## Research Unit Seminar Nov 28, 2023

**Speaker:**Lucas Huysmans (University of Cambridge) 16h00, Boualem Khouider (University of Victoria) 17h00**Date:**Nov 28, 2023 16h00 - 18h00**Location**: Room 315 (Schlossgartenstraße 7 (S2|15), 64289 Darmstadt) and online (Zoom)**Abstracts:**

## "Non-uniqueness and Inadmissibility of the Vanishing Viscosity Limit of the Passive Scalar Transport Equation"

We consider the linear transport of a passive scalar along a given bounded background incompressible flow. In this setting the viscous problem (the advection-diffusion equation) is globally well-posed, while the non-viscous problem is ill-posed unless the background velocity field is assumed to be more regular. We study the limit as viscosity goes to zero for the advection diffusion equation and construct two background velocity fields for which the vanishing viscosity/diffusion limit behaves unphysically. For the first of these, any initial data admits two different vanishing viscosity subsequences which converge to two different (renormalised) weak solutions to the transport equation. The second construction has for any initial data a unique vanishing viscosity limit, but this limit is perfectly mixed to its average, and after a short delay subsequently unmixes to its initial state, disobeying entropy admissibility for every initial data.

## "A multi-cloud and multi-mode model for convectively driven coastal flows"

Coastal areas have the peculiarity of being affected by the land-sea contrast that drives sea and land breezes oscillating back a forth between the day and night, respectively. In return, these flows characterize the weather and local climates of coastal areas especially through the associated overturning circulation that regulates local convection and precipitation both over land and over the ocean. This sometimes leads to multiple scale precipitation systems that propagate in either direction across the coastline (i.e., landward and oceanward) that are believe to interact with weather systems on synoptic and intraseanal systems that are important globally for both weather predictions on a fews weeks to a few months as well as climate variability. Despite numerous theoretical and observational efforts to understand coastal convection, global climate models still fail to represent it adequately, mainly because of limitations in spatial resolution and shortcomings in the underlying cumulus parameterization schemes. Here we use a simplified model of intermediate complexity to simulate coastal convection under the influence of the diurnal cycle of solar heating.

A key mathematical aspect of the models is that it systematically couples the dynamics in the mixed planetary boundary layer and the barotropic and first two baroclinic modes of vertical structure. Convection is parameterized via a stochastic multicloud model (SMCM), which mimics the subgrid dynamics of organized convection. In particular, the boundary layer dynamics are represented by a bulk model coupling the changing surface conditions in both space and time and free tropospheric flow through the exchange of heat and momentum fluxes at respectively the bottom and top of the boundary layer.

Numerical results demonstrate that the model is able to capture some key modes of coastal convection variability, such as the diurnal cycle of convection and the accompanying sea and land breeze reversals, the slowly propagating mesoscale convective systems that move from land to ocean and vice-versa, and numerous moisture-coupled gravity wave modes. The physical features of the simulated modes, such as their propagation speeds, the timing of rainfall peaks, the penetration of the sea and land breezes, and how they are affected by the latitudinal variation of the Coriolis force, are generally consistent with existing theoretical and observational studies.

(Joint work with Abigail Dah and Courtney Schumacher).