Effects of discrete energy and helicity conservation in numerical simulations of helical turbulence

Helicity is the scalar product between velocity and vorticity and, just like energy, its integral is an in-viscid invariant of the three-dimensional incompressible Navier-Stokes equations. However, space-and time-discretization methods typically corrupt this property, leading to violation of the inviscid conservation principles. This work investigates the discrete helicity conservation properties of spectral and finite-differencing methods, in relation to the form employed for the convective term. Effects due to Runge-Kutta time-advancement schemes are also taken into consideration in the analysis. The theoretical results are proved against inviscid numerical simulations, while a scale-dependent analysis of energy, helicity and their non-linear transfers is performed to further characterize the discretization errors of the different forms in forced helical turbulence simulations

Small-scale anisotropy induced by spectral forcing and by rotation in non-helical and helical turbulence

We study the effect of large-scale spectral forcing on the scale-dependent anisotropy of the velocity field in direct numerical simulations of homogeneous incompressible turbulence. Two forcing methods are considered: the steady ABC single wavenumber scheme and the unsteady non-helical or helical Euler scheme. The results are also compared with high resolution data obtained with the negative viscosity scheme. A fine-grained characterization of anisotropy, consisting in measuring some quantities related to the two-point velocity correlations, is used: we perform a modal decomposition of the spectral velocity tensor into energy, helicity and polarization spectra. Moreover, we include the explicit dependence of these three spectra on the wavevector direction. The conditions that allow anisotropy to develop in the small scales due to forcing alone are clearly identified. It is shown that, in turbulent flows expected to be isotropic, the ABC forcing yields significant energy and helicity directional anisotropy down to the smallest resolved scales, like the helical Euler scheme when an unfavourable forcing scale is used. The direction-and scale-dependent anisotropy is then studied in rotating turbulence. It is first shown that, in the ABC-forced simulations the slope of the energy spectrum is altered and the level of anisotropy is similar to that obtained at lower Rossby number in Euler-forced runs, a result due both to the nature of the forcing itself and to the fact that it allows an inverse cascade to develop. Second, we show that, even at low rotation rate, the natural anisotropy induced by the Coriolis force is visible at all scales. Finally, we identify two different wavenumber ranges in which anisotropy behaves differently, and show that if the Rossby number is not too low the characteristic lenghscale separating them is the one at which rotation and dissipation effects balance

Spectral analysis of the small-scale directional anisotropy in forced homogeneous rotating turbulence

Rotating turbulence is central in many contexts, e.g. astrophysical, geophysical and industrial flows. A background rotation about a fixed axis introduces anisotropy in the turbulent dynamics through both linear and nonlinear mechanisms. The flow regime can be characterized by two independent non-dimensional parameters, e.g. the Reynolds and Rossby numbers or, equivalently, the ratio of the integral scale to the Kolmogorov scale L/eta, and the ratio lZ/L, where lZ=sqrt(epsilon/Omega^3) is the Zeman scale, epsilon is the mean energy dissipation rate and Omega is the rotation rate. The Zeman scale is the scale l at which the inertial timescale (l^2/epsilon)^(1/3) equals the rotation timescale 1/Omega, and thus, if the Reynolds number is large, scales much larger than lZ are mainly affected by rotation while scales much smaller than lZ are dominated by the nonlinear dynamics and are expected to recover isotropy. In this work, we perform high resolution pseudo-spectral direct numerical simulations of non-helical and helical forced rotating turbulence at high Reynolds number in a 3D periodic domain. The scale-dependence of anisotropy is characterized through energy and helicity direction-dependent spectra in the Fourier space. We focus on the low rotation regime, in which the large scale separation permits to study the anisotropic features of scales much smaller than the Zeman scale. We evidence the existence of a highly anisotropic small-wavenumber range and of a weakly anisotropic large-wavenumber range. Importantly, it is observed that the anisotropy level is still significant at the smallest resolved scales (although it decreases as the Rossby number increases), in contrast with recent numerical results, but in agreement with some experiments. Finally, we estimate the value of the threshold wavenumber between large-anisotropy wavenumbers and low-anisotropy wavenumbers, and provide a physical interpretation for it

The effect of large-scale spectral forcing schemes on scale-dependent anisotropy in homogeneous turbulence

Nous présentons des simulations numériques directes de turbulence homogène qui ont pour but d'étudier les effets de schémas de forçage à grande échelle sur l'anisotropie aux différentes échelles du champ de vitesse. Cette anisotropie est caractérisée au moyen de spectres dépendant de l'orientation du vecteur d'onde, pour l'énergie, l'hélicité, et la polarisation. Deux types de forçages sont étudiés : le forçage ABC basé sur un seul nombre d'onde, et le forçage dynamique de type ""équations d'Euler"" aux nombres d'onde infrarouges. Nous sommes ainsi en mesure de caractériser précisément les conditions de création de l'anisotropie dans les échelles inertielles de la turbulence

Etude numérique de la turbulence anisotrope homogène ou confinée

Pour les écoulements turbulents d’intérêt pratique, la turbulence interagit avec le confinement et les forces externes, ce qui cause inhomogénéité et anisotropie statistiques. Isoler leur contribution à des statistiques ciblées est indispensable pour comprendre les différents phénomènes physiques. Le but de cette thèse a donc été d’acquérir une meilleure connaissance de l’anisotropie en fonction de la direction et de l’échelle dans un ensemble de contextes idéalisés et réalistes. On a utilisé une caractérisation statistique dans l’espace spectral ainsi que dans l’espace de séparation. La caractérisation dans l’espace spectral concerne les statistiques anisotropes de turbulence sous forme de spectres directionnels d’énergie, polarisation et hélicité. La caractérisation dans l’espace de séparation s’appuie sur les moments des incréments de vitesse à deux points du deuxième et troisième ordre, et sur les corrélations de vitesse à deux points. Tout d’abord, on a étudié l’effet du forçage spectral de grandes échelles. Les schémas de forçage considérés sont le schéma de forçage de type Euler, non hélicitaire et hélicitaire, et le schéma ABC. On a montré que les deux forçages ont un inconvénient, dans le sens que, si le nombre de modes suffisamment excités est petit, de l’anisotropie se produit même aux petites échelles. Dans le cas du forçage Euler, cela dépend de la gamme de nombres d’onde forcés ainsi que de leur hélicité. Le forçage ABC, pour lequel le niveau d’hélicité injectée ne peut pas être contrôlé, n’excite que six modes et donc il produit toujours de l’anisotropie et à toutes les échelles résolues. Ensuite, on a analysé l’anisotropie en fonction de l’échelle et de la direction pour la turbulence homogène en rotation. Chose étonnante, l’anisotropie se produit à toutes les échelles même si la rotation est faible. En particulier, on a identifié deux gammes d’échelles anisotropes qualitativement différentes. Aux grandes échelles, l’anisotropie directionnelle est plus grande et décroît avec le nombre d’onde. Aux petites échelles, elle est beaucoup plus faible—mais encore significative—et croit lentement avec le nombre d’onde jusqu’aux échelles dissipatives. Une autre conclusion intéressante et originale de cette partie du travail concerne le rôle de l’échelle de Zeman et son lien avec l’anisotropie aux différentes échelles de l’écoulement. D’après des travaux précédents, l’échelle de Zeman devrait être l’échelle de longueur caractéristique qui sépare les échelles affectées par la rotation par les échelles isotropes. Après une plus ample investigation, en utilisant simulations à différents paramètres, on a découvert que l’échelle de séparation entre grande et faible anisotropie est plutôt l’échelle de longueur caractéristique pour laquelle les effets de rotation et de dissipation s’équilibrent. Ce résultat, toutefois, n’est pas en contradiction avec l’argument de Zeman sur le rétablissement de l’isotropie dans la limite asymptotique de viscosité nulle, comme l’échelle de séparation s’annule à nombre de Reynolds infini, et donc seulement la gamme d’anisotropie décroissante devrait persister et les échelles beaucoup plus petite que celle de Zeman pourraient récupérer l’isotropie. Enfin, on a considéré l’écoulement de von Kármán entre deux disques équipés de pales en contre-rotation dans une cavité cylindrique. On a répété l’analyse dans l’espace de séparation dans plusieurs petites sous-régions, afin d’enquêter les analogies possibles entre la dynamique de l’écoulement et celle de la turbulence homogène en rotation. On a découvert que, dans les régions du domaine où l’écoulement a un taux de rotation moyen plus grand, les distributions des statistiques dans l’espace de séparation montrent certaines des caractéristiques typiques de la turbulence en rotation.In turbulent flows of practical interest, turbulence interacts with confinement and external forces, leading to statistical inhomogeneity and anisotropy. Isolating their contributions to some targeted statistics is indispensable for understanding the underlying physical phenomena. The aim of this thesis has therefore been to gain further insight into direction- and scale-dependent anisotropy in a set of idealized and realistic contexts. Both spectral space and separation space statistical characterizations have been employed. The spectral characterization concerns the anisotropic statistics of turbulence under the form of directional energy, polarization and helicity spectra. The separation space characterization is built on two-point second- and third-order velocity increment moments, and two-point velocity correlations. First, we studied the effect of large-scale spectral forcing. The considered forcing methods are the non-helical and the helical Euler scheme, and the ABC-scheme. We showed that both forcings have a drawback in that, if the number of sufficiently excited modes is too low, anisotropy is bound to arise even at small scales. In the case of Euler forcing, this depends on both the range of forcing wavenumbers and its helicity contents. The ABC forcing, for which the amount of injected helicity cannot be controlled, excites only six modes and therefore always generates anisotropy at all resolved scales. Our second step was to analyze the scale- and direction-dependent anisotropy of homogeneous rotating turbulence. Surprisingly, anisotropy arises at all scales even at low rotation rate. In particular, we identified two anisotropic ranges with different features. In the large scales, directional anisotropy is larger and decreases with wavenumber. At smaller scales, it is much weaker—although still significant—and slowly increases with wavenumber all the way to the dissipative scales. Another interesting and original conclusion of this part of the work concerns the role of the Zeman scale and its link with the flow scale-dependent anisotropy. The Zeman scale was previously argued to be the characteristic lengthscale separating rotation-affected scales 2 from isotropic ones. Upon closer investigation using several simulations at different parameters, we found that the separating scale between large and weak anisotropy is rather the characteristic lengthscale at which rotation and dissipation effects balance. This result, however, does not contradict Zeman’s argument about isotropy recovery in the asymptotic limit of vanishing viscosity, since the separating scale vanishes at infinite Reynolds number, and therefore only the decreasing anisotropy range should persist and scales much smaller than the Zeman one may recover isotropy. Finally, we considered the von Kármán flow between two counter-rotating bladed disks in a cylindrical cavity. We repeated the separation space analysis in different small sub-regions, in order to question the possible analogies in the flow dynamics with that of homogeneous rotating turbulence. We found that, in the regions of the domain where the mean flow has a larger average rotation rate, the distributions of the statistics in separation space display some of the features typical of rotating turbulence

The TEA C6 record: a reference archive from the Gulf of Taranto (Ionian Sea) for the last 15 ka

An integrated stratigraphic analysis was carried out on the TEA C6 gravity core raised from the Amendolara basin in the Gulf of Taranto. The 4.5 m long succession was investigated by means of sedimentology and textural analysis, petrophysics, micropaleontology and geochemistry with a refined dating framework provided by oxygen isotope, tephrochronology and 14C AMS ages. Textural and micropaleontological data were analysed by means of Compositional data analysis. The results pointed to a deep marine record with no or little disturbance and they aimed to contribute to the reconstruction of the palaeoceanographical and paleoclimatic changes occurred in this sector of the Central Mediterranean during the last 15 ka BP. In particular, data obtained along the sapropelitic interval corresponding to the Sapropel S1 deposition (9.6-7.5 ka BP), offered a detailed insight on the conditions that characterised the study area during this phase. The deposit was sampled with a continuous step of 1 cm-slides of sediment and this allowed to have resolution even in the order of 50 years. During the early Holocene, before the onset of Sapropel deposition, foraminifera show evidence of several centuries characterised by persistence of winter mixing and likely summer eutrophication. The weakening of winter mixing is simultaneous with a change in bottom conditions, leading to the dominance of oxygen resistant species and then to the establishment of anoxic conditions. During this phase, truly onoxic conditions alternate with periods of partial recovery of benthic faunas, the longest of which correspond to the Sapropel S1 interruption. This moment is time fixed by the occurrence of a tephra layer interbedded within the marine deposit. The end of the Sapropel S1 phase coincides with the re-establishment of winter mixing, although eutrophication persists during a transition interval 400 years long. Dynamics and duration of Sapropel S1 in the Gulf of Taranto show similarities with those of the Adriatic Sea. Sea Surface Temperatures (SST) recontructions obtained from planktonic foraminifera by means of CoDaMAT indicate during the stadial GS1 (Younger Dryas) summer and winter SST about 12°C and 7°C lower than present, respectively, and Holocene SST fluctuations in the range of 2°C. According to the results, TEA C6 core might represent a reference archive for the Gulf of Taranto in terms of response of the sedimentary environment to palaeoceanographical and paleoclimatic changes from the late glacial to the late Holocene