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.

Balikpapan Bay is enclosed water influenced by freshwater from river runoff and saline water from Makassar Strait. The exchange of water mass was examined by 3D numerical model simulation-Hamburg Shelf Ocean Model (HAMSOM) with horizontal resolutions approx. 150 m and 10 vertical layers applied in Balikpapan Bay. The thirteen tidal components, daily river runoff, atmospheric forcing, subsurface temperature, and Salinity in 3D used for model input. The tidal elevation from Geospatial Information Agency (BIG) model fits with this result from 01/03/2020 to 31/03/2020. It has coefficient correlation 0,99 with a significant level of 95% and Root Mean Square Error (RMSE) is 0,1 m. The volume and salt transport in the mouth (Line-A) and middle (Line-B) of bay was examined. The maximum transport in Line-A during spring (neap) high to low tide and low to high tide is −18364.72 m³/s (−1717.57 m³/s) and −17532.27 m³/s (4258.86 m³/s) for volume. Then, 531,947,898.90 kg.psu./s (−45,127,135.38 kg.psu./s) and −536,410,944.50 kg.psu./s (140,700,437.97 kg.psu./s) for salinity. Positive (negative) of water transport is inflow (outflow) to Balikpapan Bay. The net transport in a day during the spring (neap) is −832.45 m³/s (5976.43 m³/s) for volume and −4,463,045.58 kg.psu./s (185,827,573.35 kg.pau./s) for salt. The vertical structure of net volume and salt transport bot in Line-A and Line-B shows the water goes to outer bay in surface and inner bay in subsurface. While in the spring tide the surface deeper than neap tide. It indicated that water mass exchange dominantly influenced by river in surface and tidal in subsurface. It also shows that water mass from inner bay more easy flushing during spring tide than neap tide and vice versa

Kenaikan permukaan air laut merupakan ancaman serius di kawasan pesisir, khususnya di kota-kota pelabuhan seperti Jakarta, Semarang, dan Surabaya yang terletak di Laut Jawa. Penelitian ini bertujuan untuk menganalisis interaksi antara anomali tinggi muka air laut dari data satelit Altimetri AVISO, suhu permukaan laut, dan faktor oseanografi serta atmosfer lainnya. Peningkatan suhu permukaan laut akibat variasi iklim berkontribusi pada ekspansi termal air laut, yang pada gilirannya meningkatkan rata-rata tinggi muka air laut. Dinamika perairan yang menyebabkan anomali tinggi muka air laut secara spasial, dipengaruhi oleh pola musim dan fenomena seperti ekman transport, teramati berperan penting dalam redistribusi suhu permukaan air laut. Puncak anomali tinggi muka air laut terjadi pada bulan Mei, dengan tinggi anomali mencapai +0,2 m, yang bersamaan dengan suhu air laut sebesar 32°C dan transport ekman ke arah selatan. Sehingga, secara spasial anomali tinggi muka air lebih tinggi di pantai utara Pulau Jawa. Hasil analisis menunjukkan bahwa anomali tinggi muka air laut berkorelasi positif dengan suhu permukaan laut. Melalui analisis Principal Component Analysis (PCA), ditemukan bahwa dua komponen utama (F1 dan F2) menyumbang total 78,47% dari variabilitas data, dengan F1 menjelaskan 58,86% dan F2 menjelaskan 19,61%. Hubungan antara suhu permukaan laut dan anomali tinggi muka air laut tercermin pada vektor yang lebih panjang, menunjukkan pengaruh signifikan kedua variabel ini terhadap dinamika laut. Temuan penelitian ini memberikan wawasan penting untuk pengelolaan sumber daya kelautan dan strategi penanggulangan dampak variasi iklim yang lebih efektif di wilayah pesisir.

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.

Turbidity serves as a crucial indicator of coastal water health and productivity. Twenty years of remote sensing data (2003–2022) from the Aqua Moderate Resolution Imaging Spectroradiometer (MODIS) satellite were used to analyze the spatial and temporal variations in turbidity, as measured by total suspended matter (TSM), in the Berau Coastal Shelf (BCS), East Kalimantan, Indonesia. The BCS encompasses the estuary of the Berau River and is an integral part of the Coral Triangle, renowned for its rich marine and coastal habitats, including coral reefs, mangroves, and seagrasses. The aim of this research is to comprehend the seasonal and interannual patterns of turbidity and their associations with met-ocean parameters, such as wind, rainfall, and climate variations like the El Niño–Southern Oscillation (ENSO) and the Indian Ocean Dipole (IOD). The research findings indicate that the seasonal spatial pattern of turbidity is strongly influenced by monsoon winds, while its temporal patterns are closely related to river discharge and rainfall. The ENSO and IOD climate cycles exert an influence on the interannual turbidity variations, with turbidity values decreasing during La Niña and negative IOD events and conversely increasing during El Niño and positive IOD events. Furthermore, the elevated turbidity during negative IOD and La Niña coincides with rising temperatures, potentially acting as a compound stressor on marine habitats. These findings significantly enhance our understanding of turbidity dynamics in the BCS, thereby supporting the management of marine and coastal ecosystems in the face of changing climatic and environmental conditions.