Fujiwhara interaction of tropical cyclone scale vortices using a weighted residual collocation method

TL;DR

This paper introduces a novel computational model using a weighted residual collocation method to simulate Fujiwhara interactions of tropical cyclones, demonstrating high accuracy and insights into turbulence phenomena.

Contribution

The paper presents a new numerical approach combining multiresolution approximation and subgrid scale modeling for simulating cyclone interactions.

Findings

Excellent agreement with reference simulations at Re=5000.

Observation of energy cascade and enstrophy dynamics at higher Re.

Potential for improved mesoscale atmospheric circulation modeling.

Abstract

The fundamental interaction between tropical cyclones was investigated through a series of water tank experiements by Fujiwhara [20, 21, 22]. However, a complete understanding of tropical cyclones remains an open research challenge although there have been numerous investigations through measurments with aircrafts/satellites, as well as with numerical simulations. This article presents a computational model for simulating the interaction between cyclones. The proposed numerical method is presented briefly, where the time integration is performed by projecting the discrete system onto a Krylov subspace. The method filters the large scale fluid dynamics using a multiresolution approximation, and the unresolved dynamics is modeled with a Smagorinsky type subgrid scale parameterization scheme. Numerical experiments with Fujiwhara interactions are considered to verify modeling accuracy. An excellent agreement between the present simulation and a reference simulation at Re = 5000 has been demonstrated. At Re = 37440, the kinetic energy of cyclones is seen consolidated into larger scales with concurrent enstrophy cascade, suggesting a steady increase of energy containing scales, a phenomena that is typical in two-dimensional turbulence theory. The primary results of this article suggest a novel avenue for addressing some of the computational challenges of mesoscale atmospheric circulations.