Mathematical model on impact of velocities for stratified deep water under modified gravity and coriolis effect with simulation

الملخص

This study presents a mathematical model for simulating the dynamics of stratified deep water under the influence of modified gravity and the Coriolis effect. The model is developed to capture the complex interactions between density stratification, gravitational forces, and rotational effects in large-scale oceanic and geophysical fluid systems. The governing equations are derived from the principles of fluid dynamics, incorporating the effects of buoyancy, pressure gradients, and the Coriolis force, which arises due to the Earth’s rotation. A modified gravity term is introduced to account for variations in gravitational acceleration, which is essential for modeling phenomena such as oceanic circulation, geostrophic flows, and internal wave propagation in stratified fluids. The mathematical formulation includes the Navier-Stokes equations, the continuity equation, and
the equation of state for a stratified fluid. The Coriolis effect is incorporated through the Coriolis parameter, which depends on latitude and the Earth’s angular velocity. The modified gravity term is introduced as a perturbation to the standard gravitational acceleration, allowing for the simulation of non-uniform gravitational fields in different regions of the ocean. To analyze the behavior of the system, numerical simulations were performed. The simulations are validated against known solutions and experimental data to ensure the accuracy and reliability of the model. The results demonstrate the influence of modified gravity and the Coriolis effect on the velocity structure, density distribution, and overall flow patterns in stratified deep water. The model provides a valuable tool for understanding and predicting the behavior of geophysical fluids in various environmental
and climatic contexts.