arXiv subjects

Jerome Noir

Publications and source records attributed to Jerome Noir.

11 recordsLinked to original sources

arXiv2025

The reflection-transmission problem for inertial waves on geostrophic shear layers

Inertial waves in fluid regions of planets and stars play an important role in their dynamics and evolution, through energy, heat and angular momentum transport and mixing of chemicals. While inertial wave propagation in flows prescribed by solid-body rotation is well-understood, natural environments are often characterized by convection or zonal flows. In these more realistic configurations, we do not yet understand the propagation of inertial waves or their transport properties. In this work, we focus on the interaction between inertial waves and geostrophic currents, which has thus far only been investigated using ray theory, where the wave length is assumed to be small relative to the length scale of the current, or averaging/statistical approaches. We develop a quasi-two-dimensional analytical model to investigate the reflection and transmission of inertial waves in the presence of a localized geostrophic shear layer of arbitrary width and compare our theoretical findings to a set of numerical simulations. We demonstrate that, in contrast to ray theory predictions, partial reflections occur even in subcritical shear layers and tunnelling with almost total transmission is possible in supercritical shear layers, if the layer is thin compared to the wavelength. That is, supercritical shear layers act as low-pass filters for inertial wave beams allowing the low-wavenumber waves to travel through. Thus, our analytical model allows us to predict interactions between inertial waves and geostrophic shear layers not addressed by ray-based or statistical theories and conceptually understand the behaviour of the full wavefield around and inside such layers.

physics.geo-ph↗

arXiv2021

Fast Quasi-Geostrophic Magneto-Coriolis Modes in the Earth's core

Fast changes of Earth's magnetic field could be explained by inviscid and diffusion-less quasi-geostrophic (QG) Magneto-Coriolis modes. We present a hybrid QG model with columnar flows and three-dimensional magnetic fields and find modes with periods of a few years at parameters relevant to Earth's core. For the simple poloidal magnetic field that we consider here they show a localization of kinetic and magnetic energy in the equatorial region. This concentration of energy near the equator and the high frequency make them a plausible mechanism to explain similar features observed in recent geomagnetic field observations. Our model potentially opens a way to probe the otherwise inaccessible magnetic field structure in the Earth's outer core.

physics.geo-ph↗

arXiv2020

Libration-driven inertial waves and mean zonal flows in spherical shells

Several planetary bodies in our solar system undergo a forced libration owing to gravitational interactions with their orbital companions, leading to complex fluid motions in their metallic liquid cores or subsurface oceans. In this study, we numerically investigate flows in longitudinally librating spherical shells. We focus on the Ekman number dependencies of several shear layers when the libration frequency is less than twice of the rotation frequency and the libration amplitude is small. Time-dependent flows mainly consist of inertial waves excited at the critical latitudes due to the Ekman pumping singularities, forming conical shear layers. In particular, previous theoretical studies have proposed different scalings for the conical shear layers spawned from the critical latitudes at the inner boundary. Our numerical results favor the velocity amplitude scaling $\mathrm{O}(\varepsilon E^{1/12})$ predicted by Le Dizès \& Le Bars (2017) over the scaling $\mathrm{O}(\varepsilon E^{1/6})$ initially proposed by Kerswell (1995), though the Ekman numbers in our calculations are not sufficiently small to pin down this scaling. Non-linear interactions in the boundary layers drive a mean zonal flow with several geostrophic shears. Our numerical results show that geostrophic shears associated with the critical latitudes at the inner and outer boundaries exhibit the same scalings, i.e. an amplitude of $\mathrm{O}(\varepsilon^2 E^{-1/10})$ over a width of $\mathrm{O}(E^{1/5})$. Apart from the geostrophic shear associated with the critical latitude, our numerical results show that the reflection of inertial waves can induce a geostrophic shear with an amplitude of $\mathrm{O}(\varepsilon^2 E^{-1/6})$ over a width of $\mathrm{O}(E^{1/3})$.

physics.flu-dyn↗

arXiv2019

Particle streak velocimetry using Ensemble Convolutional Neural Networks

This study reports an approach and presents its open-source implementation for quantitative analysis of experimental flows using streak images and Convolutional Neural Networks (CNN). The latter are applied to retrieve a length and an angle from streaks, which can be used to deduce kinetic energy and directionality (up to 180$^{\circ}$ ambiguity) of an imaged flow. We developed a quick method for generating essentially unlimited number of training and validation images, which enabled efficient training. Additionally, we show how to apply an ensemble of CNNs to derive a formal uncertainty on the estimated quantities. The approach is validated on the numerical simulation of a convenctive turbulent flow and applied to a longitutidal libration flow experiment.

eess.IV↗

arXiv2019

Precessing spherical shells: flows, dissipation, dynamo and the lunar core

Precession of planets or moons affects internal liquid layers by driving flows, instabilities and possibly dynamos.The energy dissipated by these phenomena can influence orbital parameters such as the planet's spin rate.However, there is no systematic study of these flows in the spherical shell geometry relevant for planets, and the lack of scaling law prevents convincing extrapolation to celestial bodies.We have run more than 900 simulations of fluid spherical shells affected by precession, to systematically study basic flows, instabilities, turbulence, and magnetic field generation.We observe no significant effects of the inner core on the onset of the instabilities.We obtain an analytical estimate of the viscous dissipation, mostly due to boundary layer friction in our simulations.We propose theoretical onsets for hydrodynamic instabilities, and document the intensity of turbulent fluctuations.We extend previous precession dynamo studies towards lower viscosities, at the limits of today's computers.In the low viscosity regime, precession dynamos rely on the presence of large-scale vortices, and the surface magnetic fields are dominated by small scales.Interestingly, intermittent and self-killing dynamos are observed.Our results suggest that large-scale planetary magnetic fields are unlikely to be produced by a precession-driven dynamo in a spherical core.But this question remains open as planetary cores are not exactly spherical, and thus the coupling between the fluid and the boundary does not vanish in the relevant limit of small viscosity.Moreover, the fully turbulent dissipation regime has not yet been reached in simulations.Our results suggest that the melted lunar core has been in a turbulent state throughout its history.Furthermore, in the view of recent experimental results, we propose updated formulas predicting the fluid mean rotation vector and the associated dissipation in both the laminar and the turbulent regimes.

physics.flu-dyn↗

arXiv2017

Shear-driven parametric instability in a precessing sphere

The present numerical study aims at shedding light on the mechanism underlying the precessional instability in a sphere. Precessional instabilities in the form of parametric resonance due to topographic coupling have been reported in a spheroidal geometry both analytically and numerically. We show that such parametric resonances can also develop in spherical geometry due to the conical shear layers driven by the Ekman pumping singularities at the critical latitudes. Scaling considerations lead to a stability criterion of the form, $|P_o|>O(E^{4/5})$, where $P_o$ represents the Poincaré number and $E$ the Ekman number. The predicted threshold is consistent with our numerical simulations as well as previous experimental results. When the precessional forcing is supercriticial, our simulations show evidence of an inverse cascade, i.e. small scale flows merging into large scale cyclones with a retrograde drift. Finally, it is shown that this instability mechanism may be relevant to precessing celestial bodies such as the Earth and Earth's moon.

physics.flu-dyn↗

arXiv2016

Precession-driven dynamos in a full sphere and the role of large scale cyclonic vortices

Precession has been proposed as an alternative power source for planetary dynamos. Previous hydrodynamic simulations suggested that precession can generate very complex flows in planetary liquid cores [Y. Lin, P. Marti, and J. Noir, "Shear-driven parametric instability in a precessing sphere," Physics of Fluids 27, 046601 (2015)]. In the present study, we numerically investigate the magnetohydrodynamics of a precessing sphere. We demonstrate precession driven dynamos in different flow regimes, from laminar to turbulent flows. In particular, we highlight the magnetic field generation by large scale cyclonic vortices, which has not been explored previously. In this regime, dynamos can be sustained at relatively low Ekman numbers and magnetic Prandtl numbers, which paves the way for planetary applications.

physics.flu-dyn↗

arXiv2014

Experimental study of fluid flows in a precessing cylindrical annulus

The flow inside a precessing fluid cavity has been given particular attention since the end of the 19th century in geophysical and industrial contexts. The present study aims at shedding light on the underlying mechanism by which the flow inside a precessing cylindrical annulus transitions from laminar to multiple scale complex structures. We address this problem experimentally using ultrasonic Doppler velocimetry to diagnose the fluid velocity in a rotating and precessing cylindrical annulus. When precession is weak, the flow can be described as a superposition of forced inertial modes. Above a critical value of the precession rate, the forced flow couples with two free inertial modes satisfying triadic resonance conditions, leading to the classical growth and collapse. Using a Bayesian approach, we extract the wavenumber, frequency, growth rate and amplitude of each mode involved in the instability. In some cases, we observe for the first time ever experimentally two pairs of free modes coexisting with the forced flow. At larger precession rates, we do not observe triadic resonance any more, instead we observe several harmonics whose frequencies are integer multiples of the rotation frequency.

physics.flu-dyn↗

arXiv2014

Inertial wave and zonal flow in librating spherical shells

We numerically study the inertial waves and zonal flows in spherical shells driven by longitudinal libration, an oscillatory variation of rotation rate. Internal shear layers are generated due to breakdown of the Ekman boundary layer at critical latitudes. Our numerical results validate the scaling laws of internal shear layers predicted by previous studies. Mean zonal flows are driven by the non-linear interaction in the boundary layers. Non-linear interaction of inertial waves in the interior fluids has no significant contribution to the zonal flow. Multiple geostrophic shear layers are generated due to non-linearities in the boundary layers at critical latitudes and reflection points of internal shear layers. We also investigate the scaling laws of geostrophic shear layers and extrapolate the results to the planetary setting.

physics.flu-dyn↗

arXiv2014

Precession-driven flows in non-axisymmetric ellipsoids

We study the flow forced by precession in rigid non-axisymmetric ellipsoidal containers. To do so, we revisit the inviscid and viscous analytical models that have been previously developed for the spheroidal geometry by, respectively, Poincaré (Bull. Astronomique, vol. XXVIII, 1910, pp. 1-36) and Busse (J. Fluid Mech., vol. 33, 1968, pp. 739-751), and we report the first numerical simulations of flows in such a geometry. In strong contrast with axisymmetric spheroids, where the forced flow is systematically stationary in the precessing frame, we show that the forced flow is unsteady and periodic. Comparisons of the numerical simulations with the proposed theoretical model show excellent agreement for both axisymmetric and non-axisymmetric containers. Finally, since the studied configuration corresponds to a tidally locked celestial body such as the Earth's Moon, we use our model to investigate the challenging but planetary-relevant limit of very small Ekman numbers and the particular case of our Moon.

physics.flu-dyn↗

arXiv2013

Experimental study of libration-driven zonal flows in non-axisymmetric containers

Orbital dynamics that lead to longitudinal libration of celestial bodies also result in an elliptically deformed equatorial core-mantle boundary. The non-axisymmetry of the boundary leads to a topographic coupling between the assumed rigidmantle and the underlying low viscosity fluid.The present experimental study investigates theeffect of non axisymmetric boundaries on the zonal flow driven by longitudinal libration. For large enough equatorial ellipticity, we report intermittent space-filling turbulence in particular bands of resonant frequency correlated with larger amplitude zonal flow. The mechanism underlying the intermittent turbulence has yet to be unambiguously determined. Nevertheless, recent numerical simulations in triaxial and biaxial ellipsoids suggest that it may be associated with the growth and collapse of an elliptical instability (Cebron et al., 2012). Outside of the band of resonance, we find that the background flow is laminar and the zonal flow becomes independent of the geometry at first order, in agreement with a non linear mechanism in the Ekman boundary layer (e.g. Calkins et al.; 2010, Sauret and Le Dizes, 2012b).

physics.geo-ph↗