Non-local two-dimensional turbulence and Batchelor's regime for passive scalars

2000 ◽  
Vol 408 ◽  
pp. 301-321 ◽  
Author(s):  
S. NAZARENKO ◽  
J.-P. LAVAL
Keyword(s):  
Large Scale ◽  
Passive Scalar ◽  
Turbulent Energy ◽  
Small Scale ◽  
Two Dimensional ◽  
Passive Scalars ◽  
Initial Spectrum ◽  
Non Local ◽  
Dimensional Argument ◽  
Special Case

We study small-scale two-dimensional non-local turbulence, where interaction of small scales with large vortices dominates in the small-scale dynamics, by using a semi-classical approach developed in Dyachenko, Nazarenko & Zakharov (1992), Nazarenko, Zabusky & Scheidegger (1995), Dubrulle & Nazarenko (1997) and Nazarenko, Kevlahan & Dubrulle (1999). Also, we consider a closely related problem of passive scalars in Batchelor's regime, when the Schmidt number is much greater than unity. In our approach, we do not perform any statistical averaging, and most of our results are valid for any form of the large-scale advection. A new invariant is found in this paper for passive scalars when their initial spectrum is isotropic. It is shown, analytically, numerically and using a dimensional argument, that there is a spectrum corresponding to an inverse cascade of the new invariant, which scales like k−1 for turbulent energy and k1 for passive scalars. For passive scalars, the k1-spectrum was first found by Kraichnan (1974) in the special case of advection δ-correlated in time, and until now it was believed to correspond to an absolute thermodynamic equilibrium and not a cascade. We also obtain, both analytically and numerically, power-law spectra of decaying two-dimensional turbulence, k−2, and passive scalar, k0.

Vortices in oscillating spin-up

2007 ◽  
Vol 573 ◽  
pp. 339-369 ◽  
Author(s):  
M. G. WELLS ◽  
H. J. H. CLERCX ◽  
G. J. F. VAN HEIJST
Keyword(s):  
Numerical Simulations ◽  
Power Law ◽  
Large Scale ◽  
Laboratory Experiments ◽  
Passive Scalar ◽  
Decay Rates ◽  
Small Scale ◽  
Two Dimensional ◽  
Ekman Pumping ◽  
Viscous Boundary Layer

Laboratory experiments and numerical simulations of oscillating spin-up in a square tank have been conducted to investigate the production of small-scale vorticity near the no-slip sidewalls of the container and the formation and subsequent decay of wall-generated quasi-two-dimensional vortices. The flow is made quasi-two-dimensional by a steady background rotation, and a small sinusoidal perturbation to the background rotation leads to the periodic formation of eddies in the corners of the tank by the roll-up of vorticity generated along the sidewalls. When the oscillation period is greater than the time scale required to advect a full-grown corner vortex to approximately halfway along the sidewall, dipole structures are observed to form. These dipoles migrate away from the walls, and the interior of the tank is continually filled with new vortices. The average size of these vortices appears to be largely controlled by the initial formation mechanism. Their vorticity decays from interactions with other stronger vortices that strip off filaments of vorticity, and by Ekman pumping at the bottom of the tank. Subsequent interactions between the weaker ‘old’ vortices and the ‘young’ vortices result in the straining, and finally the destruction, of older vortices. This inhibits the formation of large-scale vortices with diameters comparable to the size of the container.The laboratory experiments revealed a k−5/3 power law of the energy spectrum for small-to-intermediate wavenumbers. Measurements of the intensity spectrum of a passive scalar were consistent with the Batchelor prediction of a k−1 power law at large wavenumbers. Two-dimensional numerical simulations, under similar conditions to those in the experiments (with weak Ekman decay), were also performed and the simultaneous presence of a k−5/3 and k−3−ζ (with 0 < ζ « 1) power spectrum is observed, with the transition occurring at the wavenumber at which vorticity is injected from the viscous boundary layer into the interior. For higher Ekman decay rates, steeper spectra are obtained for the large wavenumber range, with ζ = O(1) and proportional to the Ekman decay rate. Movies are available with the online version of the paper.

The Fully Developed Wake of a Circular Cylinder

1949 ◽  
Vol 2 (4) ◽  
pp. 451 ◽  
Author(s):  
AA Townsend
Keyword(s):  
Circular Cylinder ◽  
Diffusion Coefficients ◽  
Large Scale ◽  
Turbulent Transport ◽  
Turbulent Energy ◽  
Small Scale ◽  
Mean Velocity ◽  
Turbulent Fluid ◽  
Air Stream ◽  
Scale Motion

Extending previous work on turbulent diffusion in the wake of a circular-cylinder, a series of measurements have been made of the turbulent transport of mean stream momentum, turbulent energy, and heat in the wake of a cylinder of 0.169 cm. diameter, placed in an air-stream of velocity 1280 cm. sec.-1. It has been possible to extend the measurements to 960 diameters down-stream from the cylinder, and it 1s found that, at distances in excess of 600 diameters, the requirements of dynamical similarity are very nearly satisfied. To account for the observed rates of transport of turbulent energy and heat, it is necessary that only part of this transport be due to bulk convection by the slow large-scale motion of the jets of turbulent fluid emitted by the central, fully turbulent core of the wake, which had been supposed previously to perform most of the transport. The remainder of the transport is carried out by the small-scale diffusive motion of the turbulent eddies within the jets, and may be described by assigning diffusion coefficients to the turbulent fluid. It is found that the diffusion coefficients for momentum and heat are approximately equal, but that for turbulent energy is considerably smaller. On the basis of these hypotheses, it is possible to calculate $he form of the mean velocity distribution in good agreement with experiment, and to give a qualitative explanation of the apparently more rapid diffusion of heat.

scholarly journals Toward understanding the multiscale spatial spectrum of solar convection

2012 ◽  
Vol 8 (S294) ◽  
pp. 361-363
Author(s):  
A. V. Getling ◽  
O. S. Mazhorova ◽  
O. V. Shcheritsa
Keyword(s):  
Convective Instability ◽  
Convective Flow ◽  
Large Scale ◽  
Fluid Layer ◽  
Boussinesq Equations ◽  
Spatial Spectrum ◽  
Small Scale ◽  
Two Dimensional ◽  
Solar Convection

AbstractConvection is simulated numerically based on two-dimensional Boussinesq equations for a fluid layer with a specially chosen stratification such that the convective instability is much stronger in a thin subsurface sublayer than in the remaining part of the layer. The developing convective flow has a small-scale component superposed onto a basic large-scale roll flow.

The power distribution between the symmetric and anti-symmetric components of the tropical wavenumber-frequency spectrum

2021 ◽  
Author(s):  
Ofer Shamir ◽  
Chen Schwartz ◽  
Chaim Garfinkel ◽  
Nathan Paldor
Keyword(s):  
Frequency Spectrum ◽  
Power Distribution ◽  
Large Scale ◽  
Spectral Power ◽  
Spatial Scales ◽  
Turbulent Energy ◽  
Heat Fluxes ◽  
Small Scale ◽  
Ample Evidence ◽  
Parity Distribution

&lt;p&gt;A yet unexplained feature of the tropical wavenumber-frequency spectrum is its parity distributions, i.e., the distribution of power between the meridionally symmetric and anti-symmetric components of the spectrum. Due to the linearity of the decomposition to symmetric and anti-symmetric components and the Fourier analysis, the total spectral power equals the sum of the power contained in each of these two components. However, the spectral power need not be evenly distributed between the two components. Satellite observations and reanalysis data provide ample evidence that the parity distribution of the tropical wavenumber-frequency spectrum is biased towards its symmetric component. Using an intermediate-complexity model of an idealized moist atmosphere, we find that the parity distribution of the tropical spectrum is nearly insensitive to large-scale forcing, including topography, ocean heat fluxes, and land-sea contrast. On the other hand, by adding a small-scale (stochastic) forcing, we find that the parity distribution of the tropical spectrum is sensitive to asymmetries on small spatial scales compared to the observed large-scale spectrum. Physically, such forcing can be thought of as small-scale convection, which is believed to trigger some of the Tropics' large-scale features via an upscale (inverse) turbulent energy cascade. These results are qualitatively explained by considering the effects of triad interactions on the parity distribution. According to the proposed mechanism, any small-scale asymmetry (symmetric or anti-symmetric) in the forcing leads to symmetric bias in the spectrum, regardless of the source of variability providing the forcing.&lt;/p&gt;

Reverberation Intensity Decaying in Range-Dependent Waveguide

2019 ◽  
Vol 27 (03) ◽  
pp. 1950007
Author(s):  
J. R. Wu ◽  
T. F. Gao ◽  
E. C. Shang
Keyword(s):  
Large Scale ◽  
Back Propagation ◽  
Normal Modes ◽  
Small Scale ◽  
Signal Pulse ◽  
First Order ◽  
Orthogonal Property ◽  
Short Signal ◽  
Scale Roughness ◽  
Special Case

In this paper, an analytic range-independent reverberation model based on the first-order perturbation theory is extended to range-dependent waveguide. This model considers the effect of bottom composite roughness: small-scale bottom rough surface provides dominating energy for reverberation, whereas large-scale roughness has the effect of forward and back propagation. For slowly varying bottom and short signal pulse, analytic small-scale roughness backscattering theory is adapted in range-dependent waveguides. A parabolic equation is used to calculate Green functions in range-dependent waveguides, and the orthogonal property of local normal modes is employed to estimate the modal spectrum of PE field. Synthetic tests demonstrate that the proposed reverberation model works well, and it can also predict the reverberation of range-independent waveguide as a special case.

A new model of shoaling and breaking waves. Part 2. Run-up and two-dimensional waves

2019 ◽  
Vol 867 ◽  
pp. 146-194 ◽  
Author(s):  
G. L. Richard ◽  
A. Duran ◽  
B. Fabrèges
Keyword(s):  
Large Scale ◽  
Turbulent Viscosity ◽  
Breaking Waves ◽  
Small Scale ◽  
Two Dimensional ◽  
Numerical Resolution ◽  
Wide Range ◽  
Scale Turbulence ◽  
Run Up ◽  
Averaged Model

We derive a two-dimensional depth-averaged model for coastal waves with both dispersive and dissipative effects. A tensor quantity called enstrophy models the subdepth large-scale turbulence, including its anisotropic character, and is a source of vorticity of the average flow. The small-scale turbulence is modelled through a turbulent-viscosity hypothesis. This fully nonlinear model has equivalent dispersive properties to the Green–Naghdi equations and is treated, both for the optimization of these properties and for the numerical resolution, with the same techniques which are used for the Green–Naghdi system. The model equations are solved with a discontinuous Galerkin discretization based on a decoupling between the hyperbolic and non-hydrostatic parts of the system. The predictions of the model are compared to experimental data in a wide range of physical conditions. Simulations were run in one-dimensional and two-dimensional cases, including run-up and run-down on beaches, non-trivial topographies, wave trains over a bar or propagation around an island or a reef. A very good agreement is reached in every cases, validating the predictive empirical laws for the parameters of the model. These comparisons confirm the efficiency of the present strategy, highlighting the enstrophy as a robust and reliable tool to describe wave breaking even in a two-dimensional context. Compared with existing depth-averaged models, this approach is numerically robust and adds more physical effects without significant increase in numerical complexity.

Infrared Reynolds number dependency of the two-dimensional inverse energy cascade

2011 ◽  
Vol 667 ◽  
pp. 463-473 ◽  
Author(s):  
ANDREAS VALLGREN
Keyword(s):  
Reynolds Number ◽  
Cascade Range ◽  
Energy Cascade ◽  
Energy Spectra ◽  
Small Scale ◽  
Two Dimensional ◽  
Inverse Energy Cascade ◽  
Linear Friction ◽  
Non Local ◽  
Reynolds Number Dependency

High-resolution simulations of forced two-dimensional turbulence reveal that the inverse cascade range is sensitive to an infrared Reynolds number, Reα = kf/kα, where kf is the forcing wavenumber and kα is a frictional wavenumber based on linear friction. In the limit of high Reα, the classic k−5/3 scaling is lost and we obtain steeper energy spectra. The sensitivity is traced to the formation of vortices in the inverse energy cascade range. Thus, it is hypothesized that the dual limit Reα → ∞ and Reν = kd/kf → ∞, where kd is the small-scale dissipation wavenumber, will lead to a steeper energy spectrum than k−5/3 in the inverse energy cascade range. It is also found that the inverse energy cascade is maintained by non-local triad interactions.

Enhanced dissipation for quasi-geostrophic motion over small-scale topography

2000 ◽  
Vol 407 ◽  
pp. 105-122 ◽  
Author(s):  
JACQUES VANNESTE
Keyword(s):  
Large Scale ◽  
Spatial Scales ◽  
Additional Term ◽  
Equation Of Motion ◽  
Small Scale ◽  
Two Dimensional ◽  
Turbulent Dissipation ◽  
Dissipative Term ◽  
History Of ◽  
Large Scale Flow

The effect of a small-scale topography on large-scale, small-amplitude oceanic motion is analysed using a two-dimensional quasi-geostrophic model that includes free-surface and β effects, Ekman friction and viscous (or turbulent) dissipation. The topography is two-dimensional and periodic; its slope is assumed to be much larger than the ratio of the ocean depth to the Earth's radius. An averaged equation of motion is derived for flows with spatial scales that are much larger than the scale of the topography and either (i) much larger than or (ii) comparable to the radius of deformation. Compared to the standard quasi-geostrophic equation, this averaged equation contains an additional dissipative term that results from the interaction between topography and dissipation. In case (i) this term simply represents an additional Ekman friction, whereas in case (ii) it is given by an integral over the history of the large-scale flow. The properties of the additional term are studied in detail. For case (i) in particular, numerical calculations are employed to analyse the dependence of the additional Ekman friction on the structure of the topography and on the strength of the original dissipation mechanisms.

scholarly journals Anisotropic Characteristics of Turbulence Dissipation in Swirling Flow: A Direct Numerical Simulation Study

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Xingtuan Yang ◽  
Nan Gui ◽  
Gongnan Xie ◽  
Jie Yan ◽  
Jiyuan Tu ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Energy Dissipation ◽  
Direct Numerical Simulation ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Vortex Breakdown ◽  
Swirling Flow ◽  
Turbulent Energy ◽  
Swirling Flows ◽  
Small Scale

This study investigates the anisotropic characteristics of turbulent energy dissipation rate in a rotating jet flow via direct numerical simulation. The turbulent energy dissipation tensor, including its eigenvalues in the swirling flows with different rotating velocities, is analyzed to investigate the anisotropic characteristics of turbulence and dissipation. In addition, the probability density function of the eigenvalues of turbulence dissipation tensor is presented. The isotropic subrange of PDF always exists in swirling flows relevant to small-scale vortex structure. Thus, with remarkable large-scale vortex breakdown, the isotropic subrange of PDF is reduced in strongly swirling flows, and anisotropic energy dissipation is proven to exist in the core region of the vortex breakdown. More specifically, strong anisotropic turbulence dissipation occurs concentratively in the vortex breakdown region, whereas nearly isotropic turbulence dissipation occurs dispersively in the peripheral region of the strong swirling flows.

STUDY ON RELATIONSHIP BETWEEN CONDENSED PARTICLES AND STRUCTURE OF CONDENSATION JET USING 2D IMAGE AND DISCRETE WAVELETS MULTIRESOLUTION

2006 ◽  
Vol 04 (02) ◽  
pp. 227-238
Author(s):  
MOTOAKI KIMURA ◽  
MASAHIRO TAKEI ◽  
YOSHIFURU SAITO ◽  
KIYOSHI HORII
Keyword(s):  
Wavelet Transforms ◽  
Large Scale ◽  
Particle Density ◽  
Small Scale ◽  
Discrete Wavelet ◽  
Discrete Wavelet Transforms ◽  
Two Dimensional ◽  
Condensation Zone ◽  
Two Dimensional Image ◽  
Discrete Wavelets

This paper describes the application of discrete wavelet transforms to the analysis of condensation jets in order to clarify the associated fluid and heat transfer phenomena. An experimentally-obtained, two-dimensional image of the condensation particle density around the jet was decomposed into 7 levels of resolution with their respective wavelengths. Based on the known physical characteristics of turbulent flow around the jet, levels 0 and 1 were shown to represent the large-scale components of the condensation particle density and the higher levels represent the small-scale components. From the wavelet-analyzed images, the width of the condensation zone was obtained and this compared well with the width inferred from temperature measurements. Thus, the method was verified and also provided data not available experimentally.

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