## C06 - Multiscale structure of atmospheric vortices

**Head(s):** Prof. Dr.-Ing. Rupert Klein, Hon.-Prof. Hans-Christian Hege

**Project member(s):** Tom Dörffel, Natalia Ernst, Gottfried Hastermann

**Participating institution(s):** FU Berlin, ZIB

### Project Summary

This project aims at a multiscale theory for the intensification of tropical storms. It builds upon the asymptotic analysis of nearly axisymmetric vortices with large tilt in dry air by Päschke et al., J. Fluid Mech. 701, 137–170, (2012). This theory incorporates the multiscale effects of clouds and precipitation in a simplified way as prescribed external heat sources. It predicts that certain arrangements of non-axisymmetric heating and vortex tilt can induce vortex amplification.

During the first funding period this theory was corroborated by idealised three-dimensional numerical simulations, and vortex formation under moist aerothermodynamics was studied using a regional weather forecast code. In extending the asymptotic theory to self-consistently include moist processes, we first studied deep convective “hot towers”, which play a central role in vortex intensification, and revealed a new mechanism for their self-sustainance. In parallel, the well-posedness of the moisture transport model was proven rigorously.

From the application perspective, the project will next include key multiscale processes neglected in the theory so far. These concern the energy supply through the near-surface boundary layer, vortex stabilisation by vortex Rossby waves, and the interaction of cloud tower ensembles with the bulk vortex. The result will be a discrete-continuous hybrid multiscale model.

One methodological challenge arises from the need to combine matched asymptotic expansions, multiple scales techniques, and stochastic analysis to capture the boundary layer, the vortex Rossby waves, and the ensembles of randomly triggered cloud towers, respectively.

A second methodological challenge lies in testing the increasingly complex theoretical model. To do so, advanced data analysis and visualisation techniques shall be utilised and extended were needed. The theory will be tested against observational data and high resolution numerical simulations, pursued, e.g., by the ministry-funded HD(CP)^{2} project. The challenge is to verify the theoretically predicted asymptotic scalings from the complex three-dimensional, nonstationary data. After extracting the characteristic scales and space-time structure of the boundary layer flow and of individual convection events, data analysis methods shall be developed that allow us to assess the validity of their asymptotic description, given observations and detailed flow simulations. An additional challenge is to define techniques by which the (stochastic) organisation of convection within the simulated bulk vortex can be characterised in sufficient detail for comparison with a related idealized stochastic model.

### Project publications

Müller, A. and Névir, P. and Klein, R.
(2018)
*Scale Dependent Analytical Investigation of the Dynamic State Index Concerning the Quasi-Geostrophic Theory.*
Mathematics of Climate and Weather Forecasting, 4
(1).
pp. 1-22.
ISSN 2353-6438 (online)

Hittmeir, S. and Klein, R.
(2018)
*Asymptotics for moist deep convection I: Refined scalings and self-sustaining updrafts.*
Theoretical and Computational Fluid Dynamics, 32
(2).
pp. 137-164.
ISSN 0935-4964 (Print) 1432-2250 (Online)

Hittmeir, S. and Klein, R. and Li, J. and Titi, E.
(2017)
*Global well-posedness for passively transported nonlinear moisture dynamics with phase changes.*
Nonlinearity, 30
(10).
pp. 3676-3718.
ISSN 0951-7715

Hittmeir, S. and Klein, R. and Müller, A. and Névir, P.
(2017)
*The Dynamic State Index with Moisture and Phase Changes.*
SFB 1114 Preprint
.
pp. 1-12.
(Unpublished)

Dörffel, T. and Papke, A. and Klein, R. and Smolarkiewicz, P.
(2017)
*Intensification of tilted atmospheric vortices by asymmetric diabatic heating.*
SFB 1114 Preprint in arXiv:1708.07674
.
pp. 1-22.
(Unpublished)

Mazza, E. and Ulbrich, U. and Klein, R.
(2017)
*The Tropical Transition of the October 1996 Medicane in the Western Mediterranean Sea: A Warm Seclusion Event.*
Monthly Weather Review, 145
.
pp. 2575-2595.
ISSN Online: 1520-0493 Print: 0027-0644

### Theses

Papke, A.
(2017)
*Atmospheric vortex stability under vertical shear.*
PhD thesis, FU Berlin, FB Mathematik & Informatik.