arXiv subjects

Perry L. Johnson

Publications and source records attributed to Perry L. Johnson.

16 recordsLinked to original sources

arXiv2026

Turbulence Without the Viscous Tilting of Vorticity

Vortex stretching is a fundamental aspect of Navier-Stokes turbulence and is commonly understood in analogy to the stretching of infinitesimal material lines. However, the parallel alignment of material lines and vorticity cannot be maintained due to the role of viscosity in the directional realignment of vorticity. In Navier-Stokes turbulence, the result is relatively modest quantitative differences in the alignment and stretching rates of vorticity compared to material lines. In this study, the qualitative effect of viscous tilting of vorticity is demonstrated directly by surgically removing it from direct numerical simulations of isotropic turbulence. The result is a drastic change to the fundamental structure of the flow, including a substantial deviation from the -5/3 inertial range scaling of the energy spectrum brought about by the infiltration and prevalence of viscous effects beyond the smallest scales. These observations demonstrate that the viscous tilting of vorticity is an essential characteristic of fluid turbulence. By extension, the same may be said of the difference in orientation and stretching rates for vorticity and infinitesimal material lines.

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arXiv2025

Artificial Bottleneck Effect in Large Eddy Simulations

In Navier-Stokes turbulence, a bottleneck effect in the energy cascade near the viscous cutoff causes an overshoot in the energy spectrum, or spectral bump, relative to Kolmogorov's -5/3 scaling. A similar overshoot occurs in large-eddy simulations (LES) when an eddy viscosity model is used. It is not a viscous phenomenon but is caused by error in the residual stress model. This artificial bottleneck effect in LES leads to an over-prediction of kinetic energy even when a dynamic procedure is used to capture the spectral decay at the cutoff scale. Recently, Johnson [2022, J. Fluid Mech., 934, A30] introduced a generalization of spatial filtering that provides a dynamic procedure without a test filter. In this paper, this method of Stokes flow regularization (SFR) is used with kinetic energy considerations to generate a range of LES models and explore the bottleneck effect in more detail. The coefficients for each dynamic model are determined locally, without averaging over homogeneous directions. A posteriori tests of the models in isotropic turbulence are reported, demonstrating the robustness of the SFR-based procedure for different model forms and enabling fair comparisons in terms of their impact on the bottleneck effect. An effective way to mitigate the bottleneck is to add a nonlinear gradient component in the residual stress closure, forming a dynamic mixed model. This approach improves representation of residual stress structure and energy cascade efficiencies.

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arXiv2025

Normality-based analysis of multiscale velocity gradients and energy transfer in direct and large-eddy simulations of isotropic turbulence

Symmetry-based analyses of multiscale velocity gradients highlight that strain self-amplification (SS) and vortex stretching (VS) drive forward energy transfer in turbulent flows. By contrast, a strain-vorticity covariance mechanism produces backscatter that contributes to the bottleneck effect in the subinertial range of the energy cascade. We extend these analyses by using a normality-based decomposition of filtered velocity gradients in forced isotropic turbulence to distinguish contributions from normal straining, pure shearing and rigid rotation at a given scale. Our analysis of direct numerical simulation (DNS) data illuminates the importance of shear layers in the inertial range and (especially) the subinertial range of the cascade. Shear layers contribute significantly to SS and VS and play a dominant role in the backscatter mechanism responsible for the bottleneck effect. Our concurrent analysis of large-eddy simulation (LES) data characterizes how different closure models affect the flow structure and energy transfer throughout the resolved scales. We thoroughly demonstrate that the multiscale flow features produced by a mixed model closely resemble those in a filtered DNS, whereas the features produced by an eddy viscosity model resemble those in an unfiltered DNS at a lower Reynolds number. This analysis helps explain how small-scale shear layers, whose imprint is mitigated upon filtering, amplify the artificial bottleneck effect produced by the eddy viscosity model in the inertial range of the cascade. Altogether, the present results provide a refined interpretation of the flow structures and mechanisms underlying the energy cascade and insight for designing and evaluating LES closure models.

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arXiv2025

Turbulence-Resolving Integral Simulations for Wall-Bounded Flows

The physical fidelity of turbulence models can benefit from a partial resolution of fluctuations, but doing so often comes with an increase in computational cost. To explore this trade-off in the context of wall-bounded flows, this paper introduces a framework for Turbulence-Resolving Integral Simulations (TRIS) with the goal of efficiently resolving the largest motions using a two-dimensional, three component representation of the flow defined by instantaneous wall-normal integrals of velocity and pressure. Self-sustaining turbulence with qualitatively realistic large-scale structures is demonstrated for TRIS on an open-channel (half-channel) flow configuration using moment-of-momentum integral equations derived from Navier-Stokes with relatively simple closure approximations. Evidence from Direct Numerical Simulations (DNS) suggests that TRIS can theoretically resolve 35-40% of the turbulent skin friction enhancement for friction Reynolds numbers between 180 and 5200, without a noticeable decrease or increase as a function of Reynolds number. The current implementation of TRIS can match this resolution while simulating one flow through time in ~1 minute on a single processor, even for very large Reynolds numbers. The framework facilitates a detailed apples-to-apples comparison of predicted statistics against data from DNS. Comparisons at friction Reynolds numbers of 395 and 590 show that TRIS generates a relatively accurate representation of the flow, while highlight discrepancies that demonstrate a need for improving the closure models. The present results for open-channel flow represent a proof of concept for TRIS as a new approach for wall-bounded turbulence modeling, motivating extension to more general flow configurations such as boundary layers on immersed objects.

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arXiv2023

On the large-scale sweeping of small-scale eddies in turbulence -- A filtering approach

We present an analysis of the Navier-Stokes equations based on a spatial filtering technique to elucidate the multi-scale nature of fully developed turbulence. In particular, the advection of a band-pass-filtered small-scale contribution by larger scales is considered, and rigorous upper bounds are established for the various dynamically active scales. The analytical predictions are confirmed with direct numerical simulation data. The results are discussed with respect to the establishment of effective large-scale equations valid for turbulent flows.

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arXiv2023

New Exact Betchov-like Relation for the Helicity Flux in Homogeneous Turbulence

In homogeneous and isotropic turbulence, the relative contributions of different physical mechanisms to the energy cascade can be quantified by an exact decomposition of the energy flux (P. Johnson, Phys. Rev. Lett., 124, 104501 (2020), J. Fluid Mech. 922, A3(2021)). We extend the formalism to the transfer of kinetic helicity across scales, important in the presence of large-scale mirror breaking mechanisms, to identify physical processes resulting in helicity transfer and quantify their contributions to the mean flux in the inertial range. All subfluxes transfer helicity from large to small scales. About 50% of the mean flux is due to the scale-local vortex flattening and vortex twisting. We derive a new exact relation between these effects, similar to the Betchov relation for the energy flux, revealing that the mean contribution of the former is three times larger than that of the latter. Multi-scale effects account for the remaining 50% of the mean flux, with approximate equipartition between multi-scale vortex flattening, twisting and entangling.

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arXiv2021

On the enhancement of boundary layer skin friction by turbulence: an angular momentum approach

Turbulence enhances the wall shear stress in boundary layers, significantly increasing the drag on streamlined bodies. Other flow features such as freestream pressure gradients and streamwise boundary layer growth also strongly influence the skin friction. In this paper, an angular momentum integral (AMI) equation is introduced to quantify these effects by representing them as torques that alter the shape of the mean velocity profile. This approach uniquely isolates the skin friction of a Blasius boundary layer in a single term that depends only on the Reynolds number, so that other torques are interpreted as augmentations relative to the laminar case having the same Reynolds number. The AMI equation for external flows shares this key property with the so-called FIK relation for internal flows [Fukagata et al. 2002, Phys. Fluids, \textbf{14}, L73-L76]. Without a geometrically imposed boundary layer thickness, the length scale in the Reynolds number for the AMI equation may be chosen freely. After a brief demonstration using Falkner-Skan boundary layers, the AMI equation is applied as a diagnostic tool on four transitional and turbulent boundary layer DNS datasets. Regions of negative wall-normal velocity are shown to play a key role in limiting the peak skin friction during the late stages of transition, and the relative strengths of terms in the AMI equation become independent of the transition mechanism a very short distance into the fully-turbulent regime. The AMI equation establishes an intuitive, extensible framework for interpreting the impact of turbulence and flow control strategies on boundary layer skin friction.

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arXiv2021

A physics-inspired alternative to spatial filtering for large-eddy simulations of turbulent flows

Large-eddy simulations (LES) are widely-used for computing high Reynolds number turbulent flows. Spatial filtering theory for LES is not without its shortcomings, including how to define filtering for wall-bounded flows, commutation errors for non-uniform filters, and extensibility to flows with additional complexity, such as multiphase flows. In this paper, the theory for LES is reimagined using a coarsening procedure that imitates nature. This physics-inspired approach is equivalent to Gaussian filtering for single-phase wall-free flows but opens up new insights for modeling even in that simple case. Boundaries and nonuniform resolution can be treated seemlessly in this framework without commutation errors, and the divergence-free condition is retained for incompressible flows. An alternative to the Germano identity is introduced and used to define a dynamic procedure without the need for a test filter. Potential extensions to more complex physics are briefly discussed.

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arXiv2021

On the role of vorticity stretching and strain self-amplification in the turbulence energy cascade

The tendency of turbulent flows to produce fine-scale motions from large-scale energy injection is often viewed as a scale-wise cascade of kinetic energy driven by vorticity stretching. This has been recently evaluated by an exact, spatially-local relationship [Johnson, P. L. 2020, Phys. Rev. Lett., \textbf{124}, 104501], which also highlights the contribution of strain self-amplification. In this paper, the role of these two mechanisms is explored in more detail. Vorticity stretching and strain amplification interactions between velocity gradients filtered at the same scale account for about half of the energy cascade rate, directly connecting restricted Euler dynamics to the energy cascade. Multiscale strain amplification and vorticity stretching are equally important, however, and more closely resemble eddy viscosity physics. Moreover, ensuing evidence of a power-law decay of energy transfer contributions from disparate scales supports the notion of an energy cascade, albeit a `leaky' one. Besides vorticity stretching and strain self-amplification, a third mechanism of energy transfer is introduced and related to the vortex thinning mechanism important for the inverse cascade in two dimensions. Simulation results indicate this mechanism also provides a net source of backscatter in three-dimensional turbulence, in the range of scales associated with the bottleneck effect. Taken together, these results provide a rich set of implications for large-eddy simulation modeling.

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arXiv2020

Identifying and tracking bubbles and drops in simulations: a toolbox for obtaining sizes, lineages, and breakup and coalescence statistics

Knowledge of bubble and drop size distributions in two-phase flows is important for characterizing a wide range of phenomena, including combustor ignition, sonar communication, and cloud formation. The physical mechanisms driving the background flow also drive the time evolution of these distributions. Accurate and robust identification and tracking algorithms for the dispersed phase are necessary to reliably measure this evolution and thereby quantify the underlying mechanisms in interface-resolving flow simulations. The identification of individual bubbles and drops traditionally relies on an algorithm used to identify connected regions. This traditional algorithm can be sensitive to the presence of spurious structures. A cost-effective refinement is proposed to maximize volume accuracy while minimizing the identification of spurious bubbles and drops. An accurate identification scheme is crucial for distinguishing bubble and drop pairs with large size ratios. The identified bubbles and drops need to be tracked in time to obtain breakup and coalescence statistics that characterize the evolution of the size distribution, including breakup and coalescence frequencies, and the probability distributions of parent and child bubble and drop sizes. An algorithm based on mass conservation is proposed to construct bubble and drop lineages using simulation snapshots that are not necessarily from consecutive time-steps. These lineages are then used to detect breakup and coalescence events, and obtain the desired statistics. Accurate identification of large-size-ratio bubble and drop pairs enables accurate detection of breakup and coalescence events over a large size range. Together, these algorithms enable insights into the mechanisms behind bubble and drop formation and evolution in flows of practical importance.

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arXiv2020

The turbulent bubble break-up cascade. Part 2. Numerical simulations of breaking waves

Breaking waves generate a distribution of bubble sizes that evolves over time. Knowledge of how this distribution evolves is of practical importance for maritime and climate studies. The analytical framework developed in Part 1 examined how this evolution is governed by the bubble-mass flux from large to small bubble sizes, which depends on the rate of break-up events and the distribution of child bubble sizes. These statistics are measured in Part 2 as ensemble-averaged functions of time by simulating ensembles of breaking waves, and identifying and tracking individual bubbles and their break-up events. The break-up dynamics are seen to be statistically unsteady, and two intervals with distinct characteristics were identified. In the first interval, the dissipation rate and bubble-mass flux are quasi-steady, and the theoretical analysis of Part 1 is supported by all observed statistics, including the expected -10/3 power-law exponent for the super-Hinze-scale size distribution. Strong locality is observed in the corresponding bubble-mass flux, supporting the presence of a super-Hinze-scale break-up cascade. In the second interval, the dissipation rate decays, and the bubble-mass flux increases as small- and intermediate-sized bubbles become more populous. This flux remains strongly local with cascade-like behaviour, but the dominant power-law exponent for the size distribution increases to -8/3 as small bubbles are also depleted more quickly. This suggests the emergence of different physical mechanisms during different phases of the breaking-wave evolution, although size-local break-up remains a dominant theme. Parts 1 and 2 present an analytical toolkit for population balance analysis in two-phase flows.

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arXiv2020

On the evolution of the velocity gradient tensor in transitional boundary layers

We study the transition to turbulence from the perspective of the velocity gradient tensor dynamics. Our work is motivated by the observation of nonlinear structures emerging during transition, as revealed by vortex identifiers such as the Q-criterion. To that end, we have derived transport equations based on several invariants of the velocity gradient tensor to obtain integral budgets spanning the different stages of transition from laminar to turbulent flow. We have also discussed which quantity would be the most appropriate in our study, while keeping in mind the potential for future modeling applications.

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arXiv2019

Energy transfer from large to small scales in turbulence by multi-scale nonlinear strain and vorticity interactions

An intrinsic feature of turbulent flows is an enhanced rate of mixing and kinetic energy dissipation due to the rapid generation of small-scale motions from large-scale excitation. The transfer of kinetic energy from large to small scales is commonly attributed to the stretching of vorticity by the strain-rate, but strain self-amplification also plays a role. Previous treatments of this connection are phenomenological or inexact, or cannot distinguish the contribution of vorticity stretching from that of strain self-amplification. In this paper, an exact relationship is derived which quantitatively establishes how intuitive multi-scale mechanisms such as vorticity stretching and strain self-amplification together actuate the inter-scale transfer of energy in turbulence. Numerical evidence validates this result and uses it to demonstrate that the contribution of strain self-amplification to energy transfer is higher than that of vorticity stretching, but not overwhelmingly so.

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arXiv2019

Predicting the impact of particle-particle collisions on turbophoresis with a reduced number of computational particles

A common feature of wall-bounded turbulent particle-laden flows is enhanced particle concentrations in a thin layer near the wall due to a phenomenon known as turbophoresis. Even at relatively low bulk volume fractions, particle-particle collisions regulate turbophoresis in a critical way, making simulations sensitive to collisional effects. Lagrangian tracking of every particle in the flow can become computationally expensive when the physical number of particles in the system is large. Artificially reducing the number of particles in the simulation can mitigate the computational cost. When particle-particle collisions are an important aspect determining the simulation outcome, as in the case when turbophoresis plays an active role, simply reducing the number of particles in the simulation significantly alters the computed particle statistics. This paper introduces a computational particle treatment for particle-particle collisions which reproduces the results of a full simulation with a reduced number of particles. This is accomplished by artificially enhancing the particle collision radius based on scaling laws for the collision rates. The proposed method retains the use of deterministic collision models and is applicable for both low and high Stokes number regimes.

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arXiv2016

Restricted Euler dynamics along trajectories of small inertial particles in turbulence

The fate of small particles in turbulent flows depends strongly on the surrounding fluid's velocity gradient properties such as rotation and strain-rates. For non-inertial (fluid) particles, the Restricted Euler model provides a simple, low-dimensional dynamical system representation of Lagrangian evolution of velocity gradients in fluid turbulence, at least for short times. Here we derive a new restricted Euler dynamical system for the velocity gradient evolution of inertial particles such as solid particles in a gas or droplets and bubbles in turbulent liquid flows. The model is derived in the limit of small (sub Kolmogorov scale) particles and low Stokes number. The system exhibits interesting fixed points, stability and invariant properties. Comparisons with data from Direct Numerical Simulations show that the model predicts realistic trends such as the tendency of increased straining over rotation along heavy particle trajectories and, for light particles such as bubbles, the tendency of reduced self-stretching of strain-rate.

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arXiv2016

A closure for Lagrangian velocity gradient evolution in turbulence using recent deformation mapping of initially Gaussian fields

The statistics of the velocity gradient tensor in turbulent flows are of both theoretical and practical importance. The Lagrangian view provides a privileged perspective for studying the dynamics of turbulence in general, and of the velocity gradient tensor in particular. Stochastic models for the Lagrangian evolution of velocity gradients in isotropic turbulence, with closure models for the pressure Hesssian and viscous Laplacian, have been shown to reproduce important features such as non-Gaussian probability distributions, skewness and vorticity strain-rate alignments. The Recent Fluid Deformation (RFD) closure introduced the idea of mapping an isotropic Lagrangian pressure Hessian as upstream initial condition using the fluid deformation tensor. Recent work on a Gaussian fields closure, however, has shown that even Gaussian isotropic velocity fields contain significant anisotropy for the conditional pressure Hessian tensor due to the inherent velocity-pressure couplings, and that assuming an isotropic pressure Hessian as upstream condition may not be realistic. In this paper, Gaussian isotropic field statistics are used to generate more physical upstream conditions for the recent fluid deformation mapping. In this new framework, known isotropy relations can be satisfied {\it a priori} and no DNS-tuned coefficients are necessary. A detailed comparison of results from the new model, referred to as the recent deformation of Gaussian fields (RDGF) closure, with existing models and DNS shows the improvements gained, especially in various single-time statistics of the velocity gradient tensor at moderate Reynolds numbers. Application to arbitrarily high Reynolds numbers remains an open challenge for this type of model, however.

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