A vertical slice frontogenesis test case for compressible nonhydrostatic dynamical cores of atmospheric models

TL;DR

This paper introduces a new vertical slice frontogenesis test case for compressible atmospheric models, enabling rapid 2D testing of numerical schemes and revealing frontogenesis challenges in a simplified setting.

Contribution

It presents a novel quasi-2D test case based on a standard 3D model, facilitating quick experimentation and analysis of numerical discretisations in atmospheric modeling.

Findings

Test case effectively demonstrates frontogenesis in a simplified setting.

Comparison of advective forms reveals a Hollingsworth-like instability.

Implicit finite element scheme provides a reference solution for the test case.

Abstract

A new test case is presented for evaluating the compressible dynamical cores of the atmospheric models. The test case is based on a compressible vertical slice model that can be obtained by simple modification of a standard three dimensional compressible dynamical core. On the one hand, an advantage of the test case is that is quasi-2D, so it can be run quickly on a standard workstation, enabling rapid experimentation with numerical schemes and discretisation choices. On the other hand, the test case exhibits frontogenesis, a challenging regime for numerical discretisations which usually only arises in 3D model configurations for the compressible case. Numerical results of the test case using an implicit time-stepping method with a compatible finite element discretisation are presented as a reference solution. An example comparison between advective and vector-invariant forms for the advective nonlinearity in the velocity equation demonstrates one possible use of the scheme. The comparison shows a Hollingsworth-like instability when the vector invariant form is used.