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Jezabel Curbelo

Publications and source records attributed to Jezabel Curbelo.

13 recordsLinked to original sources
arXiv2025

Wave-like Spiral Interactions and the Emergence of Quasi-Biennial Oscillations in Strato-Rotational Flows

This study investigates the dynamics of Strato-Rotational Instability (SRI) in a stratified, rotating fluid, focusing on the interaction between axial modes and spiral components. Through numerical analysis, we find that SRI induces oscillatory behaviors that change the mean flow, leading to the selective activation of distinct axial wavenumbers associated with upward and downward propagating spiral modes. These results suggest wave-mean flow interactions. The use of Radon Transforms (RT) allowed us to separate these spiral components, showing that each upward and downward component was individually modulated, but out of phase with each other. Inspired by the RT findings, a simplified toy model was developed to interpret the spiral pattern changes linked to amplitude modulations. The model considers two wave-like spirals propagating in opposite axial directions, linearly interacting. By incorporating out-of-phase individual spiral modulations, the model reproduces the observed spiral pattern transitions, offering a straightforward interpretation of the underlying physical processes. To explore the mechanism of individual spiral modulations, we consider a Quasi-Biennial Oscillation (QBO)-like framework derived from the Navier-Stokes equations in a rotating frame. These findings contribute to a better understanding of low-frequency SRI dynamics and may offer insights into similar phenomena in geophysical and astrophysical contexts.

physics.flu-dyn↗
arXiv2024

Mixing and Geometry in the North Atlantic Meridional Overturning Circulation

Vertical motions across the ocean are central to processes, like CO$_2$ fixation, heat removal or pollutant transport, which are essential to the Earth's climate. This work explores 3D conveyor routes {associated with} the Atlantic Meridional Overturning Circulation (AMOC). Our findings show the geometry of mixing structures in the upper and deep ocean layers by means of Lagrangian Coherent Structures. This tool identifies among others, zones linked to vertical transport and characterizes vertical transport time scales. We focus the study in two regions. The first one is the Flemish Cap region, a zone of interaction between the major AMOC components, where our analysis identifies a domain of deep waters that ascend very rapidly to the ocean surface. The second one is the Irminger Sea, where our analysis confirms the existence of a downwelling zone, and reveals a previously unreported upwelling connection between very deep waters and the ocean surface.

physics.ao-ph↗
arXiv2022

A playground for compressible natural convection with a nearly uniform density

In the quest to understand the basic universal features of compressible convection, one would like to disentangle genuine consequences of compression from spatial variations of transport properties. In the present work, we consider a very peculiar equation of state, whereby entropy is solely dependent on density, so that a nearly isentropic fluid domain is nearly isochoric. Within this class of equations of state, there is a thermal adiabatic gradient and a key property of compressible convection is still present, namely its capacity to viscously dissipate a large fraction of the thermal energy involved, of the order of the well-named dissipation number. In a series of anelastic approximations, under the assumption of an infinite Prandtl number, the number of governing parameters can be brought down to two, the Rayleigh number and the dissipation number. This framework is proposed as a playground for compressible convection, an opportunity to extend the vast corpus of theoretical analyses on the Oberbeck-Boussinesq equations regarding stability, bifurcations or the determination of upper bounds for the turbulent heat transfer. Here, in a two-dimensional geometry, we concentrate on the structure of upward and downward plumes depending on the dissipation number, on the heat flux dependence on the dissipation number and on the ratio of dissipation to convective heat flux. For dissipation numbers of order unity, in the limit of large Rayleigh numbers, dissipation becomes related to the entropy heat flux at each depth, so that the vertical dissipation profile can be predicted, and consequently so does the total ratio of dissipation to convective heat flux.

physics.flu-dyn↗
arXiv2018

Lagrangian study of the final warming in the southern stratosphere during 2002: Part II. 3D structure

This two-part paper aims to provide a Lagrangian perspective of the final southern warming in spring of 2002, during which the stratospheric polar vortex (SPV) experienced a unique splitting. We approach the subject from a dynamical systems viewpoint and search for Lagrangian coherent structures using a Lagrangian descriptor that is applied to reanalysis data. Part I presents our methodology and focuses by means of a kinematic model, on the understanding of fundamental processes for filamentation and ultimately for vortex splitting on an isentropic surface in the middle stratosphere. The present Part II discusses the three dimensional (3D) evolution of the flow during the selected event. For this, we apply concepts developed in Part I concerning a definition of the vortex boundary that helps in the selection of trajectories to illuminate the evolving flow structures, and a criterion that allows to justify why at an isentropic level a pinched vortex will split in later times. Lagrangian structures identified include surfaces that are several kilometers deep, and which a particle trajectory analysis confirms as barriers to the flow. The role of Lagrangian structures in determining the fate of particles during the SPV splitting is discussed.

physics.ao-ph↗
arXiv2018

Lagrangian study of the final warming in the southern stratosphere during 2002: Part I. The Vortex Splitting at Upper Levels

The present two-part paper provides a Lagrangian perspective of the final southern warming in 2002, during which the stratospheric polar vortex (SPV) experienced a unique splitting. Part I focuses on the understanding of fundamental processes for filamentation and ultimately for vortex splitting on a selected isentropic surface in the middle stratosphere. Part II discusses the three-dimensional evolution of the selected sudden warming event. We approach the subject from a dynamical systems viewpoint and search for Lagrangian coherent structures using a Lagrangian descriptor as a tool. In this Part I we work in the idealized framework of a kinematic model that allows for an understanding of the contributing elements of the flow in late September during the splitting. We introduce a definition of kinematic SPV boundary based on a criterion for binning parcels inside and outside the vortex according to their values of the Lagrangian descriptor and associated PDF. This definition is justified by using arguments that go beyond heuristic considerations based on the potential vorticity. Next, we turn to the filamentation proceses along this kinematic boundary, and the role of Lagrangian structures in the SPV splitting. We determine a criterion for splitting based on the structure of the evolving unstable and unstable manifolds.

physics.ao-ph↗
arXiv2017

Dynamic of plumes and scaling during the melting of a Phase Change Material heated from below

We identify and describe the main dynamic regimes occurring during the melting of the PCM n-octadecane in horizontal layers of several sizes heated from below. This configuration allows to cover a wide range of effective Rayleigh numbers on the liquid PCM phase, up to $\sim 10^9$, without changing any external parameter control. We identify four different regimes as time evolves: (i) the conductive regime, (ii) linear regime, (iii) coarsening regime and (iv) turbulent regime. The first two regimes appear at all domain sizes. However the third and fourth regime require a minimum advance of the solid/liquid interface to develop, and we observe them only for large enough domains. The transition to turbulence takes places after a secondary instability that forces the coarsening of the thermal plumes. Each one of the melting regimes creates a distinct solid/liquid front that characterizes the internal state of the melting process. We observe that most of the magnitudes of the melting process are ruled by power laws, although not all of them. Thus the number of plumes, some regimes of the Rayleigh number as a function of time, the number of plumes after the primary and secondary instability, the thermal and kinetic boundary layers follow simple power laws. In particular, we find that the Nusselt number scales with the Rayleigh number as $Nu \sim Ra^{0.29}$ in the turbulent regime, consistent with theories and experiments on Rayleigh-Bénard convection that show an exponent $2/7$.

physics.flu-dyn↗
arXiv2014

Symmetry and plate-like convection in fluids with temperature-dependent viscosity

We explore the instabilities developed in a fluid in which viscosity depends on temperature. In particular, we consider a dependency that models a very viscous (and thus rather rigid) lithosphere over a convecting mantle. To this end, we study a 2D convection problem in which viscosity depends on temperature by abruptly changing its value by a factor of 400 within a narrow temperature gap. We conduct a study which combines bifurcation analysis and time-dependent simulations. Solutions such as limit cycles are found that are fundamentally related to the presence of symmetry. Spontaneous plate-like behaviors that rapidly evolve towards a stagnant lid regime emerge sporadically through abrupt bursts during these cycles. The plate-like evolution alternates motions towards either the right or the left, thereby introducing temporary asymmetries on the convecting styles. Further time-dependent regimes with stagnant and plate-like lids are found and described.

physics.flu-dyn↗
arXiv2013

Bifurcations and dynamics in convection with temperature-dependent viscosity in the presence of the O(2) symmetry

We focus the study of a convection problem in a 2D setup in the presence of the O(2) symmetry. The viscosity in the fluid depends on the temperature as it changes its value abruptly in an interval around a temperature of transition. The influence of the viscosity law on the morphology of the plumes is examined for several parameter settings, and a variety of shapes ranging from spout to mushroom shaped is found. We explore the impact of the symmetry on the time evolution of this type of fluid, and find solutions which are greatly influenced by its presence: at a large aspect ratio and high Rayleigh numbers, traveling waves, heteroclinic connections and chaotic regimes are found. These solutions, which are due to the symmetry presence, have not been previously described in the context of temperature dependent viscosities. However, similarities are found with solutions described in other contexts such as flame propagation problems or convection problems with constant viscosity also under the presence of the O(2) symmetry, thus confirming the determining role of the symmetry in the dynamics.

physics.flu-dyn↗
arXiv2013

Lagrangian Descriptors: A Method for Revealing Phase Space Structures of General Time Dependent Dynamical Systems

In this paper we develop new techniques for revealing geometrical structures in phase space that are valid for aperiodically time dependent dynamical systems, which we refer to as Lagrangian descriptors. These quantities are based on the integration, for a finite time, along trajectories of an intrinsic bounded, positive geometrical and/or physical property of the trajectory itself. We discuss a general methodology for constructing Lagrangian descriptors, and we discuss a "heuristic argument" that explains why this method is successful for revealing geometrical structures in the phase space of a dynamical system. We support this argument by explicit calculations on a benchmark problem having a hyperbolic fixed point with stable and unstable manifolds that are known analytically. Several other benchmark examples are considered that allow us the assess the performance of Lagrangian descriptors in revealing invariant tori and regions of shear. Throughout the paper "side-by-side" comparisons of the performance of Lagrangian descriptors with both finite time Lyapunov exponents (FTLEs) and finite time averages of certain components of the vector field ("time averages") are carried out and discussed. In all cases Lagrangian descriptors are shown to be both more accurate and computationally efficient than these methods. We also perform computations for an explicitly three dimensional, aperiodically time-dependent vector field and an aperiodically time dependent vector field defined as a data set. Comparisons with FTLEs and time averages for these examples are also carried out, with similar conclusions as for the benchmark examples.

nlin.CD↗
arXiv2012

$γ$-radonifying operators and UMD-valued Littlewood-Paley-Stein functions in the Hermite setting on BMO and Hardy spaces

In this paper we study Littlewood-Paley-Stein functions associated with the Poisson semigroup for the Hermite operator on functions with values in a UMD Banach space $\B.$ If we denote by $H$ the Hilbert space $L^2((0,\infty),dt/t),γ(H,\B)$ represents the space of $γ$-radonifying operators from $H$ into $\B.$ We prove that the Hermite square function defines bounded operators from $BMO_\mathcal{L}(\R,\B)$ (respectively, $H^1_\mathcal{L}(\R, \B)$) into $BMO_\mathcal{L}(\R,γ(H,\B))$ (respectively, $H^1_\mathcal{L}(\R, γ(H,\B))$), where $BMO_\mathcal{L}$ and $H^1_\mathcal{L}$ denote $BMO$ and Hardy spaces in the Hermite setting. Also, we obtain equivalent norms in $BMO_\mathcal{L}(\R, \B)$ and $H^1_\mathcal{L}(\R,\B)$ by using Littlewood-Paley-Stein functions. As a consequence of our results, we establish new characterizations of the UMD Banach spaces.

math.CA↗
arXiv2012

Square functions in the Hermite setting for functions with values in UMD spaces

In this paper we characterize the Lebesgue Bochner spaces $L^p(\mathbb{R}^n,B)$, $1<p<\infty$, by using Littlewood-Paley $g$-functions in the Hermite setting, provided that $B$ is a UMD Banach space. We use $γ$-radonifying operators $γ(H,B)$ where $H=L^2((0,\infty),\frac{dt}{t})$. We also characterize the UMD Banach spaces in terms of $L^p(\mathbb{R}^n,B)$-$L^p(\mathbb{R}^n,γ(H,B))$ boundedness of Hermite Littlewood-Paley $g$-functions.

math.CA↗
arXiv2012

Spectral numerical schemes for time-dependent convection with viscosity dependent on temperature

This article proposes spectral numerical methods to solve the time evolution of convection problems with viscosity strongly depending on temperature at infinite Prandtl number. Although we verify the proposed techniques just for viscosities that depend exponentially on temperature, the methods are extensible to other dependence laws. The set-up is a 2D domain with periodic boundary conditions along the horizontal coordinate. This introduces a symmetry in the problem, the O(2) symmetry, which is particularly well described by spectral methods and motivates the use of these methods in this context. We examine the scope of our techniques by exploring transitions from stationary regimes towards time dependent regimes. At a given aspect ratio stable stationary solutions become unstable through a Hopf bifurcation, after which the time-dependent regime is solved by the spectral techniques proposed in this article.

physics.comp-ph↗