Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 1812.05488

A bulk-interface correspondence for equatorial waves

Clément Tauber·Pierre Delplace·Antoine Venaille
View original source ↗Read source document ↗Export metadata ↓

Abstract

Topology is bringing new tools for the study of fluid waves. The existence of unidirectional Yanai and Kelvin equatorial waves has been related to a topological invariant, the Chern number, that describes the winding of $f$-plane shallow water eigenmodes around band crossing points in parameter space. In this previous study, the topological invariant was a property of the interface between two hemispheres. Here we ask whether a topological index can be assigned to each hemisphere. We show that this can be done if the shallow water model in $f$-plane geometry is regularized by an additional odd-viscous term. We then compute the spectrum of a shallow water model with a sharp equator separating two flat hemispheres, and recover the Kelvin and Yanai waves as two exponentially trapped waves along the equator, with all the other modes delocalized into the bulk. This model provides an exactly solvable example of bulk-interface correspondence in a flow with a sharp interface, and offers a topological interpretation for some of the transition modes described by [Iga, Journal of Fluid Mechanics 1995]. It also paves the way towards a topological interpretation of coastal Kelvin waves along a boundary, and more generally, to an understanding of bulk-boundary correspondence in continuous media.

Explore related subjects

physics.flu-dyncond-mat.mes-hallmath-phmath.MPphysics.ao-ph

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Clément Tauber, Pierre Delplace, Antoine Venaille. 2019-03-18. A bulk-interface correspondence for equatorial waves. https://doi.org/10.1017/jfm.2019.233

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Fast localized urban microclimate emulator: wind and temperatures in unseen urban morphologies

Urban microclimate, encompassing wind and temperature fields shaped by building geometry, strongly affects building energy use, pedestrian wind comfort, pollutant dispersion, the urban heat island, and public health. Conventional Computational Fluid Dynamics (CFD) is computationally prohibitive for rapid assessments, while many deep learning approaches require extensive training data and struggle with generalization to unseen configurations. In this work, we present the Fast Localized Urban Microclimate Emulator (FLUME), a rapid, data-efficient, and geometry-aware framework based on a Fourier neural operator for predicting three-dimensional wind and temperature fields. FLUME assumes that, under prescribed inflow and thermal forcing, much of the spatial variation of these mean fields is controlled by surrounding building geometry. The framework introduces a Multi-Directional Distance Feature (MDDF), which captures geometry over adaptive, visibility-defined spatial scales. By decomposing simulations of only 23 urban blocks into smaller 3D patches enriched with precomputed MDDF information, FLUME enables learning from limited CFD data. The model achieves mean absolute errors of 0.2 m/s for streamwise velocity and 0.19$^{\circ}$C for temperature on unseen urban configurations. A deep ensemble provides a practical proxy for epistemic uncertainty, and conformal prediction transforms these estimates into calibrated prediction intervals. Ensemble spread is positively related to local prediction error, with greater uncertainty in roof-level shear layers, building wakes, and vertical velocity near the ground. These results indicate FLUME's potential for rapid scenario assessment in urban design and urban climate studies.

physics.flu-dyn↗
arXiv2026

An Omni-Temporal Framework for Hydrodynamic Dispersion and Reaction in Porous Media

Many applications involve porous-media transport driven on time scales comparable to the pore-scale diffusion time, for which classical pseudo-steady dispersion models based on time-invariant transport coefficients may become inaccurate. While frequency-dependent dispersion has been studied in non-reactive porous media, a corresponding framework that simultaneously accounts for advection, diffusion, and heterogeneous interfacial reaction remains lacking. We address this gap by introducing an omni-temporal framework based on volume averaging of the frequency-domain pore-scale advection-diffusion equation subject to a Robin boundary condition spanning the full range of interfacial reactivity. The resulting upscaled formulation yields four frequency-dependent transfer functions: a dispersion tensor, an advection-suppression vector, a spectral Sherwood number, and a reactivity-bias vector, with the reactivity-bias vector introduced here for the first time. Analytical solutions for fully developed flow between parallel plates and through circular tubes reveal distinct kinetics- and diffusion-limited regimes, including capacitive and semi-infinite Warburg-type frequency responses. Comparisons of transient breakthrough curves with direct numerical simulations demonstrate substantial improvement over conventional pseudo-steady dispersion, particularly for short-duration pulses. Application to a periodic array of square rods under cross flow further demonstrates the frameworks applicability beyond canonical geometries.

physics.flu-dyn↗
arXiv2026

Dynamic mixed turbulence modeling using a super-resolution generative adversarial approach

A dynamic mixed super-resolution model (DMSRM) for large-eddy simulations (LESs) is proposed, which combines the traditional dynamic mixed model (DMM) formulation with the generation of super-resolved velocity fields from which the subfilter-scale (SFS) stress tensor can be computed. A data-driven super-resolution generative adversarial network (SR-GAN) is employed to upsample the grid-filtered velocity fields by a factor of two, enabling the evaluation of both scale-similarity and the dynamic Smagorinsky contributions. A priori analyses of forced homogeneous isotropic turbulence (HIT) show that the SR-GAN accurately reconstructs flow features and generalizes well across different filter sizes and higher Reynolds numbers within the same flow configuration, even for unseen input fields. The DMSRM reproduces SFS stresses and energy dissipation more accurately than the traditional DMM. A posteriori LES calculations further confirm that DMSRM predicts the energy spectrum and intermittency more accurately than DMM, even for different LES grid-scale resolutions and higher Reynolds numbers than those used for training within the same forced HIT flow configuration. Unlike DMM, DMSRM yields realistic backscatter and physically consistent SFS energy dissipation. These improvements arise from the physically accurate super-resolved fields generated by the SR-GAN, from which SFS stresses are directly computed. The result is a closure that accurately reproduces stress magnitudes and dissipation while reducing reliance on additional dissipation from the dynamic term. The DMSRM formulation achieves a balance of physical fidelity, robustness, and computational efficiency, offering a promising alternative to traditional DMMs for turbulence LES modeling.

physics.flu-dyn↗