Abstract

This article presents our exploration into how a finite-width internal gravity wave beam is modified by triadic resonance instability. We present both experimental and weakly nonlinear modelling to examine this instability mechanism, in which a primary wave beam generates two secondary wave beams of lower frequencies and shorter length scales. Through a versatile experimental set-up, we examine how this instability evolves over hundreds of buoyancy periods. Unlike predictions from previous zero-dimensional weakly nonlinear theory, we find that the wave does not monotonically approach a saturated equilibrium of triadic interactions; rather, the amplitudes and structures of the constituent beams continue to modulate without ever reaching a steady equilibrium. To understand this behaviour, we develop a weakly nonlinear approach to account for the spatiotemporal evolution of the amplitudes and structures of the beams over slow time scales and long distances, and explore the consequences using a numerical scheme to solve the resulting equations. Through this approach, we establish that the evolution of the instability is remarkably sensitive to the spatiotemporal triadic configuration for the system and how part of the observed modulations can be attributed to a competition between the linear growth rate of the secondary wave beams and the finite residence time of the triadic perturbations within the underlying primary beam.

<p>With an aim of understanding the role of internal waves to oceanic mixing, various mechanisms have been cited as a possible explanation for how they transfer energy across the wavenumber and frequency spectra and eventually contribute to small-scale turbulence. Triadic Resonance Instability (TRI) has become increasingly recognised as potentially one of these mechanisms. This talk will summarise both experimental work and theoretical modelling (using numerical solutions of a weakly non-linear system) that examines the long-term temporal and spatial evolution of this instability for a finite-width internal wave beam. Experiments have been conducted using a new generation of wave maker, featuring a flexible horizontal boundary driven by an array of independently controlled actuators. We present experimental results exploring the role that a finite width wave beam has on the evolution of TRI. Experimentally, we find that the approach to a saturated equilibrium state for the three triadic waves is not monotonic, rather their amplitudes continue to oscillate without reaching a steady equilibrium. Further theoretical modelling then suggests that part of this variability is due to multiple resonant frequencies interacting with each other, as opposed to a simple triad system. We show how a spectrum of these resonant frequencies in the flow ‘beat’ to cause interference patterns which manifest throughout the instability as slow amplitude modulations.</p>

<p>Current climate projections point towards a severe increase in the intensity, duration and frequency of heat waves under climate change conditions. Such changes are not homogeneous, with certain regions of the planet presenting a higher vulnerability to these extreme events and, therefore, greater adaptation challenges. Among the areas affected by heat waves, urban environments are particularly susceptible to their impacts due to the urban heat island (UHI) effect, which magnifies the severity of heat waves inside cities and significantly increases the health-related risks associated with heat stress. </p><p>Simulations produced by Global Climate Models (GCMs) (e.g. CMIP) are of crucial importance to better understand how the Earth’s climate system will evolve in the coming decades. Unfortunately, their coarse resolution, typically above 100 x 100 km, makes them unable to resolve fine-scale physical processes, including urban-scale phenomena such as the UHI. High-resolution simulations are therefore required to accurately represent physical processes that remain hidden to models with coarser representations of the climate system. GCMs with km-scale grids and sub-hourly output frequency provide the ability to study heat waves at global, mesoscale or even local level, together with an enhanced (i.e. better in physical terms) representation of the large-scale circulation systems (e.g. Rossby waves) that give rise to heat waves. </p><p>In the framework of Destination Earth (DestinE), we are developing an urban use case for the Climate Adaptation Digital Twin (ClimateDT) that focuses on the climate impacts produced by extreme temperatures in urban environments. We will present the background and the current state of development of the use case, together with its associated challenges. Given the high-resolution simulations envisioned for the ClimateDT are not yet available, we will use NextGEMS cycle 2-3 data, which have similar characteristics, to present several climate indicators related to heat waves and human thermal comfort (e.g. UTCI, HWMI, EHF), with a particular focus on large metropolitan areas and their immediate surroundings, though results at global scale will be also assessed. Nonetheless, the previously mentioned high spatial and temporal resolutions imply unprecedented volumes of data, which, due to limited storage capacity, need to be streamed at model runtime, without the users ever having access to the full model output, but only to a fraction of it over a limited period of time. Therefore, the innovative streaming framework introduced by DestinE requires the use of one-pass algorithms to create statistical summaries of the simulated climate fields, which in turn places particular constraints on the development of the use case.</p><p>Together with other relevant statistics, these indicators will allow us to study the spatial and temporal variability of heat waves inside urban areas, a significant knowledge gap in current climate projections. The ultimate goal of our work is to provide useful knowledge to urban planners, both in terms of storylines and climate data, which can be of use towards designing more resilient cities that are better adapted to the impacts of heat waves.</p>

<p>With an aim of understanding the role of internal waves to oceanic mixing, various mechanisms have been cited as a possible explanation for how they transfer energy across the wavenumber and frequency spectra and eventually contribute to small-scale turbulence. Triadic Resonance Instability (TRI) has become increasingly recognised as potentially one of these mechanisms. This talk will summarise experimental work that examines the long-term temporal and spatial evolution of this instability in the more realistic scenario of a finite-width internal wave beam. Experiments have been conducted using a new generation of wave maker, featuring a flexible horizontal boundary driven by an array of independently controlled actuators. We present experimental results exploring the role the finite-width of a wave beam has on the evolution of TRI. Experimentally, we find that the approach to a saturated equilibrium state for the three triadic waves is not monotonic, rather their amplitudes continue to oscillate without reaching a steady equilibrium. A detailed study into the structure of the secondary waves shows that this behaviour is also witnessed in Fourier space. We show how a spectrum of these resonant frequencies in the flow ‘beat’ to cause interference patterns which manifest throughout the instability as slow amplitude modulations.</p>