skip to main content


This content will become publicly available on July 1, 2025

Title: Quantifying small-scale anisotropy in turbulent flows
The verification of whether small-scale turbulence is isotropic remains a grand challenge. The difficulty arises because the presence of small-scale anisotropy is tied to the dissipation tensor, whose components require the full three-dimensional information of the flow field in both high spatial and temporal resolution, a condition rarely satisfied in turbulence experiments, especially during field scale measurement of atmospheric turbulence. To circumvent this issue, an intermittency-anisotropy framework is proposed through which we successfully extract the features of small-scale anisotropy from single-point measurements of turbulent time series by exploiting the properties of small-scale intermittency. Specifically, this framework quantifies anisotropy by studying the contrasting effects of burstlike activities on the scalewise production of turbulence kinetic energy between the horizontal and vertical directions. The veracity of this approach is tested by applying it over a range of datasets covering an unprecedented range in the Reynolds numbers (Re≈10^3–10^6), sampling frequencies (10 kHz to 10 Hz), surface conditions (aerodynamically smooth surfaces to typical grasslands to forest canopies), and flow types (channel flows, boundary-layer flows, atmospheric flows, and flows over forest canopies). For these diverse datasets, the findings indicate that the effects of small-scale anisotropy persists up to the integral scales of the streamwise velocity fluctuations and there exists a universal relationship to predict this anisotropy from the two-component state of the Reynolds stress tensor. This relationship is important towards the development of next-generation closure models of wall turbulence by incorporating the effects of anisotropy at smaller scales of the flow.  more » « less
Award ID(s):
2318718 2335847 2209695 2146520 2114740
NSF-PAR ID:
10523934
Author(s) / Creator(s):
;
Publisher / Repository:
APS
Date Published:
Journal Name:
Physical Review Fluids
Volume:
9
Issue:
7
ISSN:
2469-990X
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
More Like this
  1. In past experiments, simulations and theoretical analysis, rotation has been shown to dramatically effect the characteristics of turbulent flows, such as causing the mean velocity profile to appear laminar, leading to an overall drag reduction, as well as affecting the Reynolds stress tensor. The axially rotating pipe is an exemplary prototypical model problem that exhibits these complex turbulent flow physics. For this flow, the rotation of the pipe causes a region of turbulence suppression which is particularly sensitive to the rotation rate and Reynolds number. The physical mechanisms causing turbulence suppression are currently not well-understood, and a deeper understanding of these mechanisms is of great value for many practical examples involving swirling or rotating flows, such as swirl generators, wing-tip vortices, axial compressors, hurricanes, etc. In this work, Direct Numerical Simulations (DNS) of rotating turbulent pipe flows are conducted at moderate Reynolds numbers (Re=5300, 11,700, and 19,000) and rotation numbers of N=0 to 3. The main objectives of this work are to firstly quantify turbulence suppression for rotating turbulent pipe flows at different Reynolds numbers as well as study the effects of rotation on turbulence by analyzing the characteristics of the Reynolds stress tensor and the production and dissipation terms of the turbulence budgets. 
    more » « less
  2. Large-scale magnetic fields thread through the electrically conducting matter of the interplanetary and interstellar medium, stellar interiors and other astrophysical plasmas, producing anisotropic flows with regions of high-Reynolds-number turbulence. It is common to encounter turbulent flows structured by a magnetic field with a strength approximately equal to the root-mean-square magnetic fluctuations. In this work, direct numerical simulations of anisotropic magnetohydrodynamic (MHD) turbulence influenced by such a magnetic field are conducted for a series of cases that have identical resolution, and increasing grid sizes up to $2048^3$ . The result is a series of closely comparable simulations at Reynolds numbers ranging from 1400 up to 21 000. We investigate the influence of the Reynolds number from the Lagrangian viewpoint by tracking fluid particles and calculating single-particle and two-particle statistics. The influence of Alfvénic fluctuations and the fundamental anisotropy on the MHD turbulence in these statistics is discussed. Single-particle diffusion curves exhibit mildly superdiffusive behaviours that differ in the direction aligned with the magnetic field and the direction perpendicular to it. Competing alignment processes affect the dispersion of particle pairs, in particular at the beginning of the inertial subrange of time scales. Scalings for relative dispersion, which become clearer in the inertial subrange for a larger Reynolds number, can be observed that are steeper than indicated by the Richardson prediction. 
    more » « less
  3. Pressure anisotropy can strongly influence the dynamics of weakly collisional, high-beta plasmas, but its effects are missed by standard magnetohydrodynamics (MHD). Small changes to the magnetic-field strength generate large pressure-anisotropy forces, heating the plasma, driving instabilities and rearranging flows, even on scales far above the particles’ gyroscales where kinetic effects are traditionally considered most important. Here, we study the influence of pressure anisotropy on turbulent plasmas threaded by a mean magnetic field (Alfvénic turbulence). Extending previous results that were concerned with Braginskii MHD, we consider a wide range of regimes and parameters using a simplified fluid model based on drift kinetics with heat fluxes calculated using a Landau-fluid closure. We show that viscous (pressure-anisotropy) heating dissipates between a quarter (in collisionless regimes) and half (in collisional regimes) of the turbulent-cascade power injected at large scales; this does not depend strongly on either plasma beta or the ion-to-electron temperature ratio. This will in turn influence the plasma's thermodynamics by regulating energy partition between different dissipation channels (e.g. electron and ion heat). Due to the pressure anisotropy's rapid dynamic feedback onto the flows that create it – an effect we term ‘magneto-immutability’ – the viscous heating is confined to a narrow range of scales near the forcing scale, supporting a nearly conservative, MHD-like inertial-range cascade, via which the rest of the energy is transferred to small scales. Despite the simplified model, our results – including the viscous heating rate, distributions and turbulent spectra – compare favourably with recent hybrid-kinetic simulations. This is promising for the more general use of extended-fluid (or even MHD) approaches to model weakly collisional plasmas such as the intracluster medium, hot accretion flows and the solar wind.

     
    more » « less
  4. With the continuing progress in large eddy simulations (LES), and ever increasing computational resources, it is currently possible to numerically solve the time-dependent and anisotropic large scales of turbulence in a wide variety of flows. For some applications this large-scale resolution is satisfactory. However, a wide range of engineering problems involve flows at very large Reynolds numbers where the subgrid-scale dynamics of a practical LES are critically important to design and yet are out of reach given the com- putational demands of solving the Navier Stokes equations; this difficulty is particularly relevant in wall-bounded turbulence where even the large scales are often below the implied filter width of modest cost wall modeled LES. In this paper we briefly introduce a scale enrichment procedure which leverages spatially and spectrally localized Gabor modes. The method provides a physically consistent description of the small-scale velocity field without solving the full nonlinear equations. The enrichment procedure is appraised against its ability to predict small-scale contributions to the pressure field. We find that the method accurately extrapolates the pressure spectrum and recovers pressure variance of the full field remarkably well when compared to a computationally expensive, highly resolved LES. The analysis is conducted both in a priori and a posteriori settings for the case of homogeneous isotropic turbulence. 
    more » « less
  5. Abstract

    We report on a first-principles numerical and theoretical study of plasma dynamo in a fully kinetic framework. By applying an external mechanical force to an initially unmagnetized plasma, we develop a self-consistent treatment of the generation of “seed” magnetic fields, the formation of turbulence, and the inductive amplification of fields by the fluctuation dynamo. Driven large-scale motions in an unmagnetized, weakly collisional plasma are subject to strong phase mixing, which leads to the development of thermal pressure anisotropy. This anisotropy triggers the Weibel instability, which produces filamentary “seed” magnetic fields on plasma-kinetic scales. The plasma is thereby magnetized, enabling efficient stretching and folding of the fields by the plasma motions and the development of Larmor-scale kinetic instabilities such as the firehose and mirror. The scattering of particles off the associated microscale magnetic fluctuations provides an effective viscosity, regulating the field morphology and turbulence. During this process, the seed field is further amplified by the fluctuation dynamo until energy equipartition with the turbulent flow is reached. By demonstrating that equipartition magnetic fields can be generated from an initially unmagnetized plasma through large-scale turbulent flows, this work has important implications for the origin and amplification of magnetic fields in the intracluster and intergalactic mediums.

     
    more » « less