Rigorous estimates of small scales in turbulent flows

1996 ◽  
Vol 37 (12) ◽  
pp. 6152-6156 ◽  
Author(s):  
Peter Constantin ◽  
Charles R. Doering ◽  
Edriss S. Titi
Keyword(s):  
Turbulent Flows ◽  
Small Scales

Lagrangian pair dispersion in upper-ocean turbulent flows with mixed-layer instabilities

2021 ◽  
Author(s):  
Stefano Berti ◽  
Guillaume Lapeyre
Keyword(s):  
Turbulent Flows ◽  
Mixed Layer ◽  
Separation Distance ◽  
Vertical Shear ◽  
Spreading Process ◽  
Opposite Case ◽  
Dispersion Regime ◽  
Fluid Layers ◽  
Small Scales ◽  
Good Proxy

<p>Oceanic motions at scales larger than few tens of km are quasi-horizontal due to seawater stratification and Earth’s rotation and are characterized by quasi-two-dimensional turbulence. At scales around 300 km (in the mesoscale range), coherent vortices contain most of the kinetic energy in the ocean. At scales around 10 km (in the submesoscale range) the flow is populated by smaller eddies and filamentary structures associated with intense gradients (e.g. of temperature), which play an important role in both physical and biogeochemical budgets. Such small scales are found mainly in the weakly stratified mixed layer, lying on top of the more stratified thermocline. Submesoscale dynamics should strongly depend on the seasonal cycle and the associated mixed-layer instabilities. The latter are particularly relevant in winter and are responsible for the generation of energetic small scales that are not trapped at the surface, as those arising from mesoscale-driven processes, but extend down to the thermocline. The knowledge of the transport properties of oceanic flows at depth, which is essential to understand the coupling between surface and interior dynamics, however, is still limited.</p><p>By means of numerical simulations, we explore Lagrangian pair dispersion in turbulent flows from a quasi-geostrophic model consisting in two coupled fluid layers (representing the mixed layer and the thermocline) with different stratification. Such a model has been previously shown to give rise to both meso and submesoscale instabilities and subsequent turbulent dynamics that compare well with observations of wintertime submesoscale flows. We focus on the identification of different dispersion regimes and on the possibility to relate the characteristics of the spreading process at the surface and at depth, which is relevant to assess the possibility of inferring the dynamical features of deeper flows from the experimentally more accessible (e.g. by satellite altimetry) surface ones.</p><p>Using different statistical indicators, we find a clear transition of dispersion regime with depth, which is generic and can be related to the statistical features of the turbulent flows. The spreading process is local (namely, governed by eddies of the same size as the particle separation distance) at the surface. In the absence of a mixed layer it rapidly changes to nonlocal (meaning essentially driven by the largest eddies) at small depths, while in the opposite case this only occurs at larger depths, below the mixed layer. We then identify the origin of such behavior in the existence of fine-scale energetic structures due to mixed-layer instabilities. We further discuss the effect of vertical shear and address the properties of the relative motion of subsurface particles with respect to surface ones. In the absence of a mixed layer, the properties of the spreading process are found to rapidly decorrelate from those at the surface, but the relation between the surface and subsurface dispersion appears to be largely controlled by vertical shear. In the presence of mixed-layer instabilities, instead, the statistical properties of dispersion at the surface are found to be a good proxy for those in the whole mixed layer.</p>

Kolmogorov’s contributions to the physical and geometrical understanding of small-scale turbulence and recent developments

1991 ◽  
Vol 434 (1890) ◽  
pp. 183-210 ◽  
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Inertial Range ◽  
Small Scale ◽  
Small Scales ◽  
Recent Developments ◽  
Self Similar ◽  
Scale Turbulence ◽  
High Reynolds ◽  
Non Gaussian

This paper reviews how Kolmogorov postulated for the first time the existence of a steady statistical state for small-scale turbulence, and its defining parameters of dissipation rate and kinematic viscosity. Thence he made quantitative predictions of the statistics by extending previous methods of dimensional scaling to multiscale random processes. We present theoretical arguments and experimental evidence to indicate when the small-scale motions might tend to a universal form (paradoxically not necessarily in uniform flows when the large scales are gaussian and isotropic), and discuss the implications for the kinematics and dynamics of the fact that there must be singularities in the velocity field associated with the - 5/3 inertial range spectrum. These may be particular forms of eddy or ‘eigenstructure’ such as spiral vortices, which may not be unique to turbulent flows. Also, they tend to lead to the notable spiral contours of scalars in turbulence, whose self-similar structure enables the ‘box-counting’ technique to be used to measure the ‘capacity’ D K of the contours themselves or of their intersections with lines, D' K . Although the capacity, a term invented by Kolmogorov (and studied thoroughly by Kolmogorov & Tikhomirov), is like the exponent 2 p of a spectrum in being a measure of the distribution of length scales ( D' K being related to 2 p in the limit of very high Reynolds numbers), the capacity is also different in that experimentally it can be evaluated at local regions within a flow and at lower values of the Reynolds number. Thus Kolmogorov & Tikhomirov provide the basis for a more widely applicable measure of the self-similar structure of turbulence. Finally, we also review how Kolmogorov’s concept of the universal spatial structure of the small scales, together with appropriate additional physical hypotheses, enables other aspects of turbulence to be understood at these scales; in particular the general forms of the temporal statistics such as the high-frequency (inertial range) spectra in eulerian and lagrangian frames of reference, and the perturbations to the small scales caused by non-isotropic, non-gaussian and inhomogeneous large-scale motions.

Wave-vortex dynamics in rotating shallow water

1989 ◽  
Vol 206 ◽  
pp. 433-462 ◽  
Author(s):  
Marie Farge ◽  
Robert Sadourny
Keyword(s):  
Shallow Water ◽  
Turbulent Flows ◽  
Gravitational Energy ◽  
Energy Cascade ◽  
Adjustment Process ◽  
Coherent Vortices ◽  
Small Scales ◽  
Direct Energy ◽  
Incompressibility Constraint ◽  
Rotating Shallow Water

We investigate how two-dimensional turbulence is modified when the incompressibility constraint is removed, by numerically integrating the full Saint-Venant (shallow-water) equations. In the case of small geopotential fluctuations considered here, we find no energy exchange between the inertio-gravitational and the potentio-vortical components of the flow. At small scales, the potentio-vortical component behaves as if the flow were incompressible, while we observe an intense direct energy cascade within the inertio-gravitational component. At large scales, the reverse potentio-vortical energy cascade is reduced when the level of inertio-gravitational energy is high. Looking at the effect of rotation, we find that a fast rotation rate tends to inhibit all three cascades. In particular, the inhibition of the inertio-gravitational energy cascade towards small scales implies that the geostrophic adjustment process is hindered by an increase of rotation. Concerning the structure of the coherent vortices emerging out of these decaying turbulent flows, we observe that the smallest scales are concentrated inside the vortex cores and not on their periphery.

Spectral analysis of energy transfer in turbulent flows laden with heated particles

2017 ◽  
Vol 813 ◽  
pp. 1156-1175 ◽  
Author(s):  
H. Pouransari ◽  
H. Kolla ◽  
J. H. Chen ◽  
A. Mani
Keyword(s):  
Energy Transfer ◽  
Turbulent Flows ◽  
Turbulent Combustion ◽  
Stokes Number ◽  
Turbulence Modification ◽  
Wide Range ◽  
Small Scales ◽  
Divergence Free ◽  
Particle Heating ◽  
Transfer Term

In this study we consider particle-laden turbulent flows with significant heat transfer between the two phases due to sustained heating of the particle phase. The sustained heat source can be due to particle heating via an external radiation source as in the particle-based solar receivers or an exothermic reaction in the particles. Our objective is to investigate the effects of fluid heating by a dispersed phase on the turbulence evolution. An important feature in such settings is the preferential clustering phenomenon which is responsible for non-uniform distribution of particles in the fluid medium. Particularly, when the ratio of particle inertial relaxation time to the turbulence time scale, namely the Stokes number, is of order unity, particle clustering is maximized, leading to thin regions of heat source similar to the flames in turbulent combustion. However, unlike turbulent combustion, a particle-laden system involves a wide range of clustering scales that is mainly controlled by particle Stokes number. To study these effects, we considered a decaying homogeneous isotropic turbulence laden with heated particles over a wide range of Stokes numbers. Using a low-Mach-number formulation for the fluid energy equation and a Lagrangian framework for particle tracking, we performed numerical simulations of this coupled system. We then applied a high-fidelity framework to perform spectral analysis of kinetic energy in a variable-density fluid. Our results indicate that particle heating can considerably influence the turbulence cascade. We show that the pressure-dilatation term introduces turbulent kinetic energy at a range of scales consistent with the scales observed in particle clusters. This energy is then transferred to high wavenumbers via the energy transfer term. For low and moderate levels of particle heating intensity, quantified by a parameter $\unicode[STIX]{x1D6FC}$ defined as the ratio of eddy time to mean temperature increase time, turbulence modification occurs primarily in the dilatational modes of the velocity field. However, as the heating intensity is increased, the energy transfer term converts energy from dilatational modes to divergence-free modes. Interestingly, as the heating intensity is increased, the net modification of turbulence by heating is observed dominantly in divergence-free modes; the portion of turbulence modification in dilatational modes diminishes with higher heating. Moreover, we show that modification of divergence-free modes is more pronounced at intermediate Stokes numbers corresponding to the maximum particle clustering. We also present the influence of heating intensity on the energy transfer term itself. This term crosses over from negative to positive values beyond a threshold wavenumber, showing the cascade of energy from large scales to small scales. The threshold is shown to shift to higher wavenumbers with increasing heating, indicating a growth in the total energy transfer from large scales to small scales. The fundamental energy transfer analysis presented in this paper provides insightful guidelines for subgrid-scale modelling and large-eddy simulation of heated particle-laden turbulence.

scholarly journals Turbulence via information field dynamics

2015 ◽  
Vol 11 (A29B) ◽  
pp. 730-730
Author(s):  
Torsten A. Enßlin
Keyword(s):  
Turbulent Flows ◽  
Theoretical Framework ◽  
Statistical Information ◽  
Statistical Properties ◽  
Length Scales ◽  
Scale Free ◽  
Statistical Knowledge ◽  
Flow Fluctuations ◽  
Small Scales

AbstractTurbulent flows exhibit scale-free regimes, for which information on the statistical properties of the dynamics exists for many length-scales. The simulation of turbulent systems can benefit from the inclusion of such information on sub-grid process. How can statistical information about the flow on small scales be optimally incorporated into simulation schemes? Information field dynamics (IFD) is a novel information theoretical framework to design schemes that exploit such statistical knowledge on sub-grid flow fluctuations.

scholarly journals Fluctuation theorem and extended thermodynamics of turbulence

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200468
Author(s):  
Amilcare Porporato ◽  
Milad Hooshyar ◽  
Andrew D. Bragg ◽  
Gabriel Katul
Keyword(s):  
Energy Transfer ◽  
Steady State ◽  
Energy Balance ◽  
Turbulent Flows ◽  
Energy Supply ◽  
Planck Equation ◽  
Fluctuation Theorem ◽  
Spectral Energy ◽  
Small Scales ◽  
And Diffusion

Turbulent flows are out-of-equilibrium because the energy supply at large scales and its dissipation by viscosity at small scales create a net transfer of energy among all scales. This energy cascade is modelled by approximating the spectral energy balance with a nonlinear Fokker–Planck equation consistent with accepted phenomenological theories of turbulence. The steady-state contributions of the drift and diffusion in the corresponding Langevin equation, combined with the killing term associated with the dissipation, induce a stochastic energy transfer across wavenumbers. The fluctuation theorem is shown to describe the scale-wise statistics of forward and backward energy transfer and their connection to irreversibility and entropy production. The ensuing turbulence entropy is used to formulate an extended turbulence thermodynamics.

scholarly journals Small-scale universality in the spectral structure of transitional pipe flows

2020 ◽  
Vol 6 (4) ◽  
pp. eaaw6256
Author(s):  
Rory T. Cerbus ◽  
Chien-chia Liu ◽  
Gustavo Gioia ◽  
Pinaki Chakraborty
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Turbulent Flows ◽  
Turbulence Theory ◽  
Small Scale ◽  
Spectral Structure ◽  
Pipe Flows ◽  
Wide Range ◽  
Small Scales

Turbulent flows are not only everywhere, but every turbulent flow is the same at small scales. The extraordinary simplification engendered by this “small-scale universality” is a hallmark of turbulence theory. However, on the basis of the restrictive assumptions invoked by A. N. Kolmogorov to demonstrate this universality, it is widely thought that only idealized turbulent flows conform to this framework. Using experiments and simulations that span a wide range of Reynolds number, we show that small-scale universality governs the spectral structure of a class of flows with no apparent ties to the idealized flows: transitional pipe flows. Our results not only extend the universality of Kolmogorov’s framework beyond expectation but also establish an unexpected link between transitional pipe flows and Kolmogorovian turbulence.

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