arXiv subjects

Sébastien Gomé

Publications and source records attributed to Sébastien Gomé.

5 recordsLinked to original sources

arXiv2026

Helicity controls the direction of fluxes in rotating turbulence

Turbulence sustains out-of-equilibrium energy fluxes shaped by conservation laws. Three-dimensional flows conserve energy and sign-indefinite helicity, both being transferred to small scales. Yet in 3D rotating turbulence, energy is observed to flow simultaneously toward large-scale two-dimensional structures and toward small-scale three-dimensional waves. We uncover the origin of this dual behavior. When sufficiently fast inertial waves interact with a large-scale 2D flow, they conserve their helicity separately by sign, enforcing an inverse transfer of energy from 3D waves to 2D motions and promoting spectral condensation. Slower modes, by contrast, exchange helicity across sectors of opposite helicity signs and drive a forward transfer, like in non-rotating turbulence. Using a mean-wave kinetic theory, we derive analytical expressions for these competing bi-directional transfers and quantitatively predict the rotation- and Reynolds-number dependence of the large-scale 2D flow in fully nonlinear simulations, unifying the picture from small to infinite rotation.

physics.flu-dyn↗

arXiv2026

Waves maintain large-scale 2D flows in rotating turbulence and cause their demise

Turbulence follows a few well-known organizational principles, rooted in conservation laws. One such principle states that a system conserving two sign-definite invariants self-organizes into large-scale structures. Ordinary three-dimensional turbulence does not fall within this paradigm, but is profoundly altered when subject to rotation. In rotating turbulence, 3D inertial waves coexist alongside emergent two-dimensional structures, which tend to take the form of domain-scale flows called condensates. This interplay raises a fundamental question: why and when are 2D flows sustained if only 3D waves are excited? We develop a quasi-linear wave-kinetic theory to answer this question. We show that near-resonant interactions between 3D waves and a large-scale 2D flow impose an additional conservation law: waves must conserve their helicity separately for each helicity sign. This emergent sign-definite invariant constrains the waves to transfer their energy to large-scale 2D motions, which maintains the latter in statistical steady state. We derive analytical expressions for the 3D-2D energy transfer as a function of rotation, Reynolds number and domain geometry in a rotation dominated regime, and compare them with extensive numerical simulations of the rotating 3D Navier-Stokes equations. As rotation increases, the energy transfer from the waves to the 2D flow progressively vanishes as the two decouple, leading to a transition between distinct classes of turbulence: from 2D-dominated to 3D-dominated wave turbulence. Our theory shows that this gradual transition is caused by a depletion of modes satisfying the resonance conditions, and exhibits good agreement with numerical simulations when the number of near-resonant modes is not too small. We discuss such limitations of our theory, as well as the validity range of its underlying assumptions.

physics.flu-dyn↗

arXiv2026

Conservation laws, fluxes, and symmetries: lessons from a perturbative approach for self-organized turbulence

Some turbulent flows self-organize into large-scale structures, rather than breaking up into ever-smaller scales. Underpinning this phenomenon is the existence of two sign-definite quantities which are conserved by the dynamics. Two-dimensional turbulence is a prime example, where large-scale mean flows, termed condensates, spontaneously emerge. We review a perturbative theoretical framework for the statistical description of such inhomogeneous turbulence, offering new perspectives on the role of the two conserved quantities. We illustrate the universal properties of the theory, comparing results from two-dimensional Navier-Stokes to those from the large-scale-quasi-geostrophic equation. These two models are limiting cases of the shallow water quasi-geostrophic equation, the former exhibiting long-range fluid element interactions, while the latter has local interactions. We then demonstrate these theoretical ideas in two new settings: first, in rotating three-dimensional turbulence, where two-dimensional condensates are known to form. Considering jet-type condensates, we derive the mean-flow profile and discuss a surprising symmetry breaking. Second, we vary the Rossby deformation radius in the shallow water quasi-geostrophic equation. We obtain novel domain-spanning condensates in all tested regimes and show that they follow two-dimensional Navier-Stokes for deformation radii above the forcing scale, and the large-scale quasi-geostrophic equation for those below, demonstrating the power of these asymptotic models.

physics.flu-dyn↗

arXiv2024

Phase transition to turbulence via moving fronts

Directed percolation (DP), a universality class of continuous phase transitions, has recently been established as a possible route to turbulence in subcritical wall-bounded flows. In canonical straight pipe or planar flows, the transition occurs via discrete large-scale turbulent structures, known as puffs in pipe flow or bands in planar flows, which either self-replicate or laminarize. However, these processes might not be universal to all subcritical shear flows. Here, we design a numerical experiment that eliminates discrete structures in plane Couette flow and show that it follows a different, simpler transition scenario: turbulence proliferates via expanding fronts and decays via spontaneous creation of laminar zones. We map this phase transition onto a stochastic one-variable system. The level of turbulent fluctuations dictates whether moving-front transition is discontinuous, or continuous and within the DP universality class, with profound implications for other hydrodynamic systems.

physics.flu-dyn↗

arXiv2020

Statistical transition to turbulence in plane channel flow

Intermittent turbulent-laminar patterns characterize the transition to turbulence in pipe, plane Couette and plane channel flows. The time evolution of turbulent-laminar bands in plane channel flow is studied via direct numerical simulations using the parallel pseudospectral code ChannelFlow in a narrow computational domain tilted by $24^{\circ}$ with respect to the streamwise direction. Mutual interactions between bands are studied through their propagation velocities. Energy profiles show that the flow surrounding isolated turbulent bands returns to the laminar base flow over large distances. Depending on the Reynolds number, a turbulent band can either decay to laminar flow or split into two bands. As with past studies of other wall-bounded shear flows, in most cases survival probabilities are found to be consistent with exponential distributions for both decay and splitting, indicating that the processes are memoryless. Statistically estimated mean lifetimes for decay and splitting are plotted as a function of the Reynolds number and lead to the estimation of a critical Reynolds number $Re_{\text{cross}}\simeq 965$, where decay and splitting lifetimes cross at greater than $10^6$ advective time units. The processes of splitting and decay are also examined through analysis of their Fourier spectra. The dynamics of large-scale spectral components seem to statistically follow the same pathway during the splitting of a turbulent band and may be considered as precursors of splitting.

physics.flu-dyn↗