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Includes bibliography (p. 191-202). Number of sources in the bibliography: 148 Thesis (doctoral) -- University of Cyprus, Department of Mechanical and Manufacturing Engineering, 2016. The University of Cyprus Library holds the printed form of the thesis. Η Θεωρία Δομής της Τύρβης (ΘΔΤ) αποτελεί ένα ολοκληρωμένο μαθηματικό πλαίσιο, όπου η ποσοτικοποίηση των ποικίλων πτυχών των συνεκτικών δομών της τύρβης επιτυγχάνεται μέσω των Τανυστών Δομής της Τύρβης (ΤΔΤ). Αυτή η θεωρία οδήγησε στην ανάπτυξη των Μοντέλων Δομής της Τύρβης (ΜΔΤ), τα οποία υπόσχονται την υπέρβαση των εγγενών περιορισμών που διέπουν τα παραδοσιακά μοντέλα τύρβης. Ωστόσο, ένα εμπόδιο στην περαιτέρω ανάπτυξη της ΘΔΤ και των ΜΔΤ ήταν η ενδογενής ασάφεια που αφορά στον υπολογισμό των ΤΔΤ σε ανομοιογενείς ροές. Στην παρούσα διατριβή παρουσιάζουμε για πρώτη φορά μια καλά τεκμηριωμένη περιγραφή ενός μαθηματικού και υπολογιστικού πλαισίου, για τον υπολογισμό των ΤΔΤ σε ροές αυθαίρετης σύνθεσης. Βασιζόμενοι στις στιγμιαίες τιμές των ΤΔΤ, αναπτύσσουμε μια νέα τεχνική εξαγωγής δομών για την ταυτοποίηση παθητικών δομών (δηλ. δομών μεγάλης κλίμακας αλλά με ασήμαντη τυρβώδη κινητική ενέργεια). Αυτή η μέθοδος οδηγεί στην απεικόνιση «δομών έρπουσας στροβιλότητας»⋅ δομών μεγάλης κλίμακας με χαμηλό ενεργειακό περιεχόμενο που εμφανίζονται πλησίον των τοιχωμάτων. Επιπλέον, σύγκριση με στιγμιαίες τιμές της τυρβώδους κινητικής ενέργειας δείχνει ότι αυτή η νέα μέθοδος εξαγωγής δομών μπορεί να αναδείξει και τις ενεργητικές δομές (δηλ. δομές μεγάλης κλίμακας με σημαντική τυρβώδη κινητική ενέργεια) που εμφανίζονται πιο μακριά από τα τοιχώματα. Ακολούθως, αναδεικνύουμε τις διαγνωστικές ιδιότητες των ΤΔΤ μέσω της ανάλυσης αποτελεσμάτων από προσομοίωση τυρβώδους ροής σε αγωγό. Δείχνουμε ότι οι ΤΔΤ αντανακλούν τη μορφολογία των παθητικών δομών στην περιοχή πλησίον των τοιχωμάτων και αυτήν των ενεργητικών δομών πιο μακριά από τα τοιχώματα. Επιπλέον, με τη χρήση της νέας τεχνικής εξαγωγής δομών ως κριτήριο για την υπό συνθήκη συλλογή στατιστικών, καταδεικνύεται ότι οι χαρακτηριστικές τάσεις στα στατιστικά που συνδέονται με το νόμο του τοιχώματος οφείλονται κατά κύριο λόγο στις παθητικές δομές. Αντιθέτως, στην περιοχή που επικρατεί ο λογαριθμικός νόμος, τόσο οι ενεργητικές όσο και οι παθητικές δομές συμβάλλουν εξίσου στα στατιστικά, κάτι που βρίσκεται σε συμφωνία με τη μερική ομοιογένεια που χαρακτηρίζει τη ροή σε αυτήν την περιοχή. Για την προώθηση της ανάπτυξης ΜΔΤ κατάλληλων για βιολογικές ροές, εκτελούμε προσομοιώσεις τυρβώδους ροής σε μοντέλο αεραγωγού μιας διακλάδωσης κάτω από συνθήκες σταθερής και παρατεταμένης εισπνοής και εκπνοής. Χρησιμοποιώντας την πλειάδα πληροφοριών διαθέσιμη από τις προσομοιώσεις μας, προσδιορίζουμε τις χαρακτηριστικές δομές του πεδίου ροής, καθώς και την επίδρασή τους στα τελικά μοτίβα εναπόθεσης σωματιδίων στα τοιχώματα του αγωγού διακλάδωσης. Υπό το πρίσμα αυτών των δομών, παρουσιάζουμε και αναλύουμε τα προφίλ των ΤΔΤ σε συγκεκριμένες θέσεις της γεωμετρίας του αγωγού διακλάδωσης. Προς την κατεύθυνση ανάπτυξης ΜΔΤ, αναδεικνύουμε την ικανότητα του Μοντέλου Σωματιδιακής Αναπαράστασης (ΜΣΑ) να προβλέπει με ικανοποιητική ακρίβεια τα επίπεδα ανισοτροπίας των κανονικοποιημένων ΤΔΤ κατά την ακτινική θέση μέσα στο σωλήνα τυρβώδους ροής, όπου η παράμετρος 6 ρυθμού διάτμησης παίρνει τη μέγιστη τιμή της. Επανεξετάζουμε το ΜΣΑ και επισημαίνουμε τα αριθμητικά του προβλήματα, τα οποία μας οδήγησαν στην ανάπτυξη του Ψευδό-ΜΣΑ⋅ μια σταθερή και αποτελεσματική εκδοχή του ΜΣΑ. Το Ψευδό-ΜΣΑ αποτελεί το θεμέλιο λίθο για την ανάπτυξη ΜΔΤ. Οι πληροφορίες που διατίθενται στην παρούσα διατριβή θα δώσουν σημαντική ώθηση στην ανάπτυξη ΜΔΤ και θα ενθαρρύνουν τη χρήση των ΤΔΤ ως διαγνωστικό εργαλείο για τις τυρβώδεις ροές. The Structure-Based turbulence Theory (SBT) is a comprehensive mathematical framework that employs the Turbulence Structure Tensors (TSTs) to quantify the different aspects of the coherent structures of turbulence. This theory led to the development of the Structure-Based turbulence Models (SBMs) which hold promise for resolving inherent limitations of traditional turbulence models. However, an obstacle in the further development of SBT and SBMs has been the underlying ambiguity over how one can compute the TSTs in inhomogeneous flows. In this thesis, we present for the first a time a well-documented description of a mathematical and computational framework for the calculation of the TSTs in arbitrary flow configurations. Based on the instantaneous values of the TSTs, we develop a new eduction technique for the identification of inactive structures (i.e. large-scale structures without significant turbulent kinetic energy). This leads naturally to the visualization of “vorticity crawlers”; large-scale structures with low energy content in the extreme vicinity of the wall. Furthermore, comparison with instantaneous values of turbulent kinetic energy shows that our eduction method seamlessly captures the active structures (i.e. large-scale structures with significant turbulent kinetic energy) further away from the wall. Subsequently, we demonstrate the diagnostic properties of the TSTs, by analyzing simulation results from a turbulent pipe flow. We show that the TSTs reflect the morphology of the inactive structures in the extreme vicinity of the wall, and that of the active structures further away from the wall. Furthermore, by performing conditional averaging via our eduction technique, we reveal that the inactive structures are primarily responsible for the characteristic trends in the turbulence statistics associated with the law of the wall. Contrariwise, in the log-law region, the active and inactive structures contribute equally to the turbulence statistics, in agreement with the quasi-homogeneity of the flow in this region. To promote the development of turbulence SBMs, suitable for biological flows, we perform simulations of turbulent flow through a single airway bifurcation model, emulating steady prolonged inspiration and expiration. We use the rich information obtained from our simulations in order to identify key structures in the flow field and scrutinize their role in determining deposition patterns in the bifurcation. In view of these structures, we report and discuss the profiles of the TSTs at specific stations of the bifurcation. Towards the development of SBMs, we demonstrate the ability of the Particle Representation Model (PRM) to predict remarkably well the anisotropy levels of the normalized TSTs at the radial location of maximum shear rate parameter in a turbulent pipe flow. We revisit the PRM and point out its numerical issues that led us to the development of the Pseudo-PRM; a robust and efficient version of the PRM. The Pseudo-PRM constitutes a solid foundation for the development of SBMs. The information made available herein will provide a significant boost to the development of turbulence SBMs, and will encourage the use of the TSTs in the diagnostics of turbulent flows.

Perturbative and non-perturbative results are presented on the renormalization constants of the quark field and the vector, axial-vector, pseudoscalar, scalar and tensor currents. The perturbative computation, carried out at one-loop level and up to second order in the lattice spacing, is performed for a fermion action, which includes the clover term and the twisted mass parameter yielding results that are applicable for unimproved Wilson fermions, as well as for improved clover and twisted mass fermions. We consider ten variants of the Symanzik improved gauge action corresponding to ten different values of the plaquette coefficients. Non-perturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations are performed for pion masses in the range of 480 MeV to 260 MeV and at three values of the lattice spacing, a, corresponding to beta=3.9, 4.05, 4.20. For each renormalization factor computed non-perturbatively we subtract its perturbative O(a^2) terms so that we eliminate part of the cut-off artifacts. The renormalization constants are converted to MS-bar at a scale of mu=2 GeV. The perturbative results depend on a large number of parameters and are made easily accessible to the reader by including them in the distribution package of this paper, as a Mathematica input file., 36 pages, 11 figures and 6 tables. The results are included in electronic form (Mathematica files)

In this work we calculate the corrections to the amputated Green's functions of four-fermion operators, in 1-loop lattice perturbation theory. One of the novel aspects of our calculations is that they are carried out to second order in the lattice spacing, O(a2). We employ the Wilson/clover action for massless fermions (also applicable for the twisted mass action in the chiral limit) and a family of Symanzik improved actions for gluons. Our calculations have been carried out in a general covariant gauge. Results have been obtained for several popular choices of values for the Symanzik coefficients (Plaquette, Tree-level Symanzik, Iwasaki, TILW and DBW2 action). While our Green's function calculations regard any pointlike four-fermion operators which do not mix with lower dimension ones, we pay particular attention to ΔF=2 operators, both parity conserving and parity violating (F stands for flavor: S, C, B). By appropriately projecting those bare Green's functions we compute the perturbative renormalization constants for a complete basis of four-fermion operators and we study their mixing pattern. For some of the actions considered here, even O(a0) results did not exist in the literature to date. The correction terms which we calculate (along with our previous O(a2) calculation of Z Ψ) are essential ingredients for minimizing the lattice artifacts which are present in nonperturbative evaluations of renormalization constants with the RI′-MOM method. Our perturbative results, for the matrix elements of ΔF=2 operators and for the corresponding renormalization matrices, depend on a large number of parameters: coupling constant, number of colors, lattice spacing, external momentum, clover parameter, Symanzik coefficients, gauge parameter. To make these results most easily accessible to the reader, we have included them in the distribution package of this paper, as an ASCII file named: 4-fermi.m the file is best perused as Mathematica input. The main results of this work have been applied to improve nonperturbative estimates of the BK-parameter in N F=2 twisted mass lattice QCD. © 2011 American Physical Society. 83 7

We present an unquenched Nf=2 lattice computation of the B K parameter which controls K0-K̄0 oscillations. A partially quenched setup is employed with two maximally twisted dynamical (sea) light Wilson quarks, and valence quarks of both the maximally twisted and the Osterwalder-Seiler variety. Suitable combinations of these two kinds of valence quarks lead to a lattice definition of the BK parameter which is both multiplicatively renormalizable and O(a) improved. Employing the nonperturbative RI-MOM scheme, in the continuum limit and at the physical value of the pion mass we get BKRGI=0.729±0.030, a number well in line with the existing quenched and unquenched determinations. © 2011 American Physical Society. 83 1 Cited By :29

Perturbative and non-perturbative results on the renormalization constants of the fermion field and the twist-2 fermion bilinears are presented with emphasis on the non-perturbative evaluation of the one-derivative twist-2 vector and axial vector operators. Non-perturbative results are obtained using the twisted mass Wilson fermion formulation employing two degenerate dynamical quarks and the tree-level Symanzik improved gluon action. The simulations have been performed for pion masses in the range of about 450-260 MeV and at three values of the lattice spacing $a$ corresponding to $\beta=3.9, 4.05, 4.20$. Subtraction of ${\cal O}(a^2)$ terms is carried out by performing the perturbative evaluation of these operators at 1-loop and up to ${\cal O}(a^2)$. The renormalization conditions are defined in the RI$'$-MOM scheme, for both perturbative and non-perturbative results. The renormalization factors, obtained for different values of the renormalization scale, are evolved perturbatively to a reference scale set by the inverse of the lattice spacing. In addition, they are translated to ${\bar{\rm MS}}$ at 2 GeV using 3-loop perturbative results for the conversion factors., Comment: ETM Collaboration, 25 pages, 15 figures. Improvement on the continuum extrapolation and clarification on the estimate of the systematic errors. Typos corrected

We present results for the renormalization constants of bilinear quark operators obtained by using the tree-level Symanzik improved gauge action and the Nf=2 twisted mass fermion action at maximal twist, which guarantees automatic O(a)-improvement. Our results are also relevant for the corresponding standard (un-twisted) Wilson fermionic action since the two actions only differ, in the massless limit, by a chiral rotation of the quark fields. The scale-independent renormalization constants ZV, ZA and the ratio ZP/ZS have been computed using the RI-MOM approach, as well as other alternative methods. For ZA and ZP/ZS, the latter are based on both standard twisted mass and Osterwalder-Seiler fermions, while for ZV a Ward Identity has been used. The quark field renormalization constant Zq and the scale dependent renormalization constants ZS, ZP and ZT are determined in the RI-MOM scheme. Leading discretization effects of O(g^2 a^2), evaluated in one-loop perturbation theory, are explicitly subtracted from the RI-MOM estimates., Comment: 31 pages, 11 figures

We calculate corrections to the fermion propagator and to the Green's functions of all fermion bilinear operators of the form $\bar\Psi \Gamma \Psi$, to one-loop in perturbation theory. We employ the Wilson/clover action for fermions and a family of Symanzik improved actions for gluons. The novel aspect of our calculations is that they are carried out to second order in the lattice spacing, $O(a^2)$. Consequently, they have addressed a number of new issues, most notably the appearance of loop integrands with strong IR divergences (convergent only beyond 6 dimensions). Such integrands are not present in $O(a^1)$ improvement calculations; there, IR divergent terms are seen to have the same structure as in the $O(a^0)$ case, by virtue of parity under integration, and they can thus be handled by well-known techniques. We explain how to correctly extract the full $O(a^2)$ dependence; in fact, our method is generalizable to any order in $a$. The $O(a^2)$ corrections to the quark propagator and Green's functions computed in this paper are useful to improve the nonperturbative RI-MOM determination of renormalization constants for quark bilinear operators. Our results depend on a large number of parameters: coupling constant, number of colors, lattice spacing, external momentum, clover parameter, Symanzik coefficients, gauge parameter. To make these results most easily accessible to the reader, we have included them in the distribution package of this paper, as an ASCII file named: Oa2results.m ; the file is best perused as Mathematica input., Comment: 37 pages, 3 figures, 27 tables. Results are also presented online, in a Mathematica input file. Version 2 (to appear in JHEP): Added a comment regarding Fig.3, corrected typo on Eq.A3