Numerical simulation of the 2D trajectory of a non-buoyant fluid parcel under the influence of inertial oscillation

The trajectory of non-buoyant fluid parcels under the influence of inertial oscillations is a pivotal phenomenon in geophysical fluid dynamics, impacting processes such as tracer transport, pollutant dispersion, and the dynamics of marine organisms. This study presents a comprehensive numerical investigation of the two-dimensional trajectory of a non-buoyant fluid parcel subjected to inertial oscillations, complemented by abrupt external forcing events. The simulations were implemented using multiple open-source, code-based general programming languages, including Fortran, Python, GNU Octave, R, and Julia. By running 1,000 iterations in each environment, we rigorously evaluated the computational performance and accuracy of these languages in tackling this idealized problem. The results, visualized through static plots and an animation generated using the Matplotlib library, capture the oscillatory trajectories and the influence of rotational effects, validating the numerical models' ability to represent the fundamental physics governing fluid motion. Furthermore, a robust statistical analysis compared the execution times across the programming environments. The Kruskal-Wallis test and Dunn's post-hoc test with Bonferroni correction reveal that Fortran exhibits significantly faster execution times compared to the other environments, highlighting its suitability for computationally intensive simulations in geophysical fluid dynamics. This study provides valuable insights into selecting appropriate computational tools and contributes to educational resources for teaching idealized fluid dynamics models, laying the foundation for more sophisticated hierarchical models applicable to ocean circulation, atmospheric dispersion, and biological transport influenced by oscillating currents.