Numerical simulations of freely evolving turbulence in stably stratified fluids

1989 ◽  
Vol 202 ◽  
pp. 117-148 ◽  
Author(s):  
Olivier Métais ◽  
Jackson R. Herring
Keyword(s):  
Initial Data ◽  
Numerical Simulations ◽  
Initial Conditions ◽  
Vertical Shear ◽  
Temperature Structure ◽  
Two Dimensional ◽  
Stratified Turbulence ◽  
Statistical Parameters ◽  
Frequency Spectra ◽  
Thorpe Scale

Results of direct numerical simulations of stably stratified, freely evolving, homogeneous turbulence are presented. An examination of initial data designed to give insight into laboratory flows suggests that the numerical simulations have a satisfactory degree of realism, insofar as statistical parameters such as total energy and length scales are concerned. The motion is decomposed into a stratified turbulence (vortical) component and a wave component. For initial-value problems similar to laboratory studies of stratified flows, the vortical component decays at a rate virtually identical to that of the non-buoyant case up to t = 6N−1 (N is the Brunt-Väisälä frequency). The decay rate decreases after this time, suggesting a kind of turbulence ‘collapse’. The temperature structure that emerges clearly shows the development of the collapse stage of the flow, which is also diagnosed by the behaviour of parameters such as the Thorpe scale.We next examine the very small-Froude-number regime in order to understand possible universal aspects of the flow. An examination of various initial conditions with different proportions of stratified and wave components indicates a lack of universality. For initial data containing only vortical motion (motions derived from the vertical vorticity field), the vortical field tends to dominate, in subsequent evolution, at strong stratification. However, contrary to two-dimensional turbulence, the flow is more strongly dissipative than two-dimensional flows due to the frictional effect associated with layering. Other quantities examined are frequency spectra, and the probability distribution for vertical shear. The frequency spectra exhibit some features in common with spectra extracted from oceanographic data.

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 Исследование наносекундного разряда в аргоне при атмосферном давлении с предварительной ионизацией

2019 ◽  
Vol 45 (2) ◽  
pp. 6
Author(s):  
В.С. Курбанисмаилов ◽  
О.А. Омаров ◽  
Г.Б. Рагимханов ◽  
Д.В. Терешонок
Keyword(s):  
Numerical Simulations ◽  
Time Resolution ◽  
Atmospheric Pressure ◽  
High Speed ◽  
Initial Conditions ◽  
Ionization Wave ◽  
Two Dimensional ◽  
Drift Model ◽  
Nanosecond Time Resolution

AbstractThe influence of initial conditions on specific features of the formation and development of a cathode-directed ionization wave between two flat electrodes in argon at atmospheric pressure was studied at nanosecond time resolution using a high-speed photoelectron monitor and numerical simulations based on the two-dimensional axisymmetric diffusion–drift model.

The turbulent wake of a towed grid in a stratified fluid

2015 ◽  
Vol 775 ◽  
pp. 149-177 ◽  
Author(s):  
X. Xiang ◽  
T. J. Madison ◽  
P. Sellappan ◽  
G. R. Spedding
Keyword(s):  
Density Gradient ◽  
Turbulent Flows ◽  
Initial Conditions ◽  
Local Density ◽  
Vertical Plane ◽  
Stratified Fluid ◽  
Vertical Shear ◽  
Gradient Field ◽  
Stratified Turbulence ◽  
Background Density

In a stable background density gradient, initially turbulent flows eventually evolve into a state dominated by low-Froude-number dynamics and frequently also contain persistent pattern information. Much empirical evidence has been gathered on these latter stages, but less on how they first got that way, and how information on the turbulence generator may potentially be encoded into the flow in a robust and long-lasting fashion. Here an experiment is described that examines the initial stages of evolution in the vertical plane of a turbulent grid-generated wake in a stratified ambient. Refractive-index-matched fluids allow optically based measurement of early ($Nt<2$) stages of the flow, even when there are strong variations in the local density gradient field. Suitably averaged flow measures show the interplay between internal wave motions and Kelvin–Helmholtz-generated vortical modes. The vertical shear is dominant at the wake edge, and the decay of horizontal vorticity is observed to be independent of $\mathit{Fr}$. Stratified turbulence, originating from Kelvin–Helmholtz instabilities, develops up to non-dimensional time $Nt\approx 10$, and the scale separation between Ozmidov and Kolmogorov scales is independent of $\mathit{Fr}$ at higher $Nt$. The detailed measurements in the near wake, with independent variation of both Reynolds and Froude numbers, while limited to one particular case, are sufficient to show that the initial turbulence in a stratified fluid is neither three-dimensional nor universal. The search for appropriately generalizable initial conditions may be more involved than hoped for.

scholarly journals The fate of random initial vorticity distributions for two-dimensional Euler equations on a sphere

2015 ◽  
Vol 786 ◽  
pp. 1-4 ◽  
Author(s):  
Paul K. Newton
Keyword(s):  
Numerical Simulations ◽  
Euler Equations ◽  
Large Scale ◽  
Initial Conditions ◽  
Infinite Family ◽  
Small Scale ◽  
Two Dimensional ◽  
Random Initial Conditions ◽  
Long Time ◽  
Initial Vorticity

The paper by Dritschel et al. (J. Fluid Mech., vol. 783, 2015, pp. 1–22) describes the long-time behaviour of inviscid two-dimensional fluid dynamics on the surface of a sphere. At issue is whether the flow settles down to an equilibrium or whether, for generic (random) initial conditions, the long-time solution is periodic, quasi-periodic or chaotic. While it might be surprising that this issue is not settled in the literature, it is important to keep in mind that the Euler equations form a dissipationless Hamiltonian system, hence the set of equations only redistributes the initial vorticity, generating smaller and smaller scales, while keeping kinetic energy, angular impulse and an infinite family of vorticity moments (Casimirs) intact. While special solutions that never settle down to an equilibrium state can be constructed using point vortices, vortex patches and other distributions, the fate of random initial conditions is a trickier problem. Previous statistical theories indicate that the long-time state should be a stationary large-scale distribution of vorticity. By carrying out careful numerical simulations using two different methods, the authors make a compelling case that the generic long-time state resembles a large-scale oscillating quadrupolar vorticity field, surrounded by persistent small-scale vortices. While numerical simulations can never conclusively settle this issue, the results might help guide future theories that seek to prove the existence of such an interesting dynamical long-time state.

scholarly journals Testing the Assumptions Underlying Ocean Mixing Methodologies Using Direct Numerical Simulations

2019 ◽  
Vol 49 (11) ◽  
pp. 2761-2779 ◽  
Author(s):  
J. R. Taylor ◽  
S. M. de Bruyn Kops ◽  
C. P. Caulfield ◽  
P. F. Linden
Keyword(s):  
Numerical Simulations ◽  
Field Measurements ◽  
Direct Numerical Simulations ◽  
Buoyancy Flux ◽  
Theoretical Development ◽  
Computational Domain ◽  
Vertical Profiles ◽  
Stratified Turbulence ◽  
Vertical Diffusivity ◽  
Thorpe Scale

AbstractDirect numerical simulations of stratified turbulence are used to test several fundamental assumptions involved in the Osborn, Osborn–Cox, and Thorpe methods commonly used to estimate the turbulent diffusivity from field measurements. The forced simulations in an idealized triply periodic computational domain exhibit characteristic features of stratified turbulence including intermittency and layer formation. When calculated using the volume-averaged dissipation rates from the simulations, the vertical diffusivities inferred from the Osborn and Osborn–Cox methods are within 40% of the value diagnosed using the volume-averaged buoyancy flux for all cases, while the Thorpe-scale method performs similarly well in the simulation with a relatively large buoyancy Reynolds number (Reb ≃ 240) but significantly overestimates the vertical diffusivity in simulations with Reb < 60. The methods are also tested using a limited number of vertical profiles randomly selected from the computational volume. The Osborn, Osborn–Cox, and Thorpe-scale methods converge to their respective estimates based on volume-averaged statistics faster than the vertical diffusivity calculated directly from the buoyancy flux, which is contaminated with reversible contributions from internal waves. When applied to a small number of vertical profiles, several assumptions underlying the Osborn and Osborn–Cox methods are not well supported by the simulation data. However, the vertical diffusivity inferred from these methods compares reasonably well to the exact value from the simulations and outperforms the assumptions underlying these methods in terms of the relative error. Motivated by a recent theoretical development, it is speculated that the Osborn method might provide a reasonable approximation to the diffusivity associated with the irreversible buoyancy flux.

scholarly journals The Generation of Turbulence below Midlevel Cloud Bases: The Effect of Cooling due to Sublimation of Snow

2013 ◽  
Vol 52 (4) ◽  
pp. 819-833 ◽  
Author(s):  
Atsushi Kudo
Keyword(s):  
Numerical Simulations ◽  
Initial Conditions ◽  
Three Dimensional ◽  
Vertical Motion ◽  
Vertical Shear ◽  
Cloud Base ◽  
Base Temperature ◽  
Sequence Of Events ◽  
Frontal Zones ◽  
The Stability

AbstractIn the author’s experience as a forecaster, commercial aircraft sometimes report turbulence beneath midlevel clouds that extend above upper frontal zones. Turbulence caused by Kelvin–Helmholtz instability occurs in upper frontal zones with strong vertical shear of horizontal winds. However, the turbulence seems to occur not only in the cloud bases (where upper frontal zones are) but also below the cloud bases where the vertical shear is not strong. Because those clouds are usually accompanied by precipitation that does not reach the ground, cooling by evaporation or sublimation seems to contribute to the generation of turbulence. In this paper, the mechanisms generating turbulence below midlevel cloud bases are examined by using observations and high-resolution three-dimensional numerical simulations with idealized initial conditions. The numerical simulations showed that the following sequence of events led to turbulence. Falling snow sublimated below cloud bases and cooled the air, which created absolute instability. This generated Rayleigh–Bénard convection cells. The vertical motion caused turbulence. The horizontal scale of the convection was about 800–1000 m, and the variations of vertical wind velocity were up to about 7 m s−1. The cloud base was accompanied by a virga-like distribution of snow. Sensitivity experiments showed the appropriate conditions to cause the turbulence: 1) the cloud-base temperature was between about 0° and −15°C, 2) the relative humidity in subcloud layers was sufficiently low, and 3) the stability in subcloud layers was weak. The results of the numerical simulations agreed well with the observations.

Study on the influence of linear and nonlinear distribution of crosswind on the motion of aircraft wake vortex

2021 ◽  
pp. 095441002098743
Author(s):  
Dong Li ◽  
Ziming Xu ◽  
Ke Zhang ◽  
Zeyu Zhang ◽  
Jinxin Zhou ◽  
...  
Keyword(s):  
Numerical Simulations ◽  
Dissipation Rate ◽  
Vortex Pair ◽  
Vertical Shear ◽  
Wake Vortex ◽  
Analysis Method ◽  
Velocity Magnitude ◽  
Aircraft Wake ◽  
Linear And Nonlinear ◽  
Nonlinear Distribution

Environmental crosswind can greatly affect the development of aircraft wake vortex pair. Previous numerical simulations and experiments have shown that the nonlinear vertical shear of the crosswind velocity can affect the dissipation rate of the aircraft wake vortex, causing each vortex of the vortex pair descent with different velocity magnitude, which will lead to the asymmetrical settlement and tilt of the wake vortex pair. Through numerical simulations, this article finds that uniform crosswind convection and linear vertical shear crosswind convection can also have an effect on the strength of the vortex. This effect is inversely proportional to the cube of the vortex spacing, so it is more intense on small separation vortex pair. In addition, the superposition of crosswind and vortex-induced velocities will lead to the asymmetrical pressure distribution around the vortex pair, which will also cause the tilt of the vortex pair. Furthermore, a new analysis method for wake vortex is proposed, which can be used to predict the vortex trajectory.

scholarly journals Towards explicit regulating-ion-transport: nanochannels with only function-elements at outer-surface

2021 ◽  
Vol 12 (1) ◽  
Author(s):  
Qun Ma ◽  
Yu Li ◽  
Rongsheng Wang ◽  
Hongquan Xu ◽  
Qiujiao Du ◽  
...  
Keyword(s):  
Ion Transport ◽  
Numerical Simulations ◽  
Power Density ◽  
Outer Surface ◽  
Internal Resistance ◽  
Porous Membranes ◽  
Two Dimensional ◽  
Ionic Selectivity ◽  
Key Features ◽  
Energy Conversion Devices

AbstractFunction elements (FE) are vital components of nanochannel-systems for artificially regulating ion transport. Conventionally, the FE at inner wall (FEIW) of nanochannel−systems are of concern owing to their recognized effect on the compression of ionic passageways. However, their properties are inexplicit or generally presumed from the properties of the FE at outer surface (FEOS), which will bring potential errors. Here, we show that the FEOS independently regulate ion transport in a nanochannel−system without FEIW. The numerical simulations, assigned the measured parameters of FEOS to the Poisson and Nernst-Planck (PNP) equations, are well fitted with the experiments, indicating the generally explicit regulating-ion-transport accomplished by FEOS without FEIW. Meanwhile, the FEOS fulfill the key features of the pervious nanochannel systems on regulating-ion-transport in osmotic energy conversion devices and biosensors, and show advantages to (1) promote power density through concentrating FE at outer surface, bringing increase of ionic selectivity but no obvious change in internal resistance; (2) accommodate probes or targets with size beyond the diameter of nanochannels. Nanochannel-systems with only FEOS of explicit properties provide a quantitative platform for studying substrate transport phenomena through nanoconfined space, including nanopores, nanochannels, nanopipettes, porous membranes and two-dimensional channels.

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