31 research outputs found
Internal stresses and breakup of rigid isostatic aggregates in homogeneous and isotropic turbulence
By characterising the hydrodynamic stresses generated by statistically
homogeneous and isotropic turbulence in rigid aggregates, we estimate
theoretically the rate of turbulent breakup of colloidal aggregates and the
size distribution of the formed fragments. The adopted method combines Direct
Numerical Simulation of the turbulent field with a Discrete Element Method
based on Stokesian dynamics. In this way, not only the mechanics of the
aggregate is modelled in detail, but the internal stresses are evaluated while
the aggregate is moving in the turbulent flow. We examine doublets and
cluster-cluster isostatic aggregates, where the failure of a single contact
leads to the rupture of the aggregate and breakup occurs when the tensile force
at a contact exceeds the cohesive strength of the bond. Due to the different
role of the internal stresses, the functional relationship between breakup
frequency and turbulence dissipation rate is very different in the two cases.
In the limit of very small and very large values, the frequency of breakup
scales exponentially with the turbulence dissipation rate for doublets, while
it follows a power law for cluster-cluster aggregates. For the case of large
isostatic aggregates it is confirmed that the proper scaling length for maximum
stress and breakup is the radius of gyration. The cumulative fragment
distribution function is nearly independent of the mean turbulence dissipation
rate and can be approximated by the sum of a small erosive component and a term
that is quadratic with respect to fragment size.Comment: 31 pages, 19 figure
Scalar Turbulence in Convective Boundary Layers by Changing the Entrainment Flux
Abstract
A large-eddy simulation model is adopted to investigate the evolution of scalars transported by atmospheric cloud-free convective boundary layer flows. Temperature fluctuations due to the ground release of sensible heat and concentration fluctuations of a trace gas emitted at the homogeneous surface are mixed by turbulence within the unstable boundary layer. On the top, the entrainment zone is varied to obtain two distinct situations: (i) the temperature inversion is strong and the trace gas increment across the entrainment region is small, yielding to a small top flux with respect to the surface emission; (ii) the temperature inversion at the top of the convective boundary layer is weak, and the scalar increment large enough to achieve a concentration flux toward the free atmosphere that overwhelms the surface flux. In both cases, an estimation of the entrainment flux is obtained within a simple model, and it is tested against numerical data. The evolution of the scalar profiles is discussed in terms of the different entrainmentâsurface flux ratios.
Results show that, when entrainment at the top of the boundary layer is weak, temperature and trace gas scalar fields are strongly correlated, particularly in the lower part of the boundary layer. This means that they exhibit similar behavior from the largest down to the smallest spatial scales. However, when entrainment is strong, as moving from the surface, differences in the transport of the two scalars arise.
Finally, it is shown that, independently of the scalar regime, the temperature field exhibits more intermittent fluctuations than the trace gas
An accurate and efficient Lagrangian sub-grid model
A computationally efficient model is introduced to account for the sub-grid
scale velocities of tracer particles dispersed in statistically homogeneous and
isotropic turbulent flows. The model embeds the multi-scale nature of turbulent
temporal and spatial correlations, that are essential to reproduce
multi-particle dispersion. It is capable to describe the Lagrangian diffusion
and dispersion of temporally and spatially correlated clouds of particles.
Although the model neglects intermittent corrections, we show that pair and
tetrad dispersion results nicely compare with Direct Numerical Simulations of
statistically isotropic and homogeneous turbulence. This is in agreement
with recent observations that deviations from self-similar pair dispersion
statistics are rare events
Breakup of small aggregates driven by turbulent hydrodynamic stress
Breakup of small solid aggregates in homogeneous and isotropic turbulence is
studied theoretically and by using Direct Numerical Simulations at high
Reynolds number, Re_{\lambda} \simeq 400. We show that turbulent fluctuations
of the hydrodynamic stress along the aggregate trajectory play a key role in
determining the aggregate mass distribution function. Differences between
turbulent and laminar flows are discussed. A novel definition of the
fragmentation rate is proposed in terms of the typical frequency at which the
hydrodynamic stress becomes sufficiently high to cause breakup along each
Lagrangian path. We also define an Eulerian proxy of the real fragmentation
rate, based on the joint statistics of the stress and its time derivative,
which should be easier to measure in any experimental set-up. Both our Eulerian
and Lagrangian formulations define a clear procedure for the computation of the
mass distribution function due to fragmentation. Contrary, previous estimates
based only on single point statistics of the hydrodynamic stress exhibit some
deficiencies. These are discussed by investigating the evolution of an ensemble
of aggregates undergoing breakup and aggregation.Comment: 4 Latex pages, 4 figure
Effects of forcing in three dimensional turbulent flows
We present the results of a numerical investigation of three-dimensional
homogeneous and isotropic turbulence, stirred by a random forcing with a power
law spectrum, . Numerical simulations are performed at
different resolutions up to . We show that at varying the spectrum slope
, small-scale turbulent fluctuations change from a {\it forcing independent}
to a {\it forcing dominated} statistics. We argue that the critical value
separating the two behaviours, in three dimensions, is . When the
statistics is forcing dominated, for , we find dimensional scaling, i.e.
intermittency is vanishingly small. On the other hand, for , we find the
same anomalous scaling measured in flows forced only at large scales. We
connect these results with the issue of {\it universality} in turbulent flows.Comment: 4 pages, 4 figure
Numerical simulations of aggregate breakup in bounded and unbounded turbulent flows
Breakup of small aggregates in fully developed turbulence is studied by means
of direct numerical simulations in a series of typical bounded and unbounded
flow configurations, such as a turbulent channel flow, a developing boundary
layer and homogeneous isotropic turbulence. The simplest criterion for breakup
is adopted, whereas aggregate breakup occurs when the local hydrodynamic stress
, with being the energy dissipation
at the position of the aggregate, overcomes a given threshold
, which is characteristic for a given type of aggregates.
Results show that the breakup rate decreases with increasing threshold. For
small thresholds, it develops a universal scaling among the different flows.
For high thresholds, the breakup rates show strong differences between the
different flow configurations, highlighting the importance of non-universal
mean-flow properties. To further assess the effects of flow inhomogeneity and
turbulent fluctuations, theresults are compared with those obtained in a smooth
stochastic flow. Furthermore, we discuss the limitations and applicability of a
set of independent proxies.Comment: 15 pages, 12 figures, Refinded discussion in Section 2.1, results
unchange
Conformal-invariance of 2D quantum turbulence in an exciton-polariton fluid of light
The similarities of quantum turbulence with classical hydrodynamics allow
quantum fluids to provide essential models of their classical analogue, paving
the way for fundamental advances in physics and technology. Recently,
experiments on 2D quantum turbulence observed the clustering of same-sign
vortices in strong analogy with the inverse energy cascade of classical fluids.
However, self-similarity of the turbulent flow, a fundamental concept in the
study of classical turbulence, has so far remained largely unexplored in
quantum systems. Here, thanks to the unique features of exciton-polaritons, we
measure the scale invariance of velocity circulations and show that the cascade
process follows the universal scaling of critical phenomena in 2D. We
demonstrate this behaviour from the statistical analysis of the experimentally
measured incompressible velocity field and the microscopic imaging of the
quantum fluid. These results can find wide application in both quantum and
classical 2D turbulence