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

TL;DR

This paper investigates the swirling structures in axi-symmetric Navier-Stokes flows near a flat boundary through numerical simulations, revealing phenomena unique to flows with swirl, such as drastic changes in maximum velocity location and boundary phenomena.

Contribution

It provides a detailed numerical analysis of swirling versus non-swirling axi-symmetric flows, highlighting unique behaviors associated with swirl near boundaries.

Findings

Maximum velocity magnitude occurs near the axis and boundary near the turning point.

Flow with swirl exhibits drastic changes in the position of maximum velocity.

Unique boundary phenomena are observed in swirling flows.

Abstract

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.