14:00
Stratified Flows 1
14:00
15 mins
#73
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DNS study on large-scale and small-scale flow structures of stably-stratified shear layers
Tomoaki Watanabe, James J. Riley, Koji Nagata, Keigo Matsuda, Ryo Onishi
Abstract: Direct numerical simulation is performed for investigating turbulent structures in a stably-stratified, temporally-evolving, shear layer where shear and stratification are localized in a thin layer. On the horizontal plane at the center of the shear layer, regions with positive and negative streamwise velocity display elongated patterns in the streamwise direction. The length of these patterns can reach about 10 times larger than the shear layer thickness. It is also shown that there are a large number of small-scale vortices with a hairpin shape at the top of the stably-stratified shear layer. These structures are shown to have an important contribution to kinetic energy spectra and momentum and density transport.
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14:15
15 mins
#63
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Entrainment Zone Properties in the Atmospheric Boundary Layer Conditioned on Turbulent and Non-turbulent Regions
Katherine Fodor, Juan Pedro Mellado
Abstract: In the unstable regime of the atmospheric boundary layer, referred to as the convective boundary layer (CBL), cumulus clouds typically form at the top of the boundary layer. The formation and properties of these clouds depend delicately on thermodynamic fields in the entrainment zone of the CBL. This region is characterised by external turbulent intermittency, defined as the alternation between regions of strong and weak vorticity fluctuations (see Fig. 1), which poses a challenge for modelling the evolution of entrainment zone properties. Previous efforts to provide scaling laws for temperature and specific humidity statistics in the shear-free CBL relied on several assumptions regarding the behaviour within turbulent and non-turbulent regions [2, 3]. In the present study, we employ conditional analysis on direct numerical simulation data to partition the entrainment zone into turbulent and non-turbulent regions, enabling us to assess the validity of previous assumptions and identify physically tenable scaling laws.
Our first results deal with the partitioning procedure. Previous studies of shear boundary-layers and stratified turbulence have considered probability density functions (PDFs) of the enstrophy or potential enstrophy to identify the turbulent/non-turbulent interface [1, 4]. When this method is appplied to the shear-free CBL, we find that both enstrophy and potential enstrophy are equally suitable as turbulence indicators and yield similar results. The PDFs both contain two peaks: a high enstrophy peak marking the boundary layer characterised by turbulence and a low enstrophy peak marking the free atmosphere characterised by gravity waves. We also find that the saddle point between the two peaks in the enstrophy PDF and that in the potential enstrophy PDF are located at similar heights within the entrainment zone, between the height of minimum buoyancy flux and the height marking the transition from the lower to the upper entrainment zone sublayer. Using the saddle point as a threshold, we then investigate the scaling behaviour of the mean and variance of temperature and specific humidity within turbulent and non-turbulent regions.
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14:30
15 mins
#166
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Signature and energetics of internal gravity waves in stratified turbulence
Andrea Maffioli, Alexandre Delache, Fabien Godeferd
Abstract: Internal gravity waves propagate in stratified fluids, such as in the ocean waters. It is well known that in stratified turbulence, waves coexist with eddies, or vortices. Since waves and vortices occupy the same portion of space and interact between each others, decomposing an experimental or numerical field of stratified turbulence into waves and vortices is a task of chief difficulty that has so far proved prohibitive. An existing framework, the wave-vortex decomposition, allows us to divide an arbitrary stratified flow into wave and vortex components \cite{rileylelong2000} but it is a linear decomposition that is probably inapplicable to the case of strongly stratified turbulence, in which nonlinearity is important.
We explore this problem by performing a spatio-temporal analysis of Direct Numerical Simulations (DNS) of stratified turbulence with forcing. We use a time Fourier transform of DNS data to obtain velocity components, binned over the same equatorial angle $\theta$, as a function of frequency $\omega$. This allows us to verify directly if there are motions in agreement with the dispersion relation of internal gravity waves, $\omega = \pm N\cos\theta$, which we take as the definition of a wave, and to quantify their energy (here $N$ is the Brunt-V\"{a}is\"{a}l\"{a} frequency). In Figure~\ref{fig1}, we present a plot of the potential energy, $\tilde{E}_P (\theta,\omega)$, for a run at a resolution of $1024^3$ with Froude number, $Fr_h = 0.03$, and buoyancy Reynolds number, $Re_b = 3.8$. The dispersion relation is clearly visible, which is a direct signature of internal gravity waves over practically the whole range of admissible frequencies, $0\leq |\omega| \leq N$.
We quantified the kinetic and potential energy in the waves and found that they are smaller than in the vortices, despite the use of a forcing scheme that injects the same amount of energy in the wave and vortex components. In addition, our results show that the wave-vortex decomposition systematically overpredicts the energy in the waves, which may be due to KH-type instabilities visible in the DNS that are erroneously considered as being part of the wave component in the decomposition. This puts into question the use of similar decompositions in atmosphere-ocean flows \cite{callies2014,lilindborg2018}, where $Re_b$ is significantly higher and so overturning motions and instabilities are ubiquitous.
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14:45
15 mins
#266
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CAN IMPLICIT LES OF GRAVITY CURRENTS MATCH THE MIXING EFFICIENCY OF A DNS?
Bruno Avila Farenzena, Ricardo Schuh Frantz, Jorge Silvestrini
Abstract: We quantify the irreversible mixing (IM) in numerical simulations of gravity currents formed by a lock release. In this canonical set-up \cite{fragosoEtAl2013, hughesLinden2016}, a fixed volume of dense liquid solution is enclosed in a domain filled with fresh still fluid. With the removal of the lock, a direct transfer of energy occurs due to buoyancy effects with the formation of a turbulent gravity current. Due to the transient non-homogeneous nature of the flow configuration, a global energetic approach is more adequate.
In this context, the IM represents a global transformation from available potential energy to background potential energy embracing both the turbulent and mean flow contributions. We approach the mixing quantification by first decomposing the flow potential energy into a combination of available and background parcels \cite{lorenz1955} (i.e. $\mathcal{P}=\mathcal{P}_a+\mathcal{P}_b$), estimating the latter with an efficient empirical cumulative distribution function \cite{tsengFerziger2001}, and finally integrating over the whole domain.
Correctly estimating the flow mixing efficiency in this set-up (formally the ratio between the energy losses due to mixing effects and all energy losses of the total available flow energy \cite{peltierCaufield2003}), is crucial for the LES model to be accurate enough as to capture the energy transfer $\mathcal{P}_a \rightarrow \mathcal{P}_b$.
To validate our approach, high-fidelity direct and implicit large eddy simulations (DNS/ILES) are carried out with Incompact3d\footnote{Highly parallel high-order finite-difference solver, based on sixth-order compact operators, freely available at github.com/xcompact3d/Incompact3d.}.
The experiment 6 from \cite{fragosoEtAl2013} is reproduced with a direct simulation of the incompressible Navier-Stokes equations coupled with a scalar transport equation under the Boussinesq approximation at a Reynolds number $Re=O(10^4)$.
The same case is reproduced with a significantly cheaper ILES computed with a straightforward implicit spectral vanishing viscosity concept \cite{dairay2017numerical}.
Figure \ref{fig1}a presents the time evolution of the energy budget, composed by the kinetic energy ($\mathcal{K}$), both potential energy parcels ($\mathcal{P}_a$ and $\mathcal{P}_b$) and the internal energy ($\mathcal{I}$), for both cases, showing excellent reproduction of the global quantities in terms of the LES.
It is noteworthy that for the DNS, the internal energy is completely computed at the mesh level, while in the LES, the same is further decomposed into physical and modeled parcels. Figure 1a presents a complete energy budget of both DNS and LES, in the fashion of \cite{wintersEtAl1995}, showing an excellent agreement between two cases.
We note that the potential energy is decomposed and therefore one can identify the initial background parcel.
Figure 1b shows the mixing efficiency ($\eta_c$) of both cases as a function of time, where the ILES overestimate the DNS mixing efficiency by approximately $4\%$.
These encouraging results demonstrate that the implicit LES approach delivers not only a significant computational cost reduction but allows future investigations of gravity currents in larger computational domains or higher Reynolds number.
In the presentation, we will show a complete demonstration of our tools to tackle the mixing problem in lock-release gravity currents, introducing additionally comparisons between our original numerical simulations and experimental data from \cite{hughesLinden2016} at $Re = O(10^5)$.
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15:00
15 mins
#244
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Turbulent entrainment in sheared convective boundary layers
Armin Haghshenas, Juan Pedro Mellado
Abstract: Entrainment in the atmospheric boundary layer (ABL) is crucial not only for the evolution of the ABL but also for local processes such as cloud dynamics. However, understanding entrainment in the ABL remains elusive, partly because the stable stratification at the top of the ABL complicates the analysis of turbulence in this region. Entrainment in a stably stratified environment has often been studied in idealized configurations, where turbulence is forced by a grid or by an imposed mean shear \cite{Fernando:1991,Strang:2001}. However, it remains difficult to extend the results from these studies to the ABL, where turbulence has its distinct properties, such as a convective forcing and a large-scale organization in convective rolls that maintains the Kelvin-Helmholtz instability in the entrainment zone.
We employ direct numerical simulations and dimensional analysis to investigate entrainment in a sheared convective boundary layer (CBL), where turbulence is driven by both convection and wind shear. We consider a zero-pressure-gradient turbulent boundary layer that is forced by a constant surface buoyancy flux and that grows into a linearly stratified fluid. Such a configuration is representative of atmosphere in midday conditions over land. Dimensional analysis enables us to characterize the system by a normalized CBL depth, a Froude number, $Fr_0$, and a Reynolds number, $Re_0$, setting the Prandtl number to one. The first two non-dimensional quantities embed the dependence of the system on time, on the surface buoyancy flux, and on the buoyancy stratification and wind velocity in the free atmosphere.
We show that the dependence of entrainment on the first two non-dimensional quantities can be expressed in terms of just one independent variable, the ratio between a shear scale $(\Delta z_\mathrm{i})_\mathrm{s}\equiv\sqrt{1/3}\,\Delta u/N_0$ and a convective scale $(\Delta z_\mathrm{i})_\mathrm{c}\equiv 0.25\, z_\mathrm{enc}$, where $\Delta u$ is the velocity increment across the entrainment zone, $N_0$ is the buoyancy frequency of the free atmosphere, and $z_\mathrm{enc}$ is the encroachment CBL depth.
The variables $(\Delta z_\mathrm{i})_\mathrm{s}$ and $(\Delta z_\mathrm{i})_\mathrm{c}$ represent the entrainment-zone thickness in the limits of weak and strong convective instability, respectively. We derive scaling laws for the CBL depth, the entrainment-zone thickness, the mean entrainment rate, and the entrainment-flux ratio as a function of $(\Delta z_\mathrm{i})_\mathrm{s}/(\Delta z_\mathrm{i})_\mathrm{c}$ (see Figure~\ref{fig1}) \cite{Haghshenas:2018}. These scaling laws can also be expressed as a function of only a Richardson number $(N_0z_\mathrm{enc}/\Delta u)^2$. We investigate the dependence of the derived scaling laws on the last non-dimensional quantity, namely the Reynolds number, by approximately doubling its value (see Figure~\ref{fig1}). Although this range of Reynolds number is small, we observe a tendency towards Reynolds-number similarity that supports the use of direct numerical simulation to study some aspects of the
atmospheric boundary layer.
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15:15
15 mins
#274
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A simple measure for predicting vortex pairing in shear layers
Anirban Guha, Mona Rahmani
Abstract:
Vortex pairing is an important mechanism in the evolution process of a series of adjacent co-rotating vortices that commonly occur in shear layers in the atmosphere and oceans. The primary vortices arise from the growth of Kelvin-Helmholtz (KH) instabilities at the interface of two fluids with different velocities. Through the process of pairing, two neighbouring vortices are advected toward each other and merge into a larger vortex \cite{winant1974vortex}. Vortex pairing can significantly enhance the mixing induced by the evolution and turbulent breakdown of KH billows by providing more stirring of the fluids in the two layers. This enhanced mixing has important implications for the estimations of vertical mixing of heat, nutrients and pollutants in the atmosphere, oceans and lakes \cite{ivey2008density}. It is well established that vortex pairing in shear layers occurs due to the growth of a subharmonic component, i.e. instabilities with twice the wavelength of the primary KH \cite{ho1984perturbed}. From numerical simulations, it is also known that the initial conditions of the phase difference and amplitude ratio between the primary KH (fundamental) and the subharmonic components significantly influence the later evolution of the vortex pairing \cite{patnaik1976numerical}. Theoretical analysis suggests that the suppression of vortex pairing occurs only at a very specific phase difference between the fundamental and subharmonic waves and is not realized at any other phase difference \cite{monkewitz1988subharmonic}.
While the phase of the subharmonic mode is widely accepted to be an important parameter, the effects of phase differences between the fundamental mode and its higher harmonics in a broader context is yet to be explored, which is essentially the theme of this work. As an example, in the laboratory experiments of Ref.\, \cite{ho1982subharmonics}, either three or four vortices in the mixing layer merged simultaneously, a third vortex merged into a pair of merged vortices, or two pairs of merged vortices agglomerated together. These different compositions are clearly indications of the growth of higher harmonics. Moreover, quantitative investigations of the effects of phase differences on multiple vortex merging and turbulent coherent structures are still rare in the literature.
In the present study, we first develop a simple novel model that explains the interaction of the fundamental mode and its higher harmonics based on their phase difference and amplitude ratio. Next, we use DNS to examine the accuracy of this simple model and also explore the non-linear interaction of 6 vortices in a shear layer; see Fig.\ \ref{fig1}. The DNS are initially perturbed by three modes of KH instabilities with different phase shifts and amplitude ratios. These simulations will significantly improve our understanding of the evolution of vortices in shear layers compared to previous numerical studies that usually assume an optimal phase difference between the fundamental and subharmonic mode for vortex pairing, limit the domain length to one or two wavelengths of the fundamental mode and ignore higher harmonics.
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15:30
15 mins
#144
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Particles crossing density interfaces
Alex Liberzon, Lilly Verso, Maarten van Reeuwijk
Abstract: Inertial particles settling velocity in stratified environments is important for atmospheric pollutants~\cite{bib:Kok2011, bib:turco1983}, or aggregation of plankton in the ocean thermocline~\cite{bib:Burd2009}.
We measured velocity and acceleration of inertial particles with different density $\rho_p$ and diameter $a$, settling/rising in a two-layer stably stratified fluid (fig.\ref{system}, uniform density $\rho_1$ on top of a layer of density $\rho_2 > \rho_1$), $\rho_p > \rho_2$ and $\rho_p<\rho_1$ ), crossing a diffusive interfacial layer. Experiments were performed in refractive index match conditions with the steady state conditions of the position, thickness, and entrainment rate of the interface layer~\cite{bib:verso2017}. Particle image velocimetry (PIV) provides the turbulent flow fields and Particle Tracking Velocimetry (3D-PTV) gives the particle time trajectories.
For spheres in the range of $2 \leq Re_1 \leq 100$ ($Re_1= V_1 a/ \nu_1$, $V_1$ is a particle entry velocity into the interface and $\nu_1$ is the kinematic viscosity of the top layer fluid) and Froude number $2 \leq Fr_1 \leq 30$ ($Fr_1= V_1/Na $, $N$ the stratification frequency), the stratified interface drastically changes the spheres velocity. The velocity of falling and rising spheres is substantially lower in the interface, than the expected settling velocity. Present models do not predict the value and position of the local minimum velocity in the interface layer, or the time for the sphere to recover its settling velocity.
In a turbulent flow case local minimum velocity inside the interface is preserved, despite the very different particle motion. Comparing settling of spheres through a density turbulent/not-turbulent interface (TNTI) with the settling in a quiescent two-layer system, and using the combined Eulerian and Lagrangian measurements, we could develop an semi-analytical model of a settling sphere through a density TNTI. The same model based on the properties of a sphere entering an interface (Reynolds and Froude numbers) predicts settling velocity in a quiescent interface and in the TNTI case.
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