arXiv subjects

Pen-Yuan Hsu

Publications and source records attributed to Pen-Yuan Hsu.

3 recordsLinked to original sources

arXiv2025

Energy Transfer Dynamics Generated by Non-Axisymmetric Tornado-Type Flows

The energy cascade in turbulence, first statistically described by Richardson (1922) and Kolmogorov (1941), lacked connection to the underlying fluid dynamics. Recent numerical studies of Goto et al. (2017) and Yoneda et al. (2022) revealed scale-local energy transfer via vortex stretching but remained within spatial statistics. This study aims to uncover the time-dependent elementary process behind the energy cascade by constructing a tornado-type flow in a non-axisymmetric curved cylindrical domain. Our approach reveals specific vortex dynamics responsible for energy transfer, offering new insight into the physical mechanisms of turbulence.

math.AP↗

arXiv2015

A local analysis of the axi-symmetric Navier-Stokes flow near a saddle point and no-slip flat boundary

As one of the violent flow, tornadoes occur in many place of the world. In order to reduce human losses and material damage caused by tornadoes, there are many research methods. One of the effective methods is numerical simulations such as the work in a recent article Ishihara et al. (2011). The swirling structure is significant both in mathematical analysis and the numerical simulations of tornado. In this paper, we try to clarify the swirling structure. More precisely, we do numerical computations on axi-symmetric Navier-Stokes flows with no-slip flat boundary. We compare a hyperbolic flow with swirl and one without swirl and observe that the following phenomenons occur only in the swirl case: The distance between the point providing the maximum velocity magnitude |v| and the z-axis is drastically changing around some time (which we call it turning point). An "increasing velocity phenomenon" occurs near the boundary and the maximum value of |v| is obtained near the axis of symmetry and the boundary when time is close to the turning point.

math.AP↗

arXiv2013

A Liouville theorem for the planer Navier-Stokes equations with the no-slip boundary condition and its application to a geometric regularity criterion

We establish a Liouville type result for a backward global solution to the Navier-Stokes equations in the half plane with the no-slip boundary condition. No assumptions on spatial decay for the vorticity nor the velocity field are imposed. We study the vorticity equations instead of the original Navier-Stokes equations. As an application, we extend the geometric regularity criterion for the Navier-Stokes equations in the three-dimensional half space under the no-slip boundary condition.

math.AP↗