This study presents the complexity and sensitivity of chaotic system dynamics in the case of the double pendulum. It applied detailed numerical analyses of the double pendulum in multiple computing platforms in order to demonstrate the complexity in behavior of the system of double pendulums. The equations of motion were derived from the Euler-Lagrange formalism, in order to capture the system's dynamics, which is coupled nonlinearly. These were solved numerically using the efficient Runge-Kutta-Fehlberg method, implemented in Python, R, GNU Octave, and Julia, while runtimes and memory usage were extensively benchmarked across these environments. Time series analyses, including the calculation of Shannon entropy and the Kolmogorov - Smirnov test, quantified the system's unpredictability and sensitivity to infinitesimal perturbations of the initial conditions. Phase space diagrams illustrated the intricate trajectories and strange attractors, as further confirmation of the chaotic nature of the double pendulum. All the findings have a clear indication of the importance of accurate measurements of the initial condition in a chaotic system, contributing to an increased understanding of nonlinear dynamics. Future research directions are faster simulations using Numba and GPU computing, stochastic effects, chaotic synchronization, and applications in climate modeling. This work will be useful for understanding chaos theory and efficient computational approaches in complex systems of dynamical nature.

This study presents an open-source Python library for simulating two-dimensional incompressible Kelvin-Helmholtz (KH) instabilities in stratified shear flows. The solver employs a fractional-step projection method with spectral Poisson solution via fast sine transform (FST). While diffusion and pressure terms achieve second-order spatial accuracy through central differencing and spectral methods respectively, advection employs first-order upwind differencing that provides numerical stability for sharp gradients characteristic of KH billows. Implementation leverages NumPy for array operations, SciPy for spectral methods, and Numba just-in-time (JIT) compilation, balancing computational performance with code transparency and accessibility. Four canonical test cases systematically explore parameter space spanning Reynolds numbers 1,000-5,000 and Richardson numbers 0.1-0.3: classical shear layer, double shear configuration, rotating flow, and forced turbulence. Statistical analysis employing Shannon entropy, complexity indices, and nonparametric tests reveals non-monotonic relationships between flow parameters and mixing efficiency, with double shear layers achieving 4.3x higher mixing rates than forced turbulence despite lower Reynolds numbers. The developed complexity metrics combining entropy, gradient variability, and higher-order moments provide quantitative benchmarks for turbulence model validation complementing conventional statistical measures. While the two-dimensional framework excludes spanwise secondary instabilities, it isolates primary mixing mechanisms relevant for understanding atmospheric and oceanic transport processes. The solver executes efficiently on standard desktop hardware, with the most demanding 384x192 grid simulation completing in approximately 31 minutes for 30 seconds physical time, enabling systematic parameter studies on modest computational resources. Results demonstrate that mixing efficiency depends fundamentally on instability generation pathways rather than intensity measures alone, challenging existing Richardson number-based parameterizations and suggesting refinements for subgrid-scale representation in climate models.

Kali Kupang plays an important role in the life of the people of Pekalongan and its surrounding areas. However, until recently, not many hydrological studies have been carried out in this area. This study presents how Extreme Value Analysis (EVA) can predict future extreme hydrological events and how a dynamic-programming-based change point detection algorithm can detect the abrupt transition in discharge events variability. Using the annual block maxima, we can predict the upper extreme discharge probability from the generalized extreme value distribution (GEVD) that best fits the data by using the Markov Chain Monte Carlo (MCMC) algorithm as a distribution fitting method. Metropolis-Hasting (MH) algorithm with 500 walkers and 2,500 samples for each walker is used to generate random samples from the prior distribution. As a result, this discharge data can be categorized as a Gumbel distribution (  = 6.818,  = 3.456, and  = 0). The recurrence intervals (RI) for this discharge data can be calculated through this distribution. The changepoint location of the annual standard deviation of this discharge data in the mid-1990s is detected by using the pruned exact linear time (PELT) algorithm. Despite some shortcomings, this study can pave the way for using data-driven algorithms, along with more traditional numerical and descriptive approaches, to analyze hydrological time-series data in Indonesia. This is crucial, considering an increasing number of hydro climatological disasters in the future as a consequence of global climate change.

The Korteweg–de Vries (KdV) equation is a foundational model in geophysical fluid dynamics (GFD), governing the propagation of long internal and surface gravity waves in stratified and shallow ocean environments where the interplay between nonlinear steepening and frequency-dependent dispersion gives rise to solitons. Although the analytical tractability of the KdV equation through inverse scattering is well established, systematic numerical exploration of multi-soliton interactions remains valuable for benchmarking solvers, probing conservation properties under varied oceanic initial conditions, and building intuition for more complex ocean wave phenomena. This article presents sangkuriang, an open-source Python library that solves the KdV equation using Fourier pseudo-spectral spatial discretization and adaptive eighth-order Runge–Kutta time integration. The implementation leverages just-in-time (JIT) compilation to achieve research-grade computational efficiency on standard hardware, making it readily accessible for coastal and ocean engineering applications, including idealized modeling of internal solitary waves on continental shelves, rapid parameter studies for solitary wave propagation in stratified basins, and pedagogical investigations of nonlinear dispersive wave dynamics. The solver is validated through four progressively complex idealized scenarios motivated by oceanic wave dynamics: isolated soliton propagation, symmetric interactions, overtaking collisions, and three-body interactions. High-fidelity conservation of mass, momentum, and energy is demonstrated, with relative errors remaining below $\mathcal{O}\left({10}^{-4}\right)$ across all test cases. Measured soliton velocities align with theoretical predictions within 5%, confirming the capture of the amplitude-dependent dispersion characteristic of oceanic solitary waves. Complementary diagnostics, including spectral entropy and recurrence quantification analysis (RQA), verify that the numerical solutions preserve the regular phase-space structure characteristic of integrable Hamiltonian systems. These results establish sangkuriang as a robust, lightweight platform for reproducible numerical investigation of idealized nonlinear dispersive wave dynamics relevant to coastal and ocean engineering applications.

Buku ini menyajikan pengantar yang sistematis dan mendalam mengenai dinamika fluida geofisika ( Geophysical Fluid Dynamics , GFD), bidang ilmu yang mempelajari pergerakan fluida di atmosfer dan lautan dalam skala besar. Fokus utama pembahasan mencakup dua faktor penting yang membedakan GFD dari mekanika fluida klasik, yaitu pengaruh rotasi Bumi dan stratifikasi densitas fluida. Materi disusun secara bertahap, dimulai dari konsep dasar seperti persamaan Navier-Stokes dalam kerangka rotasional, hingga fenomena yang lebih kompleks seperti gelombang Rossby, penyesuaian geostrofik, dan prinsip kekekalan vortisitas potensial. Buku ini menjelaskan berbagai fenomena fisik yang terjadi di atmosfer dan lautan, termasuk pergerakan fluida berskala besar yang dipengaruhi oleh rotasi Bumi dan gaya pemulih gravitasi. Pembaca akan diajak memahami bagaimana keseimbangan geostrofik terbentuk, bagaimana gelombang bergerak dalam sistem perairan dangkal, serta bagaimana sirkulasi dan ketidakstabilan berkembang dalam aliran fluida yang kompleks. Semua pembahasan dikemas dengan pendekatan yang mudah dipahami namun tetap memuat kedalaman ilmiah. Dirancang sebagai sumber belajar sekunder bagi mahasiswa, peneliti, dan peminat ilmu meteorologi dan oseanografi, buku ini memberikan penjelasan mendalam tentang prinsip-prinsip dasar yang membentuk dinamika fluida di Bumi. Dengan materi yang tersusun secara runtut, buku ini diharapkan dapat memperkaya pemahaman pembaca tentang fenomena fisis yang mendasari dinamika atmosfer dan lautan, serta interaksi kompleks di antara keduanya.