MATHEMATICAL MODEL ON DILATATION EQUATIONS AND ANALYSIS WITH SIMULATION OF STRATIFIED DEEP WATER UNDER MODIFIED GRAVITY WITHOUT CORIOLIS EFFECT

MATHEMATICAL MODEL ON DILATATION EQUATIONS

Abstract

The dilatation of stratified deep water under modified gravity is investigated through a stress–strain formulation describing volumetric fluid deformation in a vertically stratified domain. The study examines how mechanical stress, density variation, and gravitational forcing influence the deformation and expansion of stratified fluid layers under modified gravitational conditions. Unlike conventional formulations based primarily on velocity fields, the governing equations are reformulated explicitly in terms of dilatation, thereby providing a direct framework for analysing volumetric deformation and weak compressibility effects in deep-water systems. Using analytical formulation together with numerical simulation implemented in the R programming environment, the temporal evolution of the dilatation field is examined within a 5 km deep-water column. The simulations reveal that stress–strain interactions initially enhance volumetric deformation, but the effects decay rapidly as stable stratification becomes dominant. Although modified gravitational scaling slightly alters the
transient response of the system, the flow gradually approaches a stable weakly compressible equilibrium characterized by very small volumetric changes. The results demonstrate that strong stratification suppresses sustained dilatation under modified gravitational conditions and provide further insight into the behaviour of deep-water stratified systems. The study contributes to the understanding of geophysical and astrophysical fluid dynamics, with potential applications in ocean circulation and climate-related flow processes.