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Studies on buoyancy-driven instabilities are of considerable interest for its wide application in oceanic, environmental and industrial fields. For miscible two-layer stratifications in a Hele-Shaw cell, the base state density profile in the diffusion regime can be predicted by linear stability analysis such that the buoyancy-driven instabilities can be classified in (R, δ) parameter space, where R is the initial density stability ratio and δ is the diffusion coefficient ratio. However, flow dynamics in extended geometry do not satisfy Darcy's law. Hence, linear stability analysis cannot be applied to unbounded flow with nonlinear momentum convection. In this study, we carry out a series of numerical simulations to investigate buoyancy-driven instability for thermohaline stratification in both a Hele-Shaw cell and extended geometry at a high thermal Rayleigh number, Ra T = 7 · 10 6 , with R = 0.05, 0.25, 0.8, 1, 4, and 20. The time evolution of the density stability ratio, temperature, salinity and base state density are calculated and compared. Fingers of unbounded thermohaline stratification have a more distorted shape due to the nonlinear momentum convection. However, the base state density profile of thermohaline stratification in extended geometry is found to be similar to that of a Hele-Shaw cell; thus, the classification of buoyancy-driven instabilities in (R, δ) space for miscible two-layer stratifications in Hele-Shaw cells can be extended to the same flow in extended geometry.

A manta ray biomimetic glider is designed and studied with both laboratory experiments and numerical simulations with a new dynamic update method called the motion-based zonal mesh update method (MBZMU method) to reveal its hydrodynamic performance. Regarding the experimental study, an ejection gliding experiment is conducted for qualitative verification, and a hydrostatic free-fall experiment is conducted to quantitatively verify the reliability of the corresponding numerical simulation. Regarding the numerical simulation, to reduce the trend of nose-up movement and to obtain a long lasting and stable gliding motion, a series of cases with the center of mass offset forward by different distances and different initial angles of attack have been calculated. The results show that the glider will show the optimal gliding performance when the center of mass is 20mm in front of the center of geometry and the initial attack angle range lies between A0 = -5° to A0 = -2.5° at the same time. The optimal gliding distance can reach six times its body length under these circumstances. Furthermore, the stability of the glider is explained from the perspective of Blended-Wing-Body (BWB) configuration.