Roughness of the surface underlying the atmospheric boundary layer causes departures of the near-surface scalar and momentum transport in comparison with aerodynamically smooth surfaces. Here, we investigate the effect of $56\times 56$ homogeneously distributed roughness elements on bulk properties of a turbulent Ekman flow. Direct numerical simulation in combination with an immersed boundary method is performed for fully resolved, three-dimensional roughness elements. The packing density is approximately $10\,\%$ and the roughness elements have a mean height in wall units of $10 \lesssim H^+ \lesssim 40$. According to their roughness Reynolds numbers, the cases are transitionally rough, although the roughest case is on the verge of being fully rough. We derive the friction of velocity and of the passive scalar through vertical integration of the respective balances. Thereby, we quantify the enhancement of turbulent activity with increasing roughness height and find a scaling for the friction Reynolds number that is verified up to $Re_\tau \approx 2700$. The higher level of turbulent activity results in a deeper logarithmic layer for the rough cases and an increase of the near-surface wind veer in spite of higher $Re_\tau$. We estimate the von Kármán constant for the horizontal velocity $\kappa _{m}=0.42$ (offset $A=5.44$) and for the passive scalar $\kappa _{h}=0.35$ (offset $\mathbb {A}=4.2$). We find an accurate collapse of the data under the rough-wall scaling in the logarithmic layer, which also yields a scaling for the roughness parameters $z$-nought for momentum ($z_{0{m}}$) and the passive scalar ($z_{0{h}}$).

European navigation in the age of sail owes much to the scientific revolution of the seventeenth century and the development of instruments and advanced mathematical techniques. Important though these developments were, it is argued here that close observation of the environment: of the weather, ocean currents, clouds, birds, mammals, and a host of other factors played a far more important role in safe navigation from one part of the globe to another.

The 2021 Nobel Prize in Physics recognizes advances in the understanding of complex systems, and underscores that ‘complex’ does not mean ‘imponderable’.

Following Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) we undertake a spectral analysis of a non-divergent flow on a sphere. It is shown that the spherical harmonic energy spectrum is invariant under rotations of the polar axis of the spherical harmonic system and argued that a constraint of isotropy would not simplify the analysis but only exclude low-order modes. The spectral energy equation is derived and it is shown that the viscous term has a slightly different form than given in previous studies. The relations involving energy transfer within a triad of modes, which Fjørtoft (Tellus, vol. 5, 1953, pp. 225–230) derived under the condition that energy transfer is restricted to three modes, are derived under general conditions. These relations show that there are two types of interaction within a triad. The first type is where the middle mode acts as a source for the two other modes and the second type is where it acts as a sink. The inequality indicating cascade directions which was derived by Gkioulekas & Tung (J. Fluid Mech., vol. 576, 2007, pp. 173–189) in Fourier space under the assumptions of narrow band forcing and stationarity is derived in spherical harmonic space under the assumption of dominance of first type interactions. The double cascade theory of Kraichnan (Phys. Fluids, vol. 10, 1967, pp. 1417–1423) is discussed in the light of the derived equations and it is hypothesised that in flows with limited scale separation the two cascades may, to a large extent, be produced by the same triad interactions. Finally, we conclude that the spherical geometry is the optimal test ground for exploration of two-dimensional turbulence by means of simulations.

Condensation inside marine containers occurs during voyages owing to weather changes. In this study, we define the condensation probability along one of the major routes for container ships between Asia and Europe. First, the inside and outside air conditions were measured on land in Japan, and a correlation analysis was conducted to derive their relationship. Second, onboard measurements were conducted for 20,000 twenty-foot equivalent unit (TEU) ships to determine the variation in outside air conditions. Complicated patterns of weather change were observed with changes in latitude, sea area, and season. Third, condensation probability was estimated based on a multi-regression analysis with land and onboard measured data. The maximum condensation probability in westbound or eastbound voyages in winter was found to be approximately 50%. The condensation probability estimation method established in this study can contribute to the quantification of cargo damage risks for the planning of marine container transportation voyages.

This article considers two passages in which either the sky (Plin. HN 17.74) or the sun (Manilius 2.941) is described as ‘green’; it argues that in both cases such a colour epithet is out of place and proposes to correct uiridi caelo to nitido caelo in the former case, and uiridis … Phoebus to rutilus … Phoebus in the latter.

The Real Time Mesoscale Analysis (RTMA), a two-dimensional variational analysis algorithm, is used to provide hourly analyses of surface sensible weather elements for situational awareness at spatial resolutions of 3 km over Alaska. In this work we focus on the analysis of horizontal visibility in Alaska, which is a region prone to weather related aviation accidents that are in part due to a relatively sparse observation network. In this study we evaluate the impact of assimilating estimates of horizontal visibility derived from a novel network of web cameras in Alaska with the RTMA. Results suggest that the web camera-derived estimates of visibility can capture low visibility conditions and have the potential to improve the RTMA visibility analysis under conditions of low instrument flight rules and instrument flight rules.

This work is focused on the development of an analytical model for the axisymmetric deformation of droplets with a given velocity lag in an outer flow. This leads either to oscillations around a deformed equilibrium shape or to strong deformations which may ultimately lead to their breakup when the equilibrium shape loses its stability. To obtain an evolution equation for the droplet shape evolution, it is first supposed that the droplet deforms like a spheroid. Then, a balance between kinetic energy of deformation, surface energy creation, external pressure work and viscous dissipation within the droplet is written. This is close to the approach developed in the classical Taylor analogy breakup or droplet deformation and breakup model. The main originality of the present modelling is that pressure work can be computed at any time, assuming an outer potential flow. Pressure is assumed to work on either the whole droplet or only on the forward half of the droplet due to flow separation. Results of this model are then compared with reported droplet oscillation frequencies. For suddenly accelerated droplets, oscillations are present in the liquid–liquid metal case and successfully compared with some new direct numerical simulation results. Comparison is also successful when compared with previous results on droplet oscillating at terminal falling velocity, whether in the liquid–liquid case or for falling raindrop. Lastly, comparisons are made with previously published secondary fragmentation experiments and direct numerical simulations whether in a shock tube or for droplets falling in a cross-flow.

The number of reported cases with Legionnaires' disease (LD) is increasing in Belgium. Previous studies have investigated the associations between LD incidence and meteorological factors, but the Belgian data remained unexplored. We investigated data collected between 2011 and 2019. Daily exposure data on temperature, relative humidity, precipitation and wind speed was obtained from the Royal Meteorological Institute for 29 weather stations. Case data were collected from the national reference centre and through mandatory notification. Daily case and exposure data were aggregated by province. We conducted a time-stratified case-crossover study. The ‘at risk’ period was defined as 10 to 2 days prior to disease onset. The corresponding days in the other study years were selected as referents. We fitted separate conditional Poisson models for each day in the ‘at risk’ period and a distributed lag non-linear model (DLNM) which fitted all data in one model. LD incidence showed a yearly peak in August and September. A total of 614 cases were included. Given seasonality, a sequence of precipitation, followed by high relative humidity and low wind speed showed a statistically significant association with the number of cases 6 to 4 days later. We discussed the advantages of DLNM in this context.