Scalars convected by a 2D incompressible flow

TL;DR

This paper presents a test for numerical simulations of 2D incompressible flows with sharp fronts, demonstrating that such fronts require unbounded velocity growth.

Contribution

It introduces a new diagnostic test linking sharp front development to unbounded velocity growth in 2D incompressible flows.

Findings

Sharp fronts in simulations are associated with uncontrolled velocity growth.

The test can distinguish between physically realistic and numerical artifacts.

Flow conditions leading to sharp fronts require infinite velocity in theory.

Abstract

We provide a test for numerical simulations, for several two dimensional incompressible flows, that appear to develop sharp fronts. We show that in order to have a front the velocity has to have uncontrolled velocity growth.