This study presents a new approach to simulating large ocean density waves that travel long distances without breaking down. This new approach ensures that these waves are depicted more accurately and realistically in our models. This is particularly useful for understanding wave behavior in lakes with distinct water layers, which can help predict natural phenomena and their effects on environments like swash zones, where waves meet the shore.

With seismic data, we observed high-frequency internal waves (HIWs) with amplitudes of around 10 m. A shoaling thermocline and gentle slope suggest that HIWs result from fission. Remote sensing data support this. Strong shear caused Ri  below 0.25 over 20–30 km, indicating instability. HIWs enhance mixing, averaging 10^-4 m²s^-1, revealing a new energy cascade from shoaling waves to turbulence, and enhancing our understanding of energy dissipation and mixing in the northern South China Sea.

The shapes of clouds viewed from space reflect vertical and horizontal motions in the atmosphere. We theorize that, globally, cloud perimeter complexity is related to the dimension of turbulence also governed by horizontal and vertical motions. We find agreement between theory and observations from various satellites and a numerical model and, remarkably, that the theory applies globally using only basic planetary physical parameters from the smallest scales of turbulence to the planetary scale.

Advanced data assimilation methods are complex and computationally expensive. We compare two simpler methods, diffusive back-and-forth nudging and concave–convex nonlinearity, which account for change over time with the potential of providing accurate results with a reduced computational cost. We evaluate the accuracy of the two methods by implementing them within simple chaotic models. We conclude that the length and frequency of observations impact which method is better suited for a problem.

Understanding volcanic activity is crucial for uncovering the fundamental physical mechanisms governing this natural phenomenon. In this study, we show the application of multifractal and statistical analysis to investigate changes associated with volcanic activity. We aim to identify significant variations within the physical processes related to changes in volcanic activity. These methodologies offer the potential to identify pertinent changes preceding a high-energy explosion.

We train neural networks as denoising diffusion models for state generation in the Lorenz 1963 system and demonstrate that they learn an internal representation of the system. We make use of this learned representation and the pre-trained model in two downstream tasks: surrogate modelling and ensemble generation. For both tasks, the diffusion model can outperform other more common approaches. Thus, we see a potential of representation learning with diffusion models for dynamical systems.

The characterisation of abrupt transitions in palaeoclimate records allows understanding of millennial climate variability and potential tipping points in the context of current climate change. In our study an algorithmic method, the matrix profile, is employed to characterise abrupt warmings designated as Dansgaard–Oeschger (DO) events and to identify the most similar transitions in the palaeoclimate time series.

Our study investigates how turbulence behaves in stable conditions using direct numerical simulations. We found that rethinking how energy dissipates in these situations is crucial. By revising existing models, we uncovered limitations in understanding how temperature is transported vertically in very stable conditions. We focus on how turbulence works in extreme stability and offer new insights that could improve our understanding of natural phenomena affected by stable atmospheric conditions.

The intensification of tropical cyclones (TCs) is explored through a conceptual model derived from geophysical principals. Focus is put on the behaviour of the model with parameters which change in time. The rates of change cause the model to either tip to an alternative stable state or recover the original state. This represents intensification, dissipation, or eyewall replacement cycles (ERCs). A case study which emulates the rapid intensification events of Hurricane Irma (2017) is explored.

A methodology for directly predicting the time evolution of the assumed parameters for the distribution densities based on the Liouville equation, as proposed earlier, is extended to multidimensional cases and to cases in which the systems are constrained by integrals over a part of the variable range. The extended methodology is tested against a convective energy-cycle system as well as the Lorenz strange attractor.