Predictions of Small-Scale Statistics for a Passive Scalar in Turbulent Mixing

1997 ◽  
Vol 79 (23) ◽  
pp. 4577-4580 ◽  
Author(s):  
L. Danaila ◽  
F. Anselmet ◽  
P. Le Gal ◽  
J. Dusek ◽  
C. Brun ◽  
...  
Keyword(s):  
Turbulent Mixing ◽  
Passive Scalar ◽  
Small Scale

scholarly journals Inhomogeneous Mixing in Lagrangian Cloud Models: Effects on the Production of Precipitation Embryos

2018 ◽  
Vol 76 (1) ◽  
pp. 113-133 ◽  
Author(s):  
Fabian Hoffmann ◽  
Takanobu Yamaguchi ◽  
Graham Feingold
Keyword(s):  
Turbulent Mixing ◽  
Cloud Model ◽  
Small Scale ◽  
New Approach ◽  
Air Masses ◽  
Lagrangian Particles ◽  
Cloud Models ◽  
Large Eddy ◽  
Salutary Effect ◽  
Linear Eddy Model

Abstract Although small-scale turbulent mixing at cloud edge has substantial effects on the microphysics of clouds, most models do not represent these processes explicitly, or parameterize them rather crudely. This study presents a first use of the linear eddy model (LEM) to represent unresolved turbulent mixing at the subgrid scale (SGS) of large-eddy simulations (LESs) with a coupled Lagrangian cloud model (LCM). The method utilizes Lagrangian particles to provide the trajectory of air masses within LES grid boxes, while the LEM is used to redistribute these air masses among the Lagrangian particles based on the local features of turbulence, allowing for the appropriate representation of inhomogeneous to homogeneous SGS mixing. The new approach has the salutary effect of mitigating spurious supersaturations. At low turbulence intensities, as found in the early stages of an idealized bubble cloud simulation, cloud-edge SGS mixing tends to be inhomogeneous and the new approach is shown to be essential for the production of raindrop embryos. At higher turbulence intensities, as found in a field of shallow cumulus, SGS mixing tends to be more homogeneous and the new approach does not significantly alter the results, indicating that a grid spacing of 20 m may be sufficient to resolve all relevant scales of inhomogeneous mixing. In both cases, droplet in-cloud residence times are important for the production of precipitation embryos in the absence of small-scale inhomogeneous mixing, either naturally due to strong turbulence or artificially as a result of coarse resolution or by not using the LEM as an SGS model.

scholarly journals Goldilocks mixing in oceanic shear-induced turbulent overturns

2021 ◽  
Vol 928 ◽  
Author(s):  
A. Mashayek ◽  
C.P. Caulfield ◽  
M.H. Alford
Keyword(s):  
Ocean Circulation ◽  
Turbulent Mixing ◽  
Intermediate Phase ◽  
Turbulent Flux ◽  
Geographical Location ◽  
Small Scale ◽  
Supporting Evidence ◽  
Stratified Turbulence ◽  
Wide Range ◽  
Variable Flux

We present a new, simple and physically motivated parameterization, based on the ratio of Thorpe and Ozmidov scales, for the irreversible turbulent flux coefficient $\varGamma _{\mathcal {M}}= {\mathcal {M}}/\epsilon$ , i.e. the ratio of the irreversible rate ${\mathcal {M}}$ at which the background potential energy increases in a stratified flow due to macroscopic motions to the dissipation rate of turbulent kinetic energy $\epsilon$ . Our parameterization covers all three key phases (crucially, in time) of a shear-induced stratified turbulence life cycle: the initial, ‘hot’ growing phase, the intermediate energetically forced phase and the final ‘cold’ fossilization decaying phase. Covering all three phases allows us to highlight the importance of the intermediate one, to which we refer as the ‘Goldilocks’ phase due to its apparently optimal (and so neither too hot nor too cold, but just right) balance, in which energy transfer from background shear to the turbulent mixing is most efficient. The value of $\varGamma _{\mathcal {M}}$ is close to 1/3 during this phase, which we demonstrate appears to be related to an adjustment towards a critical or marginal Richardson number for sustained turbulence ${\sim }0.2\text {--}0.25$ . Importantly, although buoyancy effects are still significant at leading order for the turbulent dynamics during this intermediate phase, the marginal balance in the flow ensures that the turbulent mixing of the (density) scalar is nevertheless effectively ‘locked’ to the turbulent mixing of momentum. We present supporting evidence for our parameterization through comparison with six oceanographic datasets that span various turbulence generation regimes and a wide range of geographical location and depth. Using these observations, we highlight the significance of parameterizing an inherently variable flux coefficient for capturing the turbulent flux associated with rare energetic, yet fundamentally shear-driven (and so not strongly stratified) overturns that make a disproportionate contribution to the total mixing. We also highlight the importance of representation of young turbulent patches in the parameterization for connecting the small scale physics to larger scale applications of mixing such as ocean circulation and tracer budgets. Shear-induced turbulence is therefore central to irreversible mixing in the world's oceans, apparently even close to the seafloor, and it is critically important to appreciate the inherent time dependence and evolution of mixing events: history matters to mixing.

A secondary small-scale turbulent mixing phenomenon induced by shock-wave Mach-reflection slip-stream instability

Shock Waves ◽  
2009 ◽  
pp. 1347-1352 ◽  
Author(s):  
A. Rikanati ◽  
O. Sadot ◽  
G. Ben-Dor ◽  
D. Shvarts ◽  
T. Kuribayashi ◽  
...  
Keyword(s):  
Shock Wave ◽  
Turbulent Mixing ◽  
Mach Reflection ◽  
Small Scale ◽  
Stream Instability

scholarly journals Modeling the Ocean in Climate Studies

1984 ◽  
Vol 5 ◽  
pp. 133-140 ◽  
Author(s):  
Albert J. Semtner
Keyword(s):  
Turbulent Mixing ◽  
Large Scale ◽  
Deep Convection ◽  
Vertical Mixing ◽  
Mesoscale Eddies ◽  
Small Scale ◽  
Polar Regions ◽  
Sea Ice Extent ◽  
Modeling Strategy ◽  
Climate Studies

A number of processes in the ocean must be modeled properly in order to produce valid estimates of oceanic heat transport, sea-surface temperature, and sea-ice extent in climate studies. These include: wind-driven turbulent mixing and water transport in the surface layer, internal vertical mixing due to several small-scale mechanisms, horizontal and vertical exchanges by mesoscale eddies, mixing along isopycnals, large-scale transport by currents, deep convection in polar regions, and boundary exchanges with atmosphere, ice, and land. Techniques to model these processes are described. Prospects are given for parameterizing the effects of phenomena that cannot be resolved in climate studies, particularly mesoscale eddies. Past simulations of the ocean in climate studies are reviewed. A modeling strategy is outlined for an improved treatment of the ocean, consistent with the computational power soon to be available.

Shock-Wave Mach-Reflection Slip-Stream Instability: A Secondary Small-Scale Turbulent Mixing Phenomenon

2006 ◽  
Vol 96 (17) ◽  
Author(s):  
A. Rikanati ◽  
O. Sadot ◽  
G. Ben-Dor ◽  
D. Shvarts ◽  
T. Kuribayashi ◽  
...  
Keyword(s):  
Shock Wave ◽  
Turbulent Mixing ◽  
Mach Reflection ◽  
Small Scale ◽  
Stream Instability

scholarly journals Numerical simulation of mixing by Rayleigh–Taylor and Richtmyer–Meshkov instabilities

1994 ◽  
Vol 12 (4) ◽  
pp. 725-750 ◽  
Author(s):  
D.L. Youngs
Keyword(s):  
Numerical Simulation ◽  
Turbulence Model ◽  
Turbulent Mixing ◽  
Inertial Confinement Fusion ◽  
Three Dimensional ◽  
Small Scale ◽  
Inertial Confinement ◽  
Two Dimensional ◽  
Confinement Fusion ◽  
Icf Target

Rayleigh-Taylor (RT) and Richtmyer–Meshkov (RM) instabilities at the pusher–fuel interface in inertial confinement fusion (ICF) targets may significantly degrade thermonuclear burn. Present-day supercomputers may be used to understand the fundamental instability mechanisms and to model the effect of the ensuing mixing on the performance of the ICF target. Direct three-dimensional numerical simulation is used to investigate turbulent mixing due to RT and RM instability in simple situations. A two-dimensional turbulence model is used to assess the effect of small-scale turbulent mixing in the axisymmetric implosion of an idealized ICF target.

On the geometry of turbulent mixing

1999 ◽  
Vol 393 ◽  
pp. 123-147 ◽  
Author(s):  
EMMANUEL VILLERMAUX ◽  
CLAUDIA INNOCENTI
Keyword(s):  
Fractal Dimension ◽  
Scalar Field ◽  
Turbulent Mixing ◽  
Concentration Field ◽  
Volume Ratio ◽  
Passive Scalar ◽  
Global Features ◽  
Integral Scale ◽  
Scalar Dispersion ◽  
Concentration Threshold

We investigate the temporal evolution of the geometrical distribution of a passive scalar injected continuously into the far field of a turbulent water jet at a scale d smaller than the local integral scale of the turbulence. The concentration field is studied quantitatively by a laser-induced- fluorescence technique on a plane cut containing the jet axis. Global features such as the scalar dispersion from the source, as well as the fine structure of the scalar field, are analysed. In particular, we define the volume occupied by the regions whose concentration is larger than a given concentration threshold (support of the scalar field) and the surface in which this volume is enclosed (boundary of the support). The volume and surface extents, and their respective fractal dimensions are measured as a function of time t, and the concentration threshold is normalized by the initial concentration Cs/C0 for different injection sizes d. All of these quantities display a clear dependence on t, d and Cs, and their evolutions rescale with the variable ξ = (ut/d)(Cs/C0), the fractal dimension being, in addition, scale dependent. The surface-to-volume ratio and the fractal dimension of both the volume and the surface tend towards unity at large ξ, reflecting the sheet-like structure of the scalar at small scales. These findings suggest an original picture of the kinetics of turbulent mixing.

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