El Niño-Southern Oscillation (ENSO) has two major facets, namely the Eastern Pacific (EP) and the Central Pacific (CP) events, with irregular and quasi-periodic anomalies in wind currents and sea surface temperatures (SST) making it the most important climate phenomenon in the region. It also exhibits diverse characteristics in spatial pattern, peak intensity, and temporal evolution during its mature warming phase (El Niño) and mature cooling phase (La Niña), known as the ENSO diversity or complexity. Traditional methods for studying the sensitivity and response of ENSO to initial value and model parameter perturbations, are primarily based on trajectory-wise comparison. However, the intrinsic chaotic features and the model error impose significant challenges for accurately computing the statistical response in this manner. In this talk, we present a new approach to calculating the statistical response of ENSO diversity using information theory, by quantifying the intrinsic predictability and its response through a multiscale three-region stochastic model as a surrogate. It computes the response of the statistics, such as the mean and variance, to initial value or model parameter perturbations. We provide the most dangerous direction under initial and parameter perturbations for different ENSO events over the past 36 years (1982-2017). We also show that the uncertainty described by the variance and higher-order moments can have a significant response on certain perturbations, despite the insignificant change in the mean, which is a fundamental mechanism of the increment of extreme El Niño events and multi-year El Niño and La Niña, and that under a univariate SSTa regime for the probability densities, a Gaussian approximation captures most of the intricacies of intrinsic predictability and statistical response. This way of quantifying statistical response is more robust and physically meaningful, since it provides ways to inspect the response of ENSO diversity under the climate change scenario, increase or decrease of the Madden-Julian oscillation (MJO) or tropical cyclones, through model parameter perturbations, or to probe into the principal directions relating to forecast and prevention of extreme events, as well as impact on other climate variabilities, through initial value perturbations.

Souvla, which can be summed up as a chunkier version of the Greek souvlaki, is widely considered to be Cyprus' national dish. Large chunks of lamb or pork meat are pierced with a long metallic skewer, and cooked above a rectangular grill, known as foukou, by rotating the skewer using a motor. In this work we model the cooking process by initially solving the heat equation with rotating Dirichlet boundary conditions, used to simulate heat transfer through pure induction. This includes the computation of a zeroth-order accurate singular perturbation asymptotic expansion of the solution, as the angular velocity of the skewer tends to infinity, as well as an analytic expression for the theoretical cooking time (time it takes for the meat to reach the desired cooking temperature), which we validate via numerical simulations using the Python spectral solver library, Dedalus. We then expand on these findings, by extending our model to a Taylor-Couette flow heat transfer model, where the grill now surrounds the meat on one of its "sides", which leads to a heat equation with rotating Robin boundary conditions, simulating heat transfer at the meat boundary through convection (via the Boussinesq approximation of natural convection) and radiation (from the grill), after a Stefan-Boltzmann linearisation. In this elaborate setting, we again produce in the same manner a zeroth-order accurate singular perturbation asymptotic expansion of the solution and a theoretical cook-through time, as the angular velocity grows unboundedly, using a first Fourier mode approximation attributed to the sparse spectrum. This cook-through time is again validated numerically in Dedalus, by using a mixture of the Diffuse-domain method (DDM) and the Volume-penalty method (VPM) to solve the double domain heat transfer Taylor-Couette flow setting, which is driven by a combination of multiple time scales inside and outside the meat, fluid and temperature damping scales, and boundary layers developing at the meat surface.