of the bract/scale complex has 2–6 pairs of erect (orthotropous) ovules. The ovule/scale units are arranged symmetrically in two parallel rows on either side of the midline of the bract/scale. Individual ovule/scale units are comparable to those seen in extant Podocarpaceae and Taxaceae. The ovules are thin-walled and are interpreted to have a single integument and a non-thickened (non-lignified) micropyle. These new insights allow reinterpretation of material previously referred to Palissya. A new species is described from Yorkshire, England, as P. harrisii C.R. Hill ex Pattemore & Rozefelds sp. nov. All species based on well preserved cones are reconsidered herein: P. sphenolepis (Braun 1843) Nathorst 1908 emend. Florin 1958, P. elegans Parris, Drinnan & Cantrill 1995 emend. nov., P. bartrumii Edwards 1934 emend. nov., P. antarctica Cantrill 2000 and P. hunanensis Wang 2012. Palissya ovalis Parris et al. 1995 differs structurally from Palissya and is transferred to Knezourocarpon Pattemore 2000 emend. nov. Representatives of this genus may superficially resemble those of Palissya in compressions and impressions, and their congeneric status has been previously suggested; hence its inclusion in this study. Knezourocarpon has adaxial processes that are positioned in two parallel rows but it lacks ovules and paired lateral scales that formed a cup-shape, and its processes attach directly to a central vascular trace. The improved understanding of Palissya’s morphology allows for definite separation of these genera, although the higher-order affiliation of Knezourocarpon remains unclear.