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Retreat of coastal forests in relation to sea level rise has been widely documented. Recent work indicates that coastal forests on the Delmarva Peninsula, United States, can be differentiated into persistence and regenerative zones as a function of sea-level rise and storm events. In the lower persistence zone trees cannot regenerate because of frequent flooding and high soil salinity. This study aims to verify the existence of these zones using spectral remote sensing data, and determine whether the effect of large storm events that cause damage to these forests can be detected from satellite images. Spectral analysis confirms a significant difference in average Normalized Difference Vegetation Index (NDVI) and Normalized Difference Water Index (NDWI) values in the proposed persistence and regenerative zones. Both NDVI and NDWI indexes decrease after storms triggering a surge above 1.3 m with respect to the North American Vertical Datum of 1988 (NAVD88). NDWI values decrease more, suggesting that this index is better suited to detect the effect of hurricanes on coastal forests. In the regenerative zone, both NDVI and NDWI values recover three years after a storm, while in the persistence zone the NDVI and NDWI values keep decreasing, possibly due to sea level rise causing vegetation stress. As a result, the forest resilience to storms in the persistence zone is lower than in the regenerative zone. Our findings corroborate the ecological ratchet model of coastal forest disturbance.

The Froude scaling laws have been used to model a wide range of water flows at reduced size for almost a century. In such Froude scale models, significant scale effects for air–water flows (e.g. hydraulic jumps or wave breaking) are typically observed. This study introduces novel scaling laws, excluding scale effects in the modelling of air–water flows. This is achieved by deriving the conditions under which the governing equations are self-similar. The one-parameter Lie group of point-scaling transformations is applied to the Reynolds-averaged Navier–Stokes equations, including surface tension effects. The scaling relationships between variables are derived for the flow variables, fluid properties and initial and boundary conditions. Numerical simulations are conducted to validate the novel scaling laws for (i) a dam break flow interacting with an obstacle and (ii) a vertical plunging water jet. Results for flow variables, void fraction and turbulent kinetic energy are shown to be self-similar at different scales, i.e. they collapse in dimensionless form. Moreover, these results are compared with those obtained using the traditional Froude scaling laws, showing significant scale effects. The novel scaling laws are a more universal and flexible alternative with a genuine potential to improve laboratory modelling of air–water flows.

Physical modelling at reduced size is one of the oldest and most important design tools in hydraulic engineering. To predict the behaviour of the prototype, a physical model needs to incorporate all involved forces. The Froude scaling laws are being used to model a wide range of water flows at reduced size for almost a century. They are based on the invariance of the Froude number, i.e. the square root of the ratio between the inertial and gravity force between the model and its prototype. However, scale effects are observed due to forces excluded from the Froude number, for example in air-water flows, such as hydraulic jumps or wave breaking, the viscous, surface tension and air compressibility forces are scaled incorrectly at reduced size.This study introduces novel scaling laws (NSLs) to exclude scale effects in the modelling of air-water flows. This is achieved by deriving the conditions under which the governing equations are self-similar with respect to the geometric scale, i.e. they are scale-invariant. To this end, the oneparameter Lie group of point-scaling transformations are applied to the governing equations for air-water flows. These scaling laws involve relationships for all the flow parameters, fluid properties and initial and boundary conditions. First, the scaling laws are derived under the assumption of air incompressibility, subsequently, this assumption is removed. For the former, the Reynolds-averaged Navier–Stokes equations, including surface tension effects, are used. For the case in which the compressibility of air is taken into account, the equations of heat transfer and perfect gas are added to the system of governing equations.The NSLs are validated by numerically simulating different phenomena at different scales, i.e. i) a plunging water jet for incompressible air-water flows, ii) a Taylor bubble where the air is considered compressible and iii) a dam break flow impacting an obstacle for both cases. To this end, the governing equations are computed by two-phase flows solvers based on the volume of fluid method available in OpenFOAM v.1706, namely interFoamand interIsoFoamfor incompressible air-water flows and compressibleInter-IsoFoamwhen air is considered compressible. When the NSLs are used, some restrictions are applied by still maintaining self-similarity. For the incompressible air case, the gravitational acceleration is kept invariant between the model and its prototype, while the temperature is kept invariant through the scales for compressible air. Further, it is shown that the precise Froude scaling laws, i.e. when the properties of fluids are strictly scaled, are a particular configuration of the NSLs.Results for the void fraction, turbulent kinetic energy, velocity, pressure and temperature are shown to be self-similar at different scales for i) to iii), i.e. they collapse in dimensionless form. These results are compared with those obtained using the traditional Froude scaling laws, i.e. when ordinary water and air are used in the model, which, on the other hand, show significant scale effects. Furthermore, the importance of modelling air compressibility is analysed by comparing the results of the dam break flows in which the pressure on the obstacle shows an oscillation when the compressibility of air is taken into account.