In recent research published in Scientific Reports, scientists utilized Large Eddy Simulation (LES) to investigate the effects of the Froude number (Fr) on the wake and internal waves generated by a sphere moving through linearly stratified fluid at a Reynolds number of 3700. The study comprised six sets of simulations reflecting varying Froude numbers—0.05, 0.25, 0.5, 1, 2, and infinity—to understand how density stratification impacts wake characteristics.
The findings revealed that decreasing the Froude number led to greater vertical suppression of the wake, as well as increased anisotropy in the fluid's velocity distribution. As the Froude number increased from 0.05 to 2, researchers observed a transition from quasi-two-dimensional vortex shedding to a more chaotic three-dimensional turbulence.
At a Froude number of 0.05, the simulations indicated a three-layer vortex structure in the wake, showing minimal vertical fluid movement due to buoyancy overtaking inertial forces. In contrast, at a Froude number of 0.25, transitional behavior occurred where some fluid successfully ascended over the sphere, prompting oscillatory wake patterns that disrupted the initial stratification and generated internal waves.
As the Froude number further increased to 0.5, the prevalence of saturated Lee waves at the wake dominated the wake structure, with the amplitude of these waves reaching a significant peak. However, by the time Fr reached 1, the wake underwent a considerable transition as buoyant forces became negligible, giving way to turbulence and a complex recirculation zone behind the sphere.
At a Froude number of 2, the impact of density stratification on wake structure was slightly diminished, highlighting the role of inertial forces in developing turbulent flow patterns. Finally, in conditions resembling an unstratified state (Fr = infinity), researchers noted asymmetric vortex structures with active vortex shedding.
This comprehensive study not only establishes a clearer understanding of how stratification influences wake characteristics but also has practical implications for underwater vehicles such as submarines, suggesting potential advancements in flow control technologies to minimize drag and increase hydrodynamic efficiency.
In conclusion, these results underscore the pivotal role of density stratification in aquatic environments, emphasizing how varying Froude numbers can intricately shape fluid dynamics and wake behaviors specific to moving objects. The insights gained from this research are valuable for further exploration into optimizing vehicle designs and operational strategies in stratified waters.
