Pupil responses associated with the perception of gravitational vertical under directional optic flows

This study assessed the pupil responses in the sensory integration of various directional optic flows during the perception of gravitational vertical. A total of 30 healthy participants were enrolled with normal responses to conventional subjective visual vertical (SVV) which was determined by measuring the difference (error angles) between the luminous line adjusted by the participants and the true vertical. SVV was performed under various types of rotational (5°/s, 10°/s, and 50°/s) and straight (5°/s and 10°/s) optic flows presented via a head-mounted display. Error angles (°) of the SVV and changes in pupil diameters (mm) were measured to evaluate the changes in the visually assessed subjective verticality and related cognitive demands. Significantly larger error angles were measured under rotational optic flows than under straight flows (p < 0.001). The error angles also significantly increased as the velocity of the rotational optic flow increased. The pupil diameter increased after starting the test, demonstrating the largest diameter during the final fine-tuning around the vertical. Significantly larger pupil changes were identified under rotational flows than in straight flows. Pupil changes were significantly correlated with error angles and the visual analog scale representing subjective difficulties during each test. These results suggest increased pupil changes for integrating more challenging visual sensory inputs in the process of gravity perception.

The pitfalls of investigating rotational flows with the Euler equations

Small viscous effects in high-Reynolds-number rotational flows always accumulate over time to have a leading-order effect. Therefore, the high-Reynolds-number limit for the Navier–Stokes equations is singular. It is important to investigate whether a solution of the Euler equations can approximate a real flow at large Reynolds number. These facts are often overlooked and, as a result, the Euler equations are used to simulate laminar rotational flows at large Reynolds number. Based on the Fredholm alternative, an asymptotic perturbation theory is described to establish secularity conditions determined by viscosity for an inviscid solution to approximate a real viscous fluid. Four important classical inviscid solutions are investigated using the theory with the following conclusions. The Stuart cats’ eyes and Mallier–Maslowe vortices are inconsistent with any real fluid at high Reynolds number; whereas Hill's spherical vortex is confirmed to be consistent with a steady state in the spherical core region and the Lamb–Chaplygin dipole is found to be consistent with a quasi-steady state in the circular core region. These solutions have been widely used for analysing the stability of vortex flows and wakes, and their interactions with shock waves or bubbles. Serendipitously, we have revealed an original exact solution of the Navier–Stokes equations which is time dependent, has non-zero nonlinear convective terms and is restricted to a finite domain with the decay rate depending on dipole radius.

A Case Study: Response Mechanics of Irregular Rotational Tidal Flows to Outlet Regulation in Yangtze Estuary

Responses of irregular rotational tidal flows to an outlet regulation (the Guyuan Sand (GYS) regulation) in the three-level branching Yangtze Estuary are studied by a high-resolution numerical model and theoretical analysis. The project is launched around GYS at the outlet of the North Branch of the Yangtze Estuary. The tidal flows around GYS are rotational and become irregular under the influences of the runoff-tide interactions, rapidly varying topographies and complex solid boundaries in coastal areas. Three designs of GYS regulation were studied, including various diversion dikes and new outlets of different widths. The regulation disturbs the irregular rotational flows around GYS, and further changes the estuarine tidal processes and the water exchange between different branches of the branching Yangtze Estuary. It was interesting to find that additional current and additional storage are formed along the North Branch when a southward outlet and the clockwise rotational flow met around GYS. This special phenomenon is named “guide effect” in this study. The guide effect, together with common resist effect (arising from the narrowed outlet channel), reshapes the estuarine tidal processes. Based on the simulation result and a theoretical analysis, response mechanics of irregular rotational tidal flows to the outlet regulation in complex branching estuaries are quantitatively studied.