arXiv subjects

Marie Rodal

Publications and source records attributed to Marie Rodal.

4 recordsLinked to original sources

arXiv2024

Slender vortex filaments in the Boussinesq Approximation

A model for the motion of slender vortex filaments is extended to include the effect of gravity. The model, initially introduced by Callegari and Ting (SIAM, J. of App. Math., (1978), vol. 35, pp. 148-175), is based on a matched asymptotic expansion in which the outer solution, given by the Biot-Savart law, is matched with the inner solution derived from the Navier-Stokes equations. Building on recent work by Harikrishnan et al (Phys. of Fluids, (2023), vol. 35) the Boussinesq approximation is applied such that the density variations only enter in the gravity term. However, unlike Harikrishnan et al. (2023) the density variation enters at a lower order in the asymptotic expansion, and thus has a more significant impact on the self-induced velocity of the vortex filament. In this regime, which corresponds to the regime studied by Chang and Smith (J. of Fl. Mech., (2018), vol. 857), the effect of gravity is given by an alteration of the core constant, which couples the motion of the filament to the motion within the vortical core, in addition to a change in the compatability conditions (evolution equations) which determine the leading order azimuthal and tangential velocity fields in the vortex core. The results are used to explain certain properties of bouyant vortex rings, as well as qualitatively explore the impact of gravity on tornado type atmospheric vorticies.

physics.flu-dyn↗

arXiv2023

On the motion of hairpin filaments in the atmospheric boundary layer

A recent work of Harikrishnan et al. [arXiv:2110.02253 (2021)] has revealed an abundance of hairpin-like vortex structures, oriented in a similar direction, in the turbulent patches of a stably stratified Ekman flow. The Ekman flow over a smooth wall is a simplified configuration of the Atmospheric Boundary Layer (ABL) where effects of both stratification and rotation are present. In this study, hairpin-like structures are investigated by treating them as slender vortex filaments, i.e., a vortex filament whose diameter $d$ is small when compared to its radius of curvature $R$. The corrected thin-tube model of Klein and Knio [J. Fluid Mech. (1995)] is used to compute the motion of these filaments with the ABL as a background flow. The influence of the mean background flow on the filaments is studied for two stably stratified cases and a neutrally stratified case. Our results suggest that the orientation of the hairpin filament in the spanwise direction is linked to its initial starting height under stable stratification whereas no such dependency can be observed with the neutrally stratified background flow. An improved feature tracking scheme based on spatial overlap for tracking $Q$-criterion vortex structures on the Direct Numerical Simulation (DNS) data is also developed. It overcomes the limitation of using a constant threshold in time by dynamically adjusting the thresholds to accommodate the growth or deterioration of a feature. A comparison between the feature tracking and the filament simulation reveals qualitatively similar temporal developments. Finally, an extension of the asymptotic analysis of Callegari and Ting [J. App. Math (1978)] is carried out to include the effect of gravity. The results show that, in the regime considered here, a contribution from the gravity term occurs only when the tail of an infinitely long filament is tilted at an angle relative to the wall.

physics.flu-dyn↗

arXiv2022

Dynamical Stability Indicator based on Autoregressive Moving-Average Models: Critical Transitions and the Atlantic Meridional Overturning Circulation

A statistical indicator for dynamic stability known as the $\Upsilon$ indicator is used to gauge the stability and hence detect approaching tipping points of simulation data from a reduced 5-box model of the North-Atlantic Meridional Overturning Circulation (AMOC) exposed to a time dependent hosing function. The hosing function simulates the influx of fresh water due to the melting of the Greenland ice sheet and increased precipitation in the North Atlantic. The $\Upsilon$ indicator is designed to detect changes in the memory properties of the dynamics, and is based on fitting ARMA (auto-regressive moving-average) models in a sliding window approach to time series data. An increase in memory properties is interpreted as a sign of dynamical instability. The performance of the indicator is tested on time series subject to different types of tipping, namely bifurcation-induced, noise-induced and rate-induced tipping. The numerical analysis show that the indicator indeed responds to the different types of induced instabilities. Finally, the indicator is applied to two AMOC time series from a full complexity Earth systems model (CESM2). Compared with the doubling CO$_2$ scenario, the quadrupling CO$_2$ scenario results in stronger dynamical instability of the AMOC during its weakening phase.

stat.AP↗

arXiv2021

Waves in the gas centrifuge: asymptotic theory and similarities with the atmosphere

We study the stratified gas in a rapidly rotating centrifuge as a model for the Earth's atmosphere. Based on methods of perturbation theory, it is shown that in certain regimes, internal waves in the gas centrifuge have the same dispersion relation to leading order as their atmospheric siblings. Assuming an air filled centrifuge with a radius of circa 50 cm, the optimal rotational frequency for realistic atmosphere-like waves is around 10 000 rounds per minute. Using gases of lower heat capacities at constant pressure, like xenon, the rotational frequencies can be even halved to obtain the same results. Similar to the atmosphere, it is feasible in the gas centrifuge to generate a clear scale separation of wave frequencies and therefore phase speeds between acoustic waves and internal waves. In addition to the centrifugal force, the Coriolis force acts in the same plane. However, its influence on axially homogeneous internal waves appears only as a higher-order correction. We conclude that the gas centrifuge provides an unprecedented opportunity to investigate atmospheric internal waves experimentally with a compressible working fluid.

physics.flu-dyn↗