Do nonlinear effects disrupt tidal dissipation predictions in convective envelopes?

Most prior works studying tidal interactions in tight star/planet or star/star binary systems have employed linear theory of a viscous fluid in a uniformly-rotating two-dimensional spherical shell. However, compact systems may have sufficiently large tidal amplitudes for nonlinear effects to be important. We compute tidal flows subject to nonlinear effects in a 3D, thin (solar-like) convective shell, spanning the entire frequency range of inertial waves. Tidal frequency-averaged dissipation predictions of linear theory with solid body rotation are approximately reproduced in our nonlinear simulations (though we find it to be reduced by a factor of a few), but we find significant differences, potentially by orders of magnitude, at a fixed tidal frequency corresponding to a specific two-body system at a given epoch. This is largely due to tidal generation of differential rotation (zonal flows) and their effects on the waves.Comment: 2 pages, 1 figure, proceeding of the Annual meeting of the French Society of Astronomy and Astrophysics (SF2A 2023

Tidally-excited inertial waves in stars and planets: exploring the frequency-dependent and averaged dissipation with nonlinear simulations

We simulate the nonlinear hydrodynamical evolution of tidally-excited inertial waves in convective envelopes of rotating stars and giant planets modelled as spherical shells containing incompressible, viscous and adiabatically-stratified fluid. This model is relevant for studying tidal interactions between close-in planets and their stars, as well as close low-mass star binaries. We explore in detail the frequency-dependent tidal dissipation rates obtained from an extensive suite of numerical simulations, which we compare with linear theory, including with the widely-employed frequency-averaged formalism to represent inertial wave dissipation. We demonstrate that the frequency-averaged predictions appear to be quite robust and is approximately reproduced in our nonlinear simulations spanning the frequency range of inertial waves as we vary the convective envelope thickness, tidal amplitude, and Ekman number. Yet, we find nonlinear simulations can produce significant differences with linear theory for a given tidal frequency (potentially by orders of magnitude), largely due to tidal generation of differential rotation and its effects on the waves. Since the dissipation in a given system can be very different both in linear and nonlinear simulations, the frequency-averaged formalism should be used with caution. Despite its robustness, it is also unclear how accurately it represents tidal evolution in real (frequency-dependent) systems.Comment: 14 pages, 7 figures, 2 tables, to be published in ApJ

The Dynamics of Protein Kinase B Regulation during B Cell Antigen Receptor Engagement

This study has used biochemistry and real time confocal imaging of green fluorescent protein (GFP)-tagged molecules in live cells to explore the dynamics of protein kinase B (PKB) regulation during B lymphocyte activation. The data show that triggering of the B cell antigen receptor (BCR) induces a transient membrane localization of PKB but a sustained activation of the enzyme; active PKB is found in the cytosol and nuclei of activated B cells. Hence, PKB has three potential sites of action in B lymphocytes; transiently after BCR triggering PKB can phosphorylate plasma membrane localized targets, whereas during the sustained B cell response to antigen, PKB acts in the nucleus and the cytosol. Membrane translocation of PKB and subsequent PKB activation are dependent on BCR activation of phosphatidylinositol 3-kinase (PI3K). Moreover, PI3K signals are both necessary and sufficient for sustained activation of PKB in B lymphocytes. However, under conditions of continuous PI3K activation or BCR triggering there is only transient recruitment of PKB to the plasma membrane, indicating that there must be a molecular mechanism to dissociate PKB from sites of PI3K activity in B cells. The inhibitory Fc receptor, the FcγRIIB, mediates vital homeostatic control of B cell function by recruiting an inositol 5 phosphatase SHIP into the BCR complex. Herein we show that coligation of the BCR with the inhibitory FcγRIIB prevents membrane targeting of PKB. The FcγRIIB can thus antagonize BCR signals for PKB localization and prevent BCR stimulation of PKB activity which demonstrates the mechanism for the inhibitory action of the FcγRIIB on the BCR/PKB response

A model of rotating convection in stellar and planetary interiors: II -- gravito-inertial wave generation

Gravito-inertial waves are excited at the interface of convective and radiative regions and by the Reynolds stresses in the bulk of the convection zones of rotating stars and planets. Such waves have notable asteroseismic signatures in the frequency spectra of rotating stars, particularly among rapidly rotating early-type stars, which provides a means of probing their internal structure and dynamics. They can also transport angular momentum, chemical species, and energy from the excitation region to where they dissipate in radiative regions. To estimate the excitation and convective parameter dependence of the amplitude of those waves, a monomodal model for stellar and planetary convection as described in Paper I is employed, which provides the magnitude of the rms convective velocity as a function of rotation rate. With this convection model, two channels for wave driving are considered: excitation at a boundary between convectively stable and unstable regions and excitation due to Reynolds-stresses. Parameter regimes are found where the sub-inertial waves may carry a significant energy flux, depending upon the convective Rossby number, the interface stiffness, and the wave frequency. The super-inertial waves can also be enhanced, but only for convective Rossby numbers near unity. Interfacially excited waves have a peak energy flux near the lower cutoff frequency when the convective Rossby number of the flows that excite them are below a critical Rossby number that depends upon the stiffness of the interface, whereas that flux decreases when the convective Rossby number is larger than this critical Rossby number.Comment: 18 pages, 6 figures, accepted in Ap

LOISON (Marc). – École, alphabétisation et société rurale dans la France du Nord au XIXe siècle

Ce travail de recherche de Marc Loison, publié aux éditions L’Harmattan, est un condensé d’une thèse soutenue à l’Université de Lille III, en 1997, sous le titre : « Facteur d’alphabétisation et de scolarisation dans l’Arrageois au XIXe siècle ». La recherche se fonde sur l’analyse d’un échantillon de 18 000 signatures enregistrées à partir des dépouillements effectués dans les registres de mariages de plus de 70 communes de l’arrondissement d’Arras. Traditionnellement, le taux d’alphabétisat..

How do tidal waves interact with convective vortices in rapidly-rotating planets and stars?

The dissipation of tidal inertial waves in planetary and stellar convective regions is one of the key mechanisms that drive the evolution of star-planet/planet-moon systems. In this context, the interaction between tidal inertial waves and turbulent convective flows must be modelled in a realistic and robust way. In the state-of-the-art simulations, the friction applied by convection on tidal waves is modelled most of the time by an effective eddy-viscosity. This approach may be valid when the characteristic length scales of convective eddies are smaller than those of tidal waves. However, it becomes highly questionable in the case where tidal waves interact with potentially stable large-scale vortices, as those observed at the pole of Jupiter and Saturn. They are potentially triggered by convection in rapidly-rotating bodies in which the Coriolis acceleration forms the flow in columnar vortical structures along the direction of the rotation axis. In this paper, we investigate the complex interactions between a tidal inertial wave and a columnar convective vortex. We use a quasi-geostrophic semi-analytical model of a convective columnar vortex. We perform linear stability analysis to identify the unstable regime and conduct linear numerical simulations for the interactions between the convective vortex and an incoming tidal inertial wave. We verify that in the unstable regime, an incoming tidal inertial wave triggers the most unstable mode of the vortex leading to turbulent dissipation. For stable vortices, the wave-vortex interaction leads to the momentum mixing while it creates a low-velocity region around the vortex core and a new wave-like perturbation in the form of a progressive wave radiating in the far field. The emission of this secondary wave is the strongest when the wavelength of the incoming wave is close to the characteristic size of the vortex.Comment: 20 pages, 15 figures, accepted in Astronomy & Astrophysic

The complex interplay between tidal inertial waves and zonal flows in differentially rotating stellar and planetary convective regions:I. Free waves

Quantifying tidal interactions in close-in two-body systems is of prime interest since they have a crucial impact on the architecture and on the rotational history of the bodies. Various studies have shown that the dissipation of tides in either body is very sensitive to its structure and to its dynamics, like differential rotation which exists in the outer convective enveloppe of solar-like stars and giant gaseous planets. In particular, tidal waves may strongly interact with zonal flows at the so-called corotation resonances, where the wave's Doppler-shifted frequency cancels out. We aim to provide a deep physical understanding of the dynamics of tidal inertial waves at corotation resonances, in the presence of differential rotation profiles typical of low-mass stars and giant planets. By developping an inclined shearing box, we investigate the propagation and the transmission of free inertial waves at corotation, and more generally at critical levels, which are singularities in the governing wave differential equation. Through the construction of an invariant called the wave action flux, we identify different regimes of wave transmission at critical levels, which are confirmed with a one-dimensional three-layer numerical model. We find that inertial waves can be either fully transmitted, strongly damped, or even amplified after crossing a critical level. The occurrence of these regimes depends on the assumed profile of differential rotation, on the nature as well as the latitude of the critical level, and on wave parameters such as the inertial frequency and the longitudinal and vertical wavenumbers. Waves can thus either deposit their action flux to the fluid when damped at critical levels, or they can extract action flux to the fluid when amplified at critical levels. Both situations could lead to significant angular momentum exchange between the tidally interacting bodies.Comment: 25 pages, 12 figures, 4 tables, accepted for publication in Astronomy & Astrophysic

How tidal waves interact with convective vortices in rapidly rotating planets and stars

Context. The dissipation of tidal inertial waves in planetary and stellar convective regions is one of the key mechanisms that drive the evolution of star–planet and planet–moon systems. This dissipation is particularly efficient for young low-mass stars and gaseous giant planets, which are rapid rotators. In this context, the interaction between tidal inertial waves and turbulent convective flows must be modelled in a realistic and robust way. In the state-of-the-art simulations, the friction applied by convection on tidal waves is commonly modeled as an effective eddy viscosity. This approach may be valid when the characteristic length scales of convective eddies are smaller than those of the tidal waves. However, it becomes highly questionable in the case where tidal waves interact with potentially stable large-scale vortices such as those observed at the poles of Jupiter and Saturn. The large-scale vortices are potentially triggered by convection in rapidly-rotating bodies in which the Coriolis acceleration forms the flow in columnar vortical structures along the direction of the rotation axis. Aims. We investigate the complex interactions between a tidal inertial wave and a columnar convective vortex. Methods. We used a quasi-geostrophic semi-analytical model of a convective columnar vortex, which is validated by numerical simulations. First, we carried out linear stability analysis using both numerical and asymptotic Wentzel–Kramers–Brillouin–Jeffreys (WKBJ) methods. We then conducted linear numerical simulations of the interactions between a convective columnar vortex and an incoming tidal inertial wave. Results. The vortex we consider is found to be centrifugally stable in the range –Ωp ≤ Ω0 ≤ 3.62Ωp and unstable outside this range, where Ω0 is the local rotation rate of the vortex at its center and Ωp is the global planetary (stellar) rotation rate. From the linear stability analysis, we find that this vortex is prone to centrifugal instability with perturbations with azimuthal wavenumbers m = {0,1, 2}, which potentially correspond to eccentricity, obliquity, and asynchronous tides, respectively. The modes with m > 2 are found to be neutral or stable. The WKBJ analysis provides analytic expressions of the dispersion relations for neutral and unstable modes when the axial (vertical) wavenumber is sufficiently large. We verify that in the unstable regime, an incoming tidal inertial wave triggers the growth of the most unstable mode of the vortex. This would lead to turbulent dissipation. For stable convective columns, the wave-vortex interaction leads to the mixing of momentum for tidal inertial waves while it creates a low-velocity region around the vortex core and a new wave-like perturbation in the form of a progressive wave radiating in the far field. The emission of this secondary wave is the strongest when the wavelength of the incoming wave is close to the characteristic size (radius) of the vortex. Incoming tidal waves can also experience complex angular momentum exchanges locally at critical layers of stable vortices. Conclusions. The interaction between tidal inertial waves and large-scale coherent convective vortices in rapidly-rotating planets (stars) leads to turbulent dissipation in the unstable regime and complex behaviors such as mixing of momentum and radiation of new waves in the far field or wave-vortex angular momentum exchanges in the stable regime. These phenomena cannot be modeled using a simple effective eddy viscosity