Search

Linear stability theory (LST) is often used to model the large-scale flow structures in the turbulent mixing region and near pressure field of high-speed jets. For perfectly expanded single round jets, these models predict the dominance of azimuthal wavenumbers m = 0 and m = 1 helical modes for the lower frequency range, in agreement with empirical data. When LST is applied to twin-jet systems, four solution families appear following the odd/even behaviour of the pressure field about the symmetry planes. The interaction between the unsteady pressure fields of the two jets also results in their coupling. The individual modes of the different solution families no longer correspond to helical motions, but to flapping oscillations of the jet plumes. In the limit of large jet separations, when the jet coupling vanishes, the eigenvalues corresponding to the m = 1 mode in each family are identical, and a linear combination of them recovers the helical motion. Conversely, as the jet separation decreases, the eigenvalues for the m = 1 modes of each family diverge, thus favouring a particular flapping oscillation over the others and preventing the appearance of helical motions. The dominant mode of oscillation for a given jet Mach number M-j and temperature ratio T-R depends on the Strouhal number S-t and jet separation s. Increasing both M-j and T-R independently is found to augment the jet coupling and modify the (S-t, s) map of the preferred oscillation mode. Present results predict the preference of two modes when the jet interaction is relevant, namely varicose and especially sinuous flapping oscillations on the nozzles' plane.

The benefits of limiting global warming to the lower Paris Agreement target of 1.5 °C are substantial with respect to population exposure to heat, and should impel countries to strive towards greater emissions reductions. Since the Paris Agreement was reached in December 2015 there has been a drive in the scientific community to understand the impacts of global warming at the target levels of 1.5 °C and 2 °C above pre-industrial levels1,2,3. A Special Report on the pathways to limiting global warming to 1.5 °C, and the associated implications of this target, is being prepared by the IPCC. Research has so far focused on changes in different types of climate extremes globally1,3 or regionally2,4, developing and utilizing model experiments to infer differences between the two warming targets5, or the emissions and warming trajectories associated with meeting or breaching the 1.5 °C target6,7. Here we approach the question of how different a 1.5 °C world and a 2 °C world are through the lens of human population exposure to historically unprecedented heat extremes warmer than those observed since 1950 in Europe. We show that the proportion of the population exposed to hot summers above the current record increases dramatically from 1.5 °C of warming to 2 °C. In the past, record summer heat in Europe has been associated with severe heatwaves resulting in thousands of excess deaths8, albeit with high variability in impacts between events — in part due to non-climatic factors. Nonetheless, global warming must be limited to reduce human exposure to historically unprecedented heat.