K–ϵ model for rotating homogeneous decaying turbulence

2016 ◽  
Vol 94 (11) ◽  
pp. 1200-1204 ◽  
Author(s):  
Hamed Marzougui
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Decay Rate ◽  
Rate Equation ◽  
Rotation Rate ◽  
Dissipation Rate ◽  
Direct Numerical Simulations ◽  
Uniform Rotation ◽  
Axis Of Rotation ◽  
Decaying Turbulence

In the present work, we propose a modification to the standard K–ϵ model for simulating homogeneous decaying turbulence subjected to uniform rotation. In this modification, the dissipation rate equation is formulated in terms of the rotation rate Ω, the integral length scales along the axis of rotation [Formula: see text], and its isotropic value [Formula: see text]. The comparison of our results with the corresponding direct numerical simulations proves that the new model reproduces in an excellent way the decay rate of the turbulent kinetic energy.

scholarly journals Partitioning Waves and Eddies in Stably Stratified Turbulence

Atmosphere ◽  
2020 ◽  
Vol 11 (4) ◽  
pp. 420 ◽  
Author(s):  
Henri Lam ◽  
Alexandre Delache ◽  
Fabien S Godeferd
Keyword(s):  
Dispersion Relation ◽  
Kinetic Energy ◽  
Laminar Flow ◽  
Turbulent Flow ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Energy Concentration ◽  
Kinetic Energy Density ◽  
Stratified Turbulence ◽  
The Waves

We consider the separation of motion related to internal gravity waves and eddy dynamics in stably stratified flows obtained by direct numerical simulations. The waves’ dispersion relation links their angle of propagation to the vertical θ , to their frequency ω , so that two methods are used for characterizing wave-related motion: (a) the concentration of kinetic energy density in the ( θ , ω ) map along the dispersion relation curve; and (b) a direct computation of two-point two-time velocity correlations via a four-dimensional Fourier transform, permitting to extract wave-related space-time coherence. The second method is more computationally demanding than the first. In canonical flows with linear kinematics produced by space-localized harmonic forcing, we observe the pattern of the waves in physical space and the corresponding concentration curve of energy in the ( θ , ω ) plane. We show from a simple laminar flow that the curve characterizing the presence of waves is distorted differently in the presence of a background convective mean velocity, either uniform or varying in space, and also when the forcing source is moving. By generalizing the observation from laminar flow to turbulent flow, this permits categorizing the energy concentration pattern of the waves in complex flows, thus enabling the identification of wave-related motion in a general turbulent flow with stable stratification. The advanced method (b) is finally used to compute the wave-eddy partition in the velocity–buoyancy fields of direct numerical simulations of stably stratified turbulence. In particular, we use this splitting in statistics as varied as horizontal and vertical kinetic energy, as well as two-point velocity and buoyancy spectra.

scholarly journals Virtual motion of real particles

2010 ◽  
Vol 650 ◽  
pp. 1-4 ◽  
Author(s):  
G. TRYGGVASON
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Multiphase Flows ◽  
Isotropic Turbulence ◽  
Finite Size ◽  
Direct Numerical Simulations ◽  
Spherical Particles ◽  
Length Scale ◽  
Turbulent Eddies

Direct numerical simulations are rapidly becoming one of the most important techniques to examine the dynamics of multiphase flows. Lucci, Ferrante & Elghobashi (J. Fluid Mech., 2010, this issue, vol. 650, pp. 5–55) address several fundamental issues for spherical particles in isotropic turbulence. They show the importance of including the finite size of the particles and discuss how particles of a size comparable to the largest length scale at which viscosity substantially affects the turbulent eddies (i.e. the Taylor microscale) always increase the dissipation of turbulent kinetic energy.

scholarly journals Direct Numerical Simulations to Investigate Energy Transfer between Meso- and Synoptic Scales

2018 ◽  
Vol 75 (4) ◽  
pp. 1163-1171 ◽  
Author(s):  
Masih Eghdami ◽  
Shanti Bhushan ◽  
Ana P. Barros
Keyword(s):  
Energy Source ◽  
Energy Transfer ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Energy Spectra ◽  
Energy Sources ◽  
Synoptic Scale ◽  
2D Turbulence ◽  
Enstrophy Cascade

Abstract Understanding the development of the atmospheric energy spectrum across scales is necessary to elucidate atmospheric predictability. In this manuscript, the authors investigate energy transfer between the synoptic scale and the mesoscale using direct numerical simulations (DNSs) of two-dimensional (2D) turbulence transfer under forcing applied at different scales. First, DNS results forced by a single kinetic energy source at large scales show that the energy spectra slopes of the direct enstrophy cascade are steeper than the theoretically predicted −3 slope. Second, the presence of two inertial ranges in 2D turbulence at intermediate scales is investigated by introducing a second energy source in the meso-α-scale range. The energy spectra for the DNS with two kinetic energy sources exhibit flatter slopes that are closer to −3, consistent with the observed kinetic energy spectra of horizontal winds in the atmosphere at synoptic scales. Further, the results are independent of model resolution and scale separation between the two energy sources, with a robust transition region between the lower synoptic and the upper meso-α scales in agreement with classical observations in the upper troposphere. These results suggest the existence of a mesoscale feedback on synoptic-scale predictability that emerges from the concurrence of the direct (downscale) enstrophy transfer in the synoptic scales and the inverse (upscale) kinetic energy transfer from the mesoscale to the synoptic scale in the troposphere.

scholarly journals Direct numerical simulations of an inertial wave attractor in linear and nonlinear regimes

2014 ◽  
Vol 745 ◽  
pp. 223-250 ◽  
Author(s):  
Laurène Jouve ◽  
Gordon I. Ogilvie
Keyword(s):  
Numerical Simulations ◽  
Gravity Waves ◽  
Dissipation Rate ◽  
Laboratory Experiments ◽  
Rotation Axis ◽  
Internal Gravity Waves ◽  
Direct Numerical Simulations ◽  
Inertial Wave ◽  
Linear And Nonlinear ◽  
Nonlinear Regimes

AbstractIn a uniformly rotating fluid, inertial waves propagate along rays that are inclined to the rotation axis by an angle that depends on the wave frequency. In closed domains, multiple reflections from the boundaries may cause inertial waves to focus onto particular structures known as wave attractors. These attractors are likely to appear in fluid containers with at least one boundary that is neither parallel nor normal to the rotation axis. A closely related process also applies to internal gravity waves in a stably stratified fluid. Such structures have previously been studied from a theoretical point of view, in laboratory experiments, in linear numerical calculations and in some recent numerical simulations. In the present paper, two-dimensional direct numerical simulations of an inertial wave attractor are presented. By varying the amplitude at which the system is forced periodically, we are able to describe the transition between the linear and nonlinear regimes as well as the characteristic properties of the two situations. In the linear regime, we first recover the results of the linear calculations and asymptotic theory of Ogilvie (J. Fluid Mech., vol. 543, 2005, pp. 19–44) who considered a prototypical problem involving the focusing of linear internal waves into a narrow beam centred on a wave attractor in a steady state. The velocity profile of the beam and its scalings with the Ekman number, as well as the asymptotic value of the dissipation rate, are found to be in agreement with the linear theory. We also find that, as the beam builds up around the wave attractor, the power input by the applied force reaches its limiting value more rapidly than the dissipation rate, which saturates only when the beam has reached its final thickness. In the nonlinear regime, the beam is strongly affected and becomes unstable to a subharmonic instability. This instability transfers energy to secondary waves possessing shorter wavelengths and lower frequencies. The onset of the instability of a narrow inertial wave beam is investigated by means of a separate linear analysis and the results, such as the onset of the instability, are found to be consistent with the global simulations of the wave attractor. The excitation of such secondary waves described theoretically in this work has also been seen in recent laboratory experiments on internal gravity waves.

Numerical simulation of the evening transition in the atmospheric boundary layer using LES and RANS models

2021 ◽  
Author(s):  
Ekaterina Tkachenko ◽  
Andrey Debolskiy ◽  
Evgeny Mortikov
Keyword(s):  
Boundary Layer ◽  
Heat Flux ◽  
Kinetic Energy ◽  
Atmospheric Boundary Layer ◽  
Decay Rate ◽  
Surface Heat Flux ◽  
Dissipation Rate ◽  
Surface Heat ◽  
Evening Transition ◽  
Rans Models

<div>This study investigates the dynamics of the evening transition in the atmospheric boundary layer (ABL) diurnal cycle, specifically the decay of the turbulent kinetic energy (TKE) taking place there. Generally, the TKE decay is assumed to follow the power law E(t) ~ t<sup>-α,</sup> where E(t) and t are normalized TKE and normalized time, respectively, and the parameter α determines the decay rate. </div><div> <p>Two types of ABL numerical modeling are compared: three-dimensional large-eddy simulation (LES) models and one-dimensional Reynolds-averaged Navier-Stokes (RANS) models. The evening transition is simulated through facilitating the formation of the convective boundary layer (CBL) by having a constant positive surface heat flux, and the subsequent decay of the CBL when the surface heat flux is decreased. </p> <p>Several features of this process have been studied in relative depth, in particular the TKE decay rate at different stages of the evening transition, the sensitivity of the results to the domain size, and the dynamics of the large- and small-scale turbulence during the transition period. LES experiments with different setups were performed, and the results were then compared to those obtained through RANS experiments based on the k-epsilon model (a two-equation model for TKE and dissipation rate, where model constants are chosen to allow for correct simulation of SBL main properties [1], as well as CBL growth rate [2]).</p> <p>This study was funded by Russian Foundation of Basic Research within the project N 20-05-00776 and the grant of the RF President within the MK-1867.2020.5 project.</p> <div>1. Mortikov E. V., Glazunov A. V., Debolskiy A. V., Lykosov V. N., Zilitinkevich S. S. Modeling of the Dissipation Rate of Turbulent Kinetic Energy // Doklady Earth Sciences. 2019. V. 489(2). P. 1440-1443 </div> <p>2. Burchard H. Applied Turbulence Modelling in Marine Waters. Berlin, Germany: Springer, 2002. P. 57-59</p> </div>

A new approach to modelling near-wall turbulence energy and stress dissipation

2002 ◽  
Vol 459 ◽  
pp. 139-166 ◽  
Author(s):  
S. JAKIRLIĆ ◽  
K. HANJALIĆ
Keyword(s):  
Energy Dissipation ◽  
Numerical Simulations ◽  
Transport Equation ◽  
Dissipation Rate ◽  
Energy Dissipation Rate ◽  
Direct Numerical Simulations ◽  
Turbulence Energy ◽  
Viscous Term ◽  
Dissipation Equation ◽  
Near Wall

A new model for the transport equation for the turbulence energy dissipation rate ε and for the anisotropy of the dissipation rate tensor εij, consistent with the near-wall limits, is derived following the term-by-term approach and using results of direct numerical simulations (DNS) for several generic wall-bounded flows. Based on the two-point velocity covariance analysis of Jovanović, Ye & Durst (1995) and reinterpretation of the viscous term, the transport equation is derived in terms of the ‘homogeneous’ part εh of the energy dissipation rate. The algebraic expression for the components of εij was then reformulated in terms of εh, which makes it possible to satisfy the exact wall limits without using any wall-configuration parameters. Each term in the new equation is modelled separately using DNS information. The rational vorticity transport theory of Bernard (1990) was used to close the mean curvature term appearing in the dissipation equation. A priori evaluation of εij, as well as solving the new dissipation equation as a whole using DNS data for quantities other than εij, for flows in a pipe, plane channel, constant-pressure boundary layer, behind a backward-facing step and in an axially rotating pipe, all show good near-wall behaviour of all terms. Computations of the same flows with the full model in conjunction with the low-Reynolds number transport equation for (uiui) All Overbar, using εh instead of ε, agree well with the direct numerical simulations.

scholarly journals On the prediction of equilibrium states in homogeneous turbulence

1989 ◽  
Vol 209 ◽  
pp. 591-615 ◽  
Author(s):  
Charles G. Speziale ◽  
Nessan Mac Giolla Mhuiris
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Turbulent Kinetic Energy ◽  
Time Evolution ◽  
Dissipation Rate ◽  
Flow Instability ◽  
Turbulence Models ◽  
Second Order ◽  
Equilibrium States ◽  
Unstable Flow

A comparison of several commonly used turbulence models (including the K–ε model and three second-order closures) is made for the test problem of homogeneous turbulent shear flow in a rotating frame. The time evolution of the turbulent kinetic energy and dissipation rate is calculated for these models and comparisons are made with previously published experiments and numerical simulations. Particular emphasis is placed on examining the ability of each model to predict equilibrium states accurately for a range of the parameter Ω/S (the ratio of the rotation rate to the shear rate). It is found that none of the commonly used second-order closure models yield substantially improved predictions for the time evolution of the turbulent kinetic energy and dissipation rate over the somewhat defective results obtained from the simpler K–ε model for the unstable flow regime. There is also a problem with the equilibrium states predicted by the various models. For example, the K–ε model erroneously yields equilibrium states that are independent of Ω/S while the Launder, Reece & Rodi model and the Shih-Lumley model predict a flow relaminarization when Ω/S > 0.39 - a result that is contrary to numerical simulations and linear spectral analyses, which indicate flow instability for at least the range 0 [les ] Ω/S [les ] 0.5. The physical implications of the results obtained from the various turbulence models considered herein are discussed in detail along with proposals to remedy the deficiencies based on a dynamical systems approach.

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