arXiv subjects

Javier Jimenez

Publications and source records attributed to Javier Jimenez.

At least 19 recordsLinked to original sources

arXiv2026

Coherence does not always imply causality in wall-bounded turbulence

Compact structures of intense tangential Reynolds stress (Q events) are well-known components of wall-bounded turbulence, and have been shown to be coherent because they approximately govern their own evolution. It has therefore often been assumed that they also are causally significant, in the sense that they explain the evolution of the incoherent component of the flow, which could thus be modeled as a superposition of structures. Since strong events typically only fill a small percentage of the total flow volume, this is also cited as a reason for considering structures as targets for efficient engineering flow control. This paper shows that the causality assumption does not hold in general. Only about half of the structures identified in the flow are causally more significant than an equivalent volume of incoherent turbulence. To explain this variability, feature-based analysis and conditional averaging are performed. For wall-attached Q2 events and wall-detached structures, causally enhanced events are characterized by elevated strain rate and spanwise vorticity. These signatures are traced to intense upstream strain regions generated by the interaction of Q4-like motions impinging on Q2 events. For wall-attached Q4 events, the dominant indicators are instead the wall-normal and streamwise vorticity components; enhanced causal significance is associated with strong wall-normal vorticity. These findings show that quadrant events cannot be treated as a dynamically homogeneous class in causal analyses. Their causal significance depends strongly on the local flow environment, emphasizing the need to interpret coherent structures in terms of their interactions with the surrounding turbulence.

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arXiv2026

Wall-bounded turbulence needs not be long

Experiments on the regeneration of long streaks in flows in which they had originally been damped show that their initial growth is due to the interaction of the mean shear with long cross-flow velocities (rollers) that remain even when the streaks are damped. More surprisingly, turbulence also persists in simulations in which only the long rollers are damped while long streaks remain, and these flows are also able to recover when the damping is removed. Finally, simulations are presented in which both streaks and rollers longer than $\lambda_x^+ \approx 600$ are damped. They survive and regenerate, and an interpretation in terms of their energy balance is provided. In contraposition to the classical minimal channels, which include infinitely long structures, these new flows do not contain features longer than the damping wavelength, and support a model in which wall turbulence only depends on processes for which the geometric aspect ratio is of order unity.

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arXiv2025

Chaos, coherence and turbulence

This paper is a personal overview of the efforts over the last half century to understand fluid turbulence in terms of simpler coherent units. The consequences of chaos and the concept of coherence are first reviewed, using examples from free-shear and wall-bounded shear flows, and including how the simplifications due to coherent structures have been useful in the conceptualization and control of turbulence. It is remarked that, even if this approach has revolutionized our understanding of the flow, most of turbulence cannot yet be described by structures. This includes cascades, both direct and inverse, and possibly junk turbulence, whose role, if any, is currently unknown. This part of the paper is mostly a catalog of questions, some of them answered and others still open. A second part of the paper examines which new techniques can be expected to help in attacking the open questions, and which, in the opinion of the author, are the strengths and limitations of current approaches, such as data-driven science and causal inference.

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arXiv2024

Causal features in turbulent channel flow

The causal relevance of local flow conditions in wall-bounded turbulence is analysed using ensembles of interventional experiments in which the effect of perturbing the flow within a small cell is monitored at some future time. When this is done using the relative amplification of the perturbation energy, causality depends on the flow conditions within the cell before it is perturbed, and can be used as a probe of the flow dynamics. The key scaling parameter is the ambient shear, which is also the dominant diagnostic variable for wall-attached perturbations. Away from the wall, the relevant variables are the streamwise and wall-normal velocities. Causally significant cells are associated with sweeps that carry the perturbation towards the stronger shear near the wall, whereas irrelevant ones are associated with ejections that carry it towards the weaker shear in the outer layers. Causally significant and irrelevant cells are themselves organised into structures that share many characteristics with classical sweeps and ejections, such as forming spanwise pairs whose dimensions and geometry are similar to those of classical quadrants. At the wall, this is consistent with causally significant configurations in which a high-speed streak overtakes a low-speed one, and causally irrelevant ones in which the two streaks pull apart from each other. It is argued that this is probably associated with streak meandering.

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arXiv2023

A Perron-Frobenius analysis of wall-bounded turbulence

The Perron-Frobenius operator (PFO) is adapted from dynamical-system theory to the study of turbulent channel flow. It is shown that, as long as the analysis is restricted to the system attractor, the PFO can be used to differentiate causality and coherence from simple correlation without performing interventional experiments, and that the key difficulty remains collecting enough data to populate the operator matrix. This is alleviated by limiting the analysis to two-dimensional projections of the phase space, and developing a series of indicators to choose the best parameter pairs from a large number of possibilities. The techniques thus developed are applied to the study of bursting in the inertial layer of the channel, with emphasis on the process by which bursts are reinitiated after they have decayed. Conditional averaging over phase-space trajectories suggested by the PFO shows, somewhat counter-intuitively, that a key ingredient for the burst recovery is the development of a low-shear region near the wall, overlaid by a lifted shear layer. This is confirmed by a computational experiment in which the control of the mean velocity profile by the turbulence fluctuations is artificially relaxed. The behaviour of the mean velocity profile is thus modified, but the association of low wall shear with the initiation of the bursts is maintained.

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arXiv2022

The streaks of wall-bounded turbulence need not be long

The effect of damping the longest streaks in wall-bounded turbulence is explored using numerical experiments. It is found that long streaks are not required for the self-sustenance of the bursting process, which is relatively little affected by their absence. In particular, there are turbulence states in which the fluctuations of the streamwise velocity have approximately the same length as the bursts, and are thus presumably associated with the bursts themselves, while the burst structure is essentially indistinguishable from flows in which longer velocity fluctuations are present. This suggests that the long streaks found in unmodified flows may be byproducts, rather than active parts of the energy generation cycle.

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arXiv2021

Linear instability and resonance effects in large-scale opposition flow control

Opposition flow control is a robust strategy that has been proved effective in turbulent wall-bounded flows. Its conventional setup consists of measuring wall-normal velocity in the buffer layer and opposing it at the wall. This work explores the possibility of implementing this strategy with a detection plane in the logarithmic layer, where control could be feasible experimentally. We apply control on a channel flow at $Re_\tau = 932$, only on the eddies with relatively large wavelengths ($\lambda / h > 0.1$). Similarly to the buffer layer opposition control, our control strategy results in a virtual-wall effect for the wall-normal velocity, creating a minimum in its intensity. However, it also induces a large response in the streamwise velocity and Reynolds stresses near the wall, with a substantial drag increase. When the phase of the control lags with respect to the detection plane, spanwise-homogeneous rollers are observed near the channel wall. We show that they are a result of a linear instability. In contrast, when the control leads with respect to the detection plane, this instability is inactive and oblique waves are observed. Their wall-normal profiles can be predicted linearly as a response of the turbulent channel flow to a forcing with the advection velocity of the detection plane. The linearity, governing the flow, opens a possibility to affect large scales of the flow in a controlled manner, when enhanced turbulence intensity or mixing is desired.

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arXiv2021

An isolated logarithmic layer

To isolate the multiscale dynamics of the logarithmic layer of wall-bounded turbulent flows, a novel numerical experiment is conducted in which the mean tangential Reynolds stress is eliminated except in a subregion corresponding to the typical location of the logarithmic layer in channels. Various statistical comparisons against channel flow databases show that, despite some differences, this modified flow system reproduces the kinematics and dynamics of natural logarithmic layers well, even in the absence of a buffer and an outer zone. This supports the previous idea that the logarithmic layer has its own autonomous dynamics. In particular, the results suggest that the mean velocity gradient and the wall-parallel scale of the largest eddies are determined by the height of the tallest momentum-transferring motions, implying that the very large-scale motions of wall-bounded flows are not an intrinsic part of logarithmic-layer dynamics. Using a similar set-up, an isolated layer with a constant total stress, representing the logarithmic layer without a driving force, is simulated and examined.

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arXiv2020

Dipoles and streams in two-dimensional turbulence

Following the suggestion from the Monte--Carlo experiments in Jim\'enez, J. of Turbul. 2020), that dipoles are as important to the dynamics of decaying two-dimensional turbulence as individual vortex cores, it is found that the kinetic energy of this flow is carried by elongated streams formed by the concatenation of dipoles. Vortices separate into a family of small fast-moving cores, and another family of larger slowly moving ones, which can be described as `frozen' into a slowly evolving `crystal'. The kinematics of both families are very different, and only the former is self-similar. The latter is responsible for most of the kinetic energy of the flow, and its vortices form the dipoles and the streams. Mechanisms are discussed for the growth of this slow component.

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arXiv2020

Entropy, irreversibility and cascades in the inertial range of isotropic turbulence

This paper analyses the turbulent energy cascade from the perspective of statistical mechanics, and relates inter-scale energy fluxes to statistical irreversibility and information-entropy production. The microscopical reversibility of the energy cascade is tested by constructing a reversible 3D turbulent system using a dynamic model for the sub-grid stresses. This system, when reversed in time, develops a sustained inverse cascade towards the large scales, evidencing that the characterisation of the inertial energy cascade must consider the possibility of an inverse regime. This experiment is used to study the origin of statistical irreversibility and the prevalence of direct over inverse energy cascades in isotropic turbulence. Statistical irreversibility, a property of statistical ensembles in phase space related to entropy production, is connected to the dynamics of the energy cascade in physical space by considering the space locality of the energy fluxes and their relation to the local structure of the flow. A mechanism to explain the probabilistic prevalence of direct energy transfer is proposed based the dynamics of the rate-of-strain tensor, which is identified as the most important source of statistical irreversibility in the energy cascade.

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arXiv2020

Monte-Carlo science

This paper explores how far the scientific discovery process can be automated. Using the identification of causally significant flow structures in two-dimensional turbulence as an example, it probes how far the usual procedure of planning experiments to test hypotheses can be substituted by `blind' randomised experiments, and notes that the increased efficiency of computers is beginning to make such a `Monte-Carlo' approach practical in fluid mechanics. The process of data generation, classification and model creation is described in some detail, stressing the importance of validation and verification. Although the purpose of the paper is to explore the procedure, rather than to model two-dimensional turbulence, it is encouraging that the Monte Carlo process naturally leads to the consideration of vortex dipoles as building blocks of the flow, on a par with the more conventional individual vortex cores. Although not completely novel, this `spontaneous' discovery supports the claim that an important advantage of randomised experiments is to bypass researcher prejudice and alleviate paradigm lock. It is finally noted that the method can be extended to three-dimensional flows in practical times.

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arXiv2019

Momentum transfer by linearised eddies in channel flows

The presence and structure of an Orr-like inviscid mechanism is studied in fully developed, large-scale turbulent channel flow. Orr-like `bursts' are defined by the relation between the amplitude and local tilting angle of the wall-normal velocity perturbations, and extracted by means of wavelet-based filters. They span the shear-dominated region of the flow, and their sizes and lifespans are proportional to the distance from the wall in the logarithmic layer, forming a self-similar eddy hierarchy consistent with Townsend's attached-eddy model. Except for their amplitude, which has to be determined nonlinearly, linearised transient growth represents their evolution reasonably well. Conditional analysis, based on wavelet-filtered and low-pass-filtered velocity fields, reveals that bursts of opposite sign pair side-by-side to form tilted quasi-streamwise rollers, which align along the streaks of the streamwise velocity with the right sign to reinforce them, and that they preferentially cluster along pre-existing streak inhomogeneities. On the other hand, temporal analysis shows that consecutive rollers do not form simultaneously, suggesting that they incrementally trigger each other. This picture is similar to that of the streak-vortex cycle of the buffer layer, and the properties of the bursts suggest that they are different manifestations of the well-known attached Q$_2$-Q$_4$ events of the Reynolds stress.

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arXiv2019

Computers and turbulence

This paper briefly reviews the influence that the rapid evolution of computer power in the last decades has had on turbulence research. It is argued that it can be divided into three stages. In the earliest (`heroic') one, simulations were expensive and could at most be considered as substitutes for experiments. Later, as computers grew faster and some meaningful simulations could be performed overnight, it became practical to use them as (`routine') as tools to provide answers to specific theoretical questions. More recently, some turbulence simulations have become trivial, able to run in minutes, and it is possible to think of computers as `Monte Carlo' theory machines, which can be used to systematically pose a wide range of `random' theoretical questions, only to later evaluate which of them are interesting or useful. Although apparently wasteful, it is argued that this procedure has the advantage of being reasonably independence of received wisdom, and thus more able than human researchers to scape established paradigms. The rate of growth of computer power ensures that the interval between consecutive stages is about fifteen years. Rather than offering conclusions, the purpose of the paper is to stimulate discussion on whether machine- and human-generated theories can be considered comparable concepts, and on how the challenges and opportunities created by our new computer `colleagues' can be made to fit into the traditional research process.

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arXiv2018

Machine-aided turbulence theory

The question of whether significant sub-volumes of a turbulent flow can be identified by automatic means, independently of a-priori assumptions, is addressed using the example of two-dimensional decaying turbulence. Significance is defined as influence on the future evolution of the flow, and the problem is cast as an unsupervised machine `game' in which the rules are the Navier--Stokes equations. It is shown that significance is an intermittent quantity in this particular flow, and that, in accordance with previous intuition, its most significant features are vortices, while the least significant ones are dominated by strain. Subject to cost considerations, the method should be applicable to more general turbulent flows.

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arXiv2018

Intense structures of different momentum fluxes in turbulent channels

The effect of different definitions of the momentum flux on the properties of the coherent structures of the logarithmic region of wall-bounded turbulence is investigated by comparing the structures of intense tangential Reynolds stress with those of the alternative flux proposed in [J. Jimenez, J. Fluid Mech. 809, 585 (2016)]. Despite the fairly different statistical properties of the two flux definitions, it is found that their intense structures show many similarities, such as the dominance of 'wall-attached' objects, and geometric self-similarity. The new structures are wider, but not taller, than the classical ones, and include both high- and low-momentum regions within the same object. It is concluded that they represent the same phenomenon as the classical groups of a sweep, an ejection, and a roller, suggesting that these groups should be considered the fundamental coherent structures of the momentum flux. The present results show that the properties of these composite momentum structures are robust with respect to the definition of the fluxes.

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arXiv2018

Coherent structures in wall-bounded turbulence

This article discusses the description of wall-bounded turbulence as a deterministic high-dimensional dynamical system of interacting coherent structures, defined as eddies with enough internal dynamics to behave relatively autonomously from any remaining incoherent part of the flow. The guiding principle is that randomness is not a property, but a methodological choice of what to ignore in the flow, and that a complete understanding of turbulence, including the possibility of control, requires that it be kept to a minimum. After briefly reviewing the underlying low-order statistics of flows at moderate Reynolds numbers, the article examines what two-point statistics imply for the decomposition of the flow into individual eddies. Intense eddies are examined next, including their temporal evolution, and shown to satisfy many of the properties required for coherence. In particular, it is shown that coherent structures larger than the Corrsin scale are a natural consequence of the shear. In wall-bounded turbulence, they can be classified into coherent dispersive waves and transient bursts. The former are found in the viscous layer near the wall and as very-large structures spanning the boundary layer thickness. Although they are shear-driven, these waves have enough internal structure to maintain a uniform advection velocity. Conversely, bursts exist at all scales, are characteristic of the logarithmic layer, and interact almost linearly with the shear. While the waves require a wall to determine their length scale, the bursts are essentially independent from it. The article concludes with a brief review of our present theoretical understanding of turbulent structures, and with a list of open problems and future perspectives.

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arXiv2016

Optimal fluxes and Reynolds stresses

It is remarked that fluxes in conservation laws, such as the Reynolds stresses in the momentum equation of turbulent shear flows, or the spectral energy flux in isotropic turbulence, are only defined up to an arbitrary solenoidal field. While this is not usually significant for long-time averages, it becomes important when fluxes are modelled locally in large-eddy simulations, or in the analysis of intermittency and cascades. As an example, a numerical procedure is introduced to compute fluxes in scalar conservation equations in such a way that their total integrated magnitude is minimised. The result is an irrotational vector field that derives from a potential, thus minimising sterile flux `circuits'. The algorithm is generalised to tensor fluxes and applied to the transfer of momentum in a turbulent channel. The resulting instantaneous Reynolds stresses are compared with their traditional expressions, and found to be substantially different.

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arXiv2013

DNS of the very large anisotropic scales in a turbulent channel

The large structures in the outer layer of turbulent wall flows are of great physical importance, because they contain a substantial fraction of the streamwise kinetic energy and of the Reynolds stresses. Nevertheless, the organization of the outer region of wall turbulence has historically received less attention than that of the inner region, and as a consequence, it is still the subject of many open experimental and theoretical questions. In order to address some of those questions, we have performed direct numerical simulations of the turbulent incompressible flow in plane channels at Reynolds numbers 185 - 550. This paper presents some of the results of this simulation, focusing on the statistical description of the size of the large structures of the streamwise velocity and on its scaling with Reynolds number.

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