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 Waves and vortices in the inverse cascade regime of stratified turbulence with or without rotation

2016 ◽  
Vol 806 ◽  
pp. 165-204 ◽  
Author(s):  
Corentin Herbert ◽  
Raffaele Marino ◽  
Duane Rosenberg ◽  
Annick Pouquet
Keyword(s):  
Reynolds Number ◽  
Numerical Simulations ◽  
Direct Numerical Simulations ◽  
Vertical Shear ◽  
Energy Spectra ◽  
Stratified Turbulence ◽  
Viscous Effects ◽  
Inverse Cascade ◽  
Main Effects ◽  
The Waves

We study the partition of energy between waves and vortices in stratified turbulence, with or without rotation, for a variety of parameters, focusing on the behaviour of the waves and vortices in the inverse cascade of energy towards the large scales. To this end, we use direct numerical simulations in a cubic box at a Reynolds number $Re\approx 1000$, with the ratio between the Brunt–Väisälä frequency $N$ and the inertial frequency $f$ varying from $1/4$ to 20, together with a purely stratified run. The Froude number, measuring the strength of the stratification, varies within the range $0.02\leqslant Fr\leqslant 0.32$. We find that the inverse cascade is dominated by the slow quasi-geostrophic modes. Their energy spectra and fluxes exhibit characteristics of an inverse cascade, even though their energy is not conserved. Surprisingly, the slow vortices still dominate when the ratio $N/f$ increases, also in the stratified case, although less and less so. However, when $N/f$ increases, the inverse cascade of the slow modes becomes weaker and weaker, and it vanishes in the purely stratified case. We discuss how the disappearance of the inverse cascade of energy with increasing $N/f$ can be interpreted in terms of the waves and vortices, and identify the main effects that can explain this transition based on both inviscid invariants arguments and viscous effects due to vertical shear.

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.

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.

Numerical Simulations of the Kinetic Energy Transfer in the Bath of a BOF Converter

2015 ◽  
Vol 47 (1) ◽  
pp. 434-445 ◽  
Author(s):  
Xiaobin Zhou ◽  
Mikael Ersson ◽  
Liangcai Zhong ◽  
Pär Jönsson
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Kinetic Energy Transfer

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.

One-dimensional turbulence: vector formulation and application to free shear flows

2001 ◽  
Vol 447 ◽  
pp. 85-109 ◽  
Author(s):  
ALAN R. KERSTEIN ◽  
W. T. ASHURST ◽  
SCOTT WUNSCH ◽  
VEBJORN NILSEN
Keyword(s):  
Energy Transfer ◽  
Probability Density Function ◽  
Kinetic Energy ◽  
Shear Flows ◽  
Mixing Layer ◽  
Simulation Method ◽  
Direct Numerical Simulations ◽  
Line Of Sight ◽  
One Dimensional ◽  
Dimensional Domain

One-dimensional turbulence is a stochastic simulation method representing the time evolution of the velocity profile along a notional line of sight through a turbulent flow. In this paper, the velocity is treated as a three-component vector, in contrast to previous formulations involving a single velocity component. This generalization allows the incorporation of pressure-scrambling effects and provides a framework for further extensions of the model. Computed results based on two alternative physical pictures of pressure scrambling are compared to direct numerical simulations of two time-developing planar free shear flows: a mixing layer and a wake. Scrambling based on equipartition of turbulent kinetic energy on an eddy-by-eddy basis yields less accurate results than a scheme that maximizes the intercomponent energy transfer during each eddy, subject to invariance constraints. The latter formulation captures many features of free shear flow structure, energetics, and fluctuation properties, including the spatial variation of the probability density function of a passive advected scalar. These results demonstrate the efficacy of the proposed representation of vector velocity evolution on a one-dimensional domain.

Verification of Hasselmann's energy transfer among surface gravity waves by direct numerical simulations of primitive equations

2001 ◽  
Vol 444 ◽  
pp. 199-221 ◽  
Author(s):  
MITSUHIRO TANAKA
Keyword(s):  
Energy Transfer ◽  
Numerical Simulations ◽  
Gravity Waves ◽  
Direct Numerical Simulations ◽  
Rate Of Change ◽  
Surface Gravity ◽  
Primitive Equations ◽  
Surface Gravity Waves ◽  
Nonlinear Energy Transfer ◽  
Nonlinear Energy

The temporal evolution of nonlinear wave fields of surface gravity waves is studied by large-scale direct numerical simulations of primitive equations in order to verify Hasselmann's theory for nonlinear energy transfer among component gravity waves. In the simulations, all the nonlinear interactions, including both resonant and non-resonant ones, are taken into account up to the four-wave processes. The initial wave field is constructed by combining more than two million component free waves in such a way that it has the JONSWAP or the Pierson–Moskowitz spectrum. The nonlinear energy transfer is evaluated from the rate of change of the spectrum, and is compared with Hasselmann's theory. It is shown that, in spite of apparently insufficient duration of the simulations such as just a few tens of characteristic periods, the energy transfer obtained by the present method shows satisfactory agreement with Hasselmann's theory, at least in their qualitative features.

scholarly journals Cascade processes in rapidly rotating turbulence

2018 ◽  
Author(s):  
Maxim Reshetnyak ◽  
Oleg Pokhotelov
Keyword(s):  
Kinetic Energy ◽  
Turbulent Flow ◽  
Numerical Simulations ◽  
Physical Experiment ◽  
2D Turbulence ◽  
Inverse Cascade ◽  
Rotating Turbulence ◽  
Cascade Processes ◽  
Rotating Turbulent Flow

Abstract. The process of the kinetic energy and kinetic helicity transfer over the spectrum in an incompressible, rapidly rotating turbulent flow is considered. An analogue of the Fjortoft theorem for 3D rapidly rotating turbulence is proposed. It is shown that, similar to 2D turbulence, there are two cascades simultaneously: the inverse cascade of the kinetic energy and the direct cascade of the kinetic helicity, which in the case of 2D turbulence corresponds to the cascade of enstrophy. The proposed scenario is in agreement with our earlier calculations, some recent numerical simulations, and physical experiment on rotating turbulence.

Shock and Vibration Isolation Using Internally Rotating Masses

2015 ◽  
Author(s):  
Eric Smith ◽  
Al Ferri
Keyword(s):  
Energy Transfer ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Vibration Isolation ◽  
Viscous Damping ◽  
Targeted Energy Transfer ◽  
Axial Vibration ◽  
Transmitted Force ◽  
A Chain ◽  
The Masses

This paper considers the use of a chain of springs and masses to reduce the transmission of shock and vibration through the system. The masses are equipped with internally rotating masses that absorb some of the axial vibration into internal kinetic energy of the masses. The internal masses have viscous damping, but no elastic or gravitational restraint. Previous research has shown that a single cart system attached to a vibrating structure can help mitigate shock through targeted energy transfer. This paper examines the potential for shock isolation provided by a chain of such systems. Through numerical simulations, tradeoffs are examined between displacement and transmitted force.

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