The spiral vortex. A story about tornados and bathtubs

TL;DR

This paper demonstrates how equiangular spirals naturally occur in fluid flows through sinks, providing a simple mathematical model to explain natural spiral formations, aiming to inspire further study in fluid dynamics and differential equations.

Contribution

It introduces a straightforward mathematical model linking logarithmic spirals to sink flows, combining complex variables and differential equations for educational purposes.

Findings

Equiangular spirals appear naturally in sink flows.

A simple mathematical model explains spiral formations in fluids.

Educational aim to stimulate further studies in fluid theory.

Abstract

In this paper, we show that equiangular spirals (also known as logarithmic spirals) appear naturally in fluids going through sinks. We provide a simple mathematical model that explains the spiral forms in some natural formations. For this model we need only small parts from the theories of complex variables and differential equations. The purpose of this educational paper is to stimulate students for further studies in fluid theory and differential equations.