scholarly journals A Comparison of Statistical Dynamical and Ensemble Prediction Methods during Blocking

2008 ◽  
Vol 65 (2) ◽  
pp. 426-447 ◽  
Author(s):  
Terence J. O’Kane ◽  
Jorgen S. Frederiksen
Keyword(s):  
Kinetic Energy ◽  
Numerical Simulations ◽  
Direct Interaction ◽  
Gulf Of Alaska ◽  
Direct Numerical Simulations ◽  
Ensemble Prediction ◽  
Small Scale ◽  
Error Growth ◽  
Closure Model ◽  
Non Gaussian

Abstract In this paper error growth is examined using a family of inhomogeneous statistical closure models based on the quasi-diagonal direct interaction approximation (QDIA), and the results are compared with those based on ensembles of direct numerical simulations using bred perturbations. The closure model herein includes contributions from non-Gaussian terms, is realizable, and conserves kinetic energy and enstrophy. Further, unlike previous approximations, such as those based on cumulant-discard (CD) and quasi-normal (QN) hypotheses (Epstein and Fleming), the QDIA closure is stable for long integration times and is valid for both strongly non-Gaussian and strongly inhomogeneous flows. The performance of a number of variants of the closure model, incorporating different approximations to the higher-order cumulants, is examined. The roles of non-Gaussian initial perturbations and small-scale noise in determining error growth are examined. The importance of the cumulative contribution of non-Gaussian terms to the evolved error tendency is demonstrated, as well as the role of the off-diagonal covariances in the growth of errors. Cumulative and instantaneous errors are quantified using kinetic energy spectra and a small-scale palinstrophy production measure, respectively. As a severe test of the methodology herein, synoptic situations during a rapid regime transition associated with the formation of a block over the Gulf of Alaska are considered. In general, the full QDIA closure results compare well with the statistics of direct numerical simulations.

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.

Direct Numerical Simulations of Transitional Separation–Bubble Development in Swept–Blade Flow Conditions

2012 ◽  
Author(s):  
Joshua R. Brinkerhoff ◽  
Metin I. Yaras
Keyword(s):  
Boundary Layer ◽  
Numerical Simulations ◽  
Shear Layer ◽  
Pressure Field ◽  
Separation Bubble ◽  
Three Dimensional ◽  
Direct Numerical Simulations ◽  
Small Scale ◽  
Flow Conditions ◽  
Crossflow Instability

This paper describes numerical simulations of the instability mechanisms in a separation bubble subjected to a three-dimensional freestream pressure distribution. Two direct numerical simulations are performed of a separation bubble with laminar separation and turbulent reattachment under low freestream turbulence at flow Reynolds numbers and streamwise pressure distributions that approximate the conditions encountered on the suction side of typical low-pressure gas-turbine blades with blade sweep angles of 0° and 45°. The three-dimensional pressure field in the swept configuration produces a crossflow-velocity component in the laminar boundary layer upstream of the separation point that is unstable to a crossflow instability mode. The simulation results show that crossflow instability does not play a role in the development of the boundary layer upstream of separation. An increase in the amplification rate and most amplified disturbance frequency is observed in the separated-flow region of the swept configuration, and is attributed to boundary-layer conditions at the point of separation that are modified by the spanwise pressure gradient. This results in a slight upstream movement of the location where the shear layer breaks down to small-scale turbulence and modifies the turbulent mixing of the separated shear layer to yield a downstream shift in the time-averaged reattachment location. The results demonstrate that although crossflow instability does not appear to have a noticeable effect on the development of the transitional separation bubble, the 3D pressure field does indirectly alter the separation-bubble development by modifying the flow conditions at separation.

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.

A New Active Micro Mixing Strategy

2007 ◽  
Author(s):  
Sedat Tardu ◽  
Rabia Nacereddine
Keyword(s):  
Numerical Simulations ◽  
Temporal Resolution ◽  
Direct Numerical Simulations ◽  
The Other ◽  
Small Scale ◽  
Streamwise Vortices ◽  
Wall Jets ◽  
Vortical Structures ◽  
Active Structures

An active micro-mixing strategy through forcing the flow by synthetic wall jets is proposed. It is based on the interaction of induced streamwise vortices in a specific way. There is a spanwise shift between two quasi-streamwise vortices in such a way that one of them compresses the wall normal vorticity layer created by the other, leading to the generation of new wall normal vortical structures. The latter are subsequently tilted by the shear to give birth to new small-scale longitudinal active structures that are efficient in mixing. The feasibility of this strategy is shown through direct numerical simulations of high spatial and temporal resolution.

scholarly journals Spectral analysis of the transition to turbulence from a dipole in stratified fluid

2012 ◽  
Vol 713 ◽  
pp. 86-108 ◽  
Author(s):  
Pierre Augier ◽  
Jean-Marc Chomaz ◽  
Paul Billant
Keyword(s):  
Reynolds Number ◽  
Spectral Analysis ◽  
Kinetic Energy ◽  
Numerical Simulations ◽  
Scaling Laws ◽  
Stratified Fluid ◽  
Shear Instability ◽  
Transition To Turbulence ◽  
Small Scale ◽  
Wide Range

AbstractWe investigate the spectral properties of the turbulence generated during the nonlinear evolution of a Lamb–Chaplygin dipole in a stratified fluid for a high Reynolds number $Re= 28\hspace{0.167em} 000$ and a wide range of horizontal Froude number ${F}_{h} \in [0. 0225~0. 135] $ and buoyancy Reynolds number $\mathscr{R}= Re{{F}_{h} }^{2} \in [14~510] $. The numerical simulations use a weak hyperviscosity and are therefore almost direct numerical simulations (DNS). After the nonlinear development of the zigzag instability, both shear and gravitational instabilities develop and lead to a transition to small scales. A spectral analysis shows that this transition is dominated by two kinds of transfer: first, the shear instability induces a direct non-local transfer toward horizontal wavelengths of the order of the buoyancy scale ${L}_{b} = U/ N$, where $U$ is the characteristic horizontal velocity of the dipole and $N$ the Brunt–Väisälä frequency; second, the destabilization of the Kelvin–Helmholtz billows and the gravitational instability lead to small-scale weakly stratified turbulence. The horizontal spectrum of kinetic energy exhibits a ${{\varepsilon }_{K} }^{2/ 3} { k}_{h}^{\ensuremath{-} 5/ 3} $ power law (where ${k}_{h} $ is the horizontal wavenumber and ${\varepsilon }_{K} $ is the dissipation rate of kinetic energy) from ${k}_{b} = 2\lrm{\pi} / {L}_{b} $ to the dissipative scales, with an energy deficit between the integral scale and ${k}_{b} $ and an excess around ${k}_{b} $. The vertical spectrum of kinetic energy can be expressed as $E({k}_{z} )= {C}_{N} {N}^{2} { k}_{z}^{\ensuremath{-} 3} + C{{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ where ${C}_{N} $ and $C$ are two constants of order unity and ${k}_{z} $ is the vertical wavenumber. It is therefore very steep near the buoyancy scale with an ${N}^{2} { k}_{z}^{\ensuremath{-} 3} $ shape and approaches the ${{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ spectrum for ${k}_{z} \gt {k}_{o} $, ${k}_{o} $ being the Ozmidov wavenumber, which is the cross-over between the two scaling laws. A decomposition of the vertical spectra depending on the horizontal wavenumber value shows that the ${N}^{2} { k}_{z}^{\ensuremath{-} 3} $ spectrum is associated with large horizontal scales $\vert {\mathbi{k}}_{h} \vert \lt {k}_{b} $ and the ${{\varepsilon }_{K} }^{2/ 3} { k}_{z}^{\ensuremath{-} 5/ 3} $ spectrum with the scales $\vert {\mathbi{k}}_{h} \vert \gt {k}_{b} $.

scholarly journals Dynamical Subgrid-Scale Parameterizations from Direct Numerical Simulations

2006 ◽  
Vol 63 (11) ◽  
pp. 3006-3019 ◽  
Author(s):  
Jorgen S. Frederiksen ◽  
Steven M. Kepert
Keyword(s):  
Numerical Simulations ◽  
Turbulent Flows ◽  
Climate Models ◽  
Prediction Models ◽  
Isotropic Turbulence ◽  
Direct Interaction ◽  
Direct Numerical Simulations ◽  
Subgrid Scale ◽  
Direct Interaction Approximation ◽  
Barotropic Vorticity

Abstract Dynamical subgrid-scale parameterizations of stochastic backscatter, eddy drain viscosity, and net eddy viscosity have been formulated and calculated for two-dimensional turbulent flows on the sphere based on the statistics of direct numerical simulations (DNSs) with the barotropic vorticity equation. A relatively simple methodology based on a stochastic model representation of the subgrid-scale eddies, but which takes into account the memory effects of turbulent eddies, has been employed. The parameterizations have a cusp behavior at the cutoff wavenumber of the retained scales and have closely similar forms to those based on eddy damped quasi-normal Markovian (EDQNM) and direct interaction approximation (DIA) closure models. Large-eddy simulations (LESs) incorporating DNS-based subgrid-scale parameterizations are found to have kinetic energy spectra that compare closely with the results of higher-resolution DNS at the scales of LES for both isotropic turbulence and Rossby wave turbulence. The methodology presented is general and should be equally applicable to parameterizations of baroclinic processes and convective processes. Applications of the parameterizations to climate models and prediction models are discussed.

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