10:45
Stratified Flows 3
10:45
15 mins
#159
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Layering and vertical transport in sheared double diffusive convection in the diffusive regime
Yantao Yang, Roberto Verzicco, Detlef Lohse, Colm-cille Caulfield
Abstract: In the upper water of polar oceans, both the mean temperature and salinity increase as the depth becomes larger, and double diffusive convection may occur in the so-called diffusive regime. In this regime, observations have shown intriguing thermohaline staircases which contain a stack of well-mixed layers separated by sharp interfaces with high temperature and salinity gradient. Recently, Radko proved that the interplay between horizontal shearing and diffusive stratification may destabilize the system and induce layering. Here by direct numerical simulations of the fluid layer bounded by two parallel plates which are perpendicular to gravity and experiencing horizontal shearing, we realize the layering process, as shown in figure. The time evolution of the mean profiles shows distinct layering from initially linear distributions of both temperature and salinity. Layer coarsening is also observed at later stage. Based on the numerical data, we further analyze the vertical transport and mixing properties of the layering dynamics. Our findings are of great interest for understanding the robustness, transport and mixing in real diffusive staircases in polar oceans.
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11:00
15 mins
#328
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Internal gravity waves, shear, and mixing in forced stratified turbulence
Christopher Howland, John Taylor, Colm-cille Caulfield
Abstract: Wind and tides are two primary drivers of the ocean circulation.
Some of the energy input is dissipated through small-scale turbulence in boundary layers near the top and bottom of the ocean, but a large fraction of the energy input is converted to internal gravity waves.
Far from the boundaries, the distribution of internal gravity waves is well described by the empirical Garrett-Munk spectrum.
Energy is thought to cascade along this spectrum from large scales to small scales via weakly nonlinear wave-wave interactions, until the spectrum cuts off at a scale of approximately 10m.
At yet smaller scales, strongly nonlinear wave-wave interactions, shear instabilities and wave breaking lead to turbulent mixing, albeit through turbulence that is strongly affected by stratification.
This irreversible mixing is vital for maintaining the abyssal stratification of the ocean, and it also determines the rate of nutrient upwelling through the pycnocline, which controls the level of biological activity in the upper ocean.
However this turbulent mixing is intermittent in both space and time, and the nature of the mixing is not well known.
In regions such as the pycnocline, where the dynamics are well described by the internal wave spectrum, it is not clear whether shear-driven mixing or more efficient convective mixing is more prevalent.
To determine the importance of internal waves for modifying the nature of mixing in stratified turbulence, we perform direct numerical simulations of a Boussinesq fluid subject to three different types of large-scale body forcing.
The first involves forcing randomly phased vortical modes, as applied by previous studies of stratified turbulence.
The remaining simulations are forced by a field of internal gravity waves - one with the waves randomly phased at each time step, and the other with the forced waves propagating according to the dispersion relation.
All simulations are initialised using a base state representative of the Garrett-Munk spectrum, with vertical shear accounting for waves on larger horizontal scales than the domain.
We identify how key quantities such as mixing efficiency and vertical diffusivity vary with the type of forcing, and isolate the mechanisms responsible for the differences.
Since the background vertical shear varies with depth, we can also inspect the vertical structure of the flow to identify how the forcing interacts with the shear and how this leads to intermittent regions of increased dissipation.
We investigate how well existing parametrisations of mixing based on fine-scale measurements capture this intermittency, and how they compare across the simulations with different forcing regimes.
Finally, we look at the issue of sampling when measuring turbulent flows.
We determine how much information about mixing can be accurately obtained from individual vertical profiles of velocity and density perturbations.
From this sampling, we aim to improve the identification of shear driven mixing versus convective mixing in observational profiles.
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11:15
15 mins
#228
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TURBULENT MIXING DRIVEN BY THE FARADAY INSTABILITY
Antoine Briard, Benoît-Joseph Gréa, Louis Gostiaux
Abstract: When a two layer system of miscible fluids is excited periodically and vertically, a turbulent mixing zone can appear as the result of the Faraday instability. When gravity waves are no longer excited by parametric resonances, the instability saturates. We are able to predict the final size of the mixing zone at saturation of the instability. This theoretical prediction is assessed numerically with high resolution direct numerical simulations, and with recent experimental results as well.
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11:30
15 mins
#344
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VERTICAL DRAFTS AND MIXING IN STRATIFIED TURBULENT FLOWS
Fabio Feraco, Raffaele Marino, Alain Pumir, Leonardo Primavera, Pablo Mininni, Annick Pouquet, Duane Rosenberg
Abstract: Intermittency is a hallmark of fully developed turbulence in fluids. Contrary to the predictions of Kolmogorov original
theory, both experiments and numerical simulations show that dissipation exhibits intense fluctuations, localized in
space and time. This phenomenon, known as small-scale intermittency, is widely observed in the atmosphere and in
the ocean in the form of highly concentrated and sporadic dissipation. Intermittency, however, is not only present at
the smallest scales. In the problem of mixing of a passive scalar by a turbulent flow, for stratified flows as in the Earth’s
atmosphere and in the oceans, non-stationary energetic bursts at scales comparable to that of the mean flow are also
observed. Here, we investigate the large-scale intermittency of vertical velocity and temperature, and the mixing
properties of stably stratified turbulent flows using both Lagrangian and Eulerian fields from direct numerical simulations
of the Boussinesq equations with periodic boundary conditions, in a parameter space relevant for the atmosphere and the
oceans. Over a range of Froude numbers of geophysical interest (≈ 0.05 − 0.3) we observe very large fluctuations of
the vertical components of the velocity and the potential temperature, localized in space and time, with a sharp transition
leading to non-Gaussian wings of the probability distribution functions. This behavior is captured by a simple model representing the competition between gravity waves on a fast time-scale and nonlinear steepening on a slower
time-scale. The existence of a resonant regime characterized by enhanced large-scale intermittency, as understood within
the framework of the proposed model, is then linked to the emergence of structures in the velocity and potential temper-
ature fields, localized overturning and mixing (see figure). Finally, in the same regime we observe a linear scaling of
the mixing efficiency with the Froude number and an increase of its value of roughly one order of magnitude.
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11:45
15 mins
#165
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Differentially heated rotating annulus experiments to study gravity wave emission from jets and fronts
Costanza Rodda, Steffen Hien, Ulrich Achatz, Ion Dan Borcia, Patrice Le Gal, Miklòs Vincze, Uwe Harlander
Abstract: Significant internal gravity wave (IGW) activity has been frequently observed in the vicinity of jet/front systems in the atmosphere. Although many studies have established the importance of these non-orographic sources, the mechanisms responsible for spontaneous wave emissions is still not fully understood. The complexity of the three-dimensional flow pattern and distribution of the sources over large areas point towards the need of laboratory experiments and idealised numerical simulations to help with the correct interpretation of the fundamental dynamical processes in a simplified, but yet realistic flow. In this study, we emphasise that the differentially heated rotating annulus experiment, classically showing an aspect ratio of about one, is not a particularly favourable set-up to investigate atmosphere-like emission of gravity waves from baroclinic jets due to an unrealistic ratio between the buoyancy frequency $N$ and the Coriolis parameter $f$. The latter is much larger than one for the atmosphere but smaller than one for the classical annulus. Hence, we present an overview of modified versions of the classic baroclinic experiment, with a more realistic $N/f$, as a better choice for the study of IGWs.
The first modified experiment is a thermohaline version in which a juxtaposition of convective and motionless stratified layers can be created by introducing a vertical salt stratification. This new experimental setup, coined "barostrat instability", allows studying the exchange of momentum and energy between the layers, especially by the propagation of IGWs \cite{bib:Vincze}. Moreover, in contrast to the classical tank without salt stratification, we have layers with $N/f>1$. A ratio larger than unity implies that the IGW propagation in the experiment is expected to be qualitatively similar to the atmospheric case. Interestingly, we found local IGW packets along the jets in the surface and bottom layers where the local Rossby number is larger than 1, suggesting spontaneous imbalance as generating mechanism \cite{bib:Rodda}, and not boundary layer instability \cite{bib:vLarcher}.
The second experiment is a newly built rotating annulus, supported by numerical simulations \cite{bib:Hien}. This one is much wider with a small fluid depth compared to the classical set-up and has a larger temperature difference between the inner and outer cylinder walls, which is more atmosphere-like since it shows an $N/f >1$ even without the vertical salt stratification. The conditions for gravity wave emission in this new configuration are examined in detail. Moreover, we compare numerical simulations and experimental data focusing on the variations of the temperature $T$ and $N$. It becomes clear that despite the fact that the global structure and baroclinic instability characteristics are very similar, model and experiment show deviations in $N$ with implications for gravity wave emission. Nevertheless, the complex horizontal structure of $N$ with largest values along the baroclinic jet axis lend credence to the experimentally observed trapped inertia-gravity waves \cite{bib:Rodda}.
\begin{figure}[h]
\setlength{\unitlength}{1cm}
\begin{center}
\includegraphics[width=14.5cm]{diffHeatedBIG.pdf}
\end{center}
\caption{Sketch of the two experiments: barostrat on the left and atmosphere-like tank (with $H=6$ cm and $L=35$ cm) on the right.}
\label{fig1}
\end{figure}
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\begin{thebibliography}{1}
\bibitem{bib:Vincze}
M. Vincze, I.D. Borcia, U. Harlander, and P. Le Gal, "Double-diffusive convection and baroclinic instability in a differentially heated and initially stratified rotating system: the barostrat instability." Fluid Dyn. Res., 48, 061414 (19pp), 2016,
\bibitem{bib:Rodda}
C. Rodda, I. Borcia, P. Le Gal, M. Vincze and U. Harlander, "Baroclinic, Kelvin and inertia-gravity waves in the barostrat instability experiment," Geophysical and Astrophysical Fluid Dynamics, pages 1-32, 2018,
\bibitem{bib:vLarcher}
T. von Larcher, S. Viazzo, U. Harlander, M. Vincze, and A. Randriamampianina, "Instabilities and small-scale waves within the Stewartson layers of the thermally driven rotating annulus" J. Fluid Mech., 841:380--407, 2018
\bibitem{bib:Hien}
S. Hien, J. Rolland, S. Borchert, L. Schoon, C. Zülicke, and U. Achatz, "Spontaneous gravity wave emission in the differentially heated rotating annulus experiment," J. Fluid Mech., 838:5--41, 2018.
%\bibitem{bib:Borchert}
%S. Borchert, U. Achatz, and M. D. Fruman. "Gravity wave emission in an atmosphere-like configuration of the differentially heated rotating annulus experiment." J. Fluid Mech. 758 (2014): 287-311,
%
\end{thebibliography}
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12:00
15 mins
#258
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Invariant manifolds in stratified turbulence
Nicolás Sujovolsky, Pablo Mininni, Gabriel Mindlin
Abstract: The velocity gradient tensor contains fundamental information on the small-scale motions in turbulence, related to non-Gaussian statistics, intermittency, the alignment of vorticity with the strain-rate eigenvectors, and the rate of deformation of fluid material volumes. For isotropic and homogeneous turbulence, the restricted Euler model, which neglects the anisotropic components of the pressure Hessian in the Euler equation, gives a closed system of ordinary differential equations (ODEs) with only two degrees of freedom that captures many dynamical properties of the velocity gradient tensor. The reduced model also predicts the existence of an invariant manifold for the evolution of fluid elements in isotropic turbulence that is in good agreement with both numerical and laboratory measurements.
For anisotropic and more realistic flows there have been attempts to derive restricted Euler models; however, to obtain a closed system of ODEs more approximations are required, as it is known that using only two degrees of freedom is incompatible with the dynamics of anisotropic flows.
In this talk we will present a reduced system of 7 ODEs obtained by only dropping the anisotropic components of the pressure Hessian in the ideal incompressible Boussinesq equations. This system captures the time evolution of spatial gradients of the velocity and of the temperature in fluid elements of stratified turbulent flows, such as those find in the ocean and the atmosphere. We show the existence of invariant manifolds in this system (further reducing the system dimensionality), and compare the results with data from direct numerical simulations of the full incompressible Boussinesq equations in the stably stratified case. A large fraction of fluid elements accumulate over and evolve along the invariant manifolds of the reduced system. In particular, one of these manifolds is associated to the local development of convection, indicating the fluid elements live at the brink of an instability that has been linked with an enhancement in the vertical dispersion. We also study the stability of the reduced system, and show that it is compatible with recent observations in stratified turbulence of non-monotonic dependence of intermittency with stratification.
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12:15
15 mins
#56
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The linear instability of the stratified plane Poiseuille flow
Uwe Harlander, Patrice Le Gal, Ion Dan Borcia, St'ephane Le Diz'es, Jun Chen, Benjamin Favier
Abstract: \documentclass[10pt,a4paper]{article}
\usepackage[T1]{fontenc}
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\begin{document}
\title{The linear instability of the stratified plane Poiseuille flow}
\authors{\underline{U. Harlander}$^1$ \& P. Le Gal $^2$ \& I. Borcia $^1$ \& S. Le Diz\`es $^2$ \& J. Chen $^2$ \& B. Favier $^2$}
\affiliations{$^1$Department of Aerodynamics and Fluid Mechanics, BTU Cottbus-Senftenberg, Germany\\
$^2$Aix Marseille Universit\'e, CNRS, Centrale Marseille, IRPHE, France}
\maketitle
Plane Poiseuille flow is
one of the simplest parallel shear flow. In the non stratified case, it is known to be linearly unstable for Reynolds numbers
larger than $5572$ \cite{Orszag71}. Above this value, two dimensional waves - known as Tollmien-Schlichting waves - are viscously unstable and can develop and propagate in the flow.
We present here the stability analysis of a plane Poiseuille
flow which is stably stratified in density along the vertical direction, i.e. orthogonal to the horizontal shear. Density stratification is ubiquitous in nature and in a geophysical context,
we may think of water flows in submarine canyons, of winds in deep valleys or of laminar flows in rivers or canals where stratification can be due to temperature or salinity gradients.
Our study is based on laboratory experiments, on a linear stability analysis and on direct numerical simulations. This study follows recent investigations on instabilities of stratified rotating or not rotating
shear flows: the stratorotational instability (\cite{LeBars2007},\cite{Harlander}), the stratified boundary layer instability (\cite{ChenLedizes}) or the stratified Plane Couette flow instability (\cite{Facchini2018}) where it is shown that these instabilities belong to a class of instabilities caused by the resonant interaction of Doppler shifted internal gravity waves.
A particularity of the present case is that the Poiseuille flow Tollmien-Schlichting waves can themselves also interact and possibly resonate with non viscous gavity waves. The experiments are realized in an annular channel having an inner diameter of $1.4$ m and a rectangular vertical section of $85$ x $200$ mm. This canal is filled up to a level of $130$ mm (position of the free surface)
with salt stratified water using the classical double bucket technique. The free surface fluid is then entrained by the side and bottom walls of the canal when this one is set into slow rotation. However, a barrier,
placed radially inside the channel, blocks the fluid, prohibiting solid body rotation and resulting in a nearly parabolic horizontal velocity profile. Visualizations and PIV measurements show the appearance of a stationary (versus the laboratory frame) braided pattern
of waves above a given threshold that depends on the Reynolds and Froude numbers ($ Re_{c} \sim 2000, Fr_{c} \sim 0.5 $). The comparison with the theoretical threshold and the critical wavenumbers calculated by linear analysis is excellent.
Finally, direct numerical simulations permit to complete the description of this instability that can be interpreted as a resonant interaction of boundary trapped internal gravity waves.
%\begin{figure}[h]
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%\bibliographystyle{plainbv}
%\bibliography{biblio}
% Alternatively use this for the bibliography :
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\begin{thebibliography}{1}
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\bibitem{Orszag71}
S. Orszag. Accurate solution of the Orr-Sommerfeld stability equation, \textit{Journal of Fluid Mechanics}, \textbf{50}, 689--703, 1971.
\bibitem{LeBars2007}
M. Le Bars, P. Le Gal. Experimental analysis of the stratorotational instability in a
cylindrical Couette flow, \textit{Physical Review Letters}, \textbf{99}, 064502, 2007.
\bibitem{Harlander}
G. R\"udiger, T. Seelig, M. Schultz, M. Gellert, Ch. Egbers and U. Harlander. The stratorotational instability of Taylor-Couette flows with moderate Reynolds numbers,
\textit{Geophysical \& Astrophysical Fluid Dynamics}, \textbf{111}, 429--447, 2017.
\bibitem{ChenLedizes}
J. Chen, Y. Bai, and S. Le Diz\`es. Instability of a boundary layer flow on a vertical wall in a stably stratified fluid, \textit{Journal of Fluid Mechanics}, \textbf{795}, 262--277, 2016.
\bibitem{Facchini2018}
G. Facchini, B. Favier, P. Le Gal, M. Wang and M. Le Bars.
The linear instability of the stratified plane Couette flow, \textit{Journal of Fluid Mechanics}, \textbf{853}, 205--234, 2018.
%\bibitem{bib:momo1965}
%A. Momo, B. Mimi, and C. Mama. Experimental study of blibli. \textit{Journal of Blibli} \textbf{15}: 43--62, 1965.
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%\bibitem{bib:toto2002}
%A. Toto, B. Titi, Tutu and C. Tutu. Effect of blibli on blublu. \textit{Journal of Blabla} \textbf{468}: 77--105, 2002.
%
\end{thebibliography}
\end{document}
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12:30
15 mins
#309
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A SELF-ORGANIZED CRITICALITY ANALOGY OF SUBMESO MOTIONS AND INTERMITTENT TURBULENCE ACROSS A NOCTURNAL LOW-LEVEL JET
Luca Mortarini, Daniela Cava, Umberto Giostra, Otavio Acevedo, Gabriel Katul
Abstract: The switching between turbulent (active) and non-turbulent (passive) states is one of the distinctive features of stable boundary layer (SBL). In very stable conditions, the SBL becomes layered with fully developed turbulence confined to a narrow region near the surface and weak and intermittent turbulence detached from the ground in the quiescent region above, frequently associated to the development of a low-level jet (LLJ). The classical Monin-Obukhov similarity theory fails in the layered SBL because of the switching between active and passive states, and quantifying mixing and transport properties becomes challenging in numerical models. In this work, multi-level high frequency time series from a tall (140 m) meteorological tower are analysed by Telegraphic Approximation to identify connections between SBL states and a general class of intermittency models that include self-organised criticality (SOC). The analysed night includes transition from a mildly SBL to one dominated by LLJ and quiescent layers with weak or intermittent turbulence. Aspects of the submeso motions that setup after the formation of the LLJ are shown to carry signatures of co-existence of self-organized criticality (SOC) and intermittent turbulence. The observed behaviour in clustering and intermittency exponents indicates that the submeso motions are highly clustered and their influence enhanced intermittent turbulence both in the inertial subrange and at larger scales. The switching probability of active-inactive states and lifetimes of inactive states (related to intermittent turbulent burst) shows evidence of SOC-like behaviour in terms of scaling laws. The coexistence of SOC and intermittent turbulence in the SBL may offer new perspective about the genesis of scaling laws and similarity arguments improving performances of meteorological and dispersion models in stable atmosphere.
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