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Lucretius’ choice of addressee has engaged a number of critical responses, both historicizing and literary-critical. This chapter assesses what is distinctive about Lucretius’ approach to C. Memmius (taken to be the praetor of 58 BC and unsuccessful consular candidate of 53 BC) through comparison with the theory and practice of Epicureanism in contemporary sources, chiefly Philodemus. In the context of Memmius’ disgrace and exile to Athens, Lucretius’ invectives against ambition and similar vices take on an especially mordant character – a frank criticism that contrasts with Philodemus’ more deferential treatment of C. Calpurnius Piso, especially in On the Good King According to Homer. This difference suggests that Lucretius chose Memmius as his addressee for the very reason that this corrupt and failed Roman politician was far from being a promising disciple and badly in need of Epicurean teaching.
In this chapter I offer some thoughts about the models for Ennius’ divine apparatus and about the balance struck in the Annals among the Varronian theologies. Specifically, I suggest (1) that Ennius’ treatment of the gods owes as much to Hesiod as it does to Homer; (2) that this debt involves structural as well as thematic resemblances between the Annals and Hesiod’s genealogical poetry; (3) that Ennius represents the Olympians as a group very differently from Hesiod or Homer; and (4) that the rationalizing theology of Euhemerus’ Sacred History, which Ennius translated into Latin, is present in the Annals to a larger extent than is commonly assumed. On this basis I suggest (5) that the poem’s representation of the gods evolves in a way that represents the increasing eclecticism of philosophical ideas about divinity over time. The result is that the poem ends with a perspective that is overtly different from, but not fundamentally incompatible with the one with which it began.
In the context of recent challenges to long-standing assumptions about the nature of Ennius' Annals and the editorial methods appropriate to the poem's fragmentary remains, this volume seeks to move Ennian studies forward on three axes. First, a re-evaluation of the literary and historical precedents for and building blocks of Ennius' poem in order to revise the history of early Latin literature. Second, a cross-fertilization of recent critical approaches to the fields of poetry and historiography. Third, reflection on the tools and methods that will best serve future literary and historical research on the Annals and its reception. Adopting different approaches to these broad topics, the fourteen papers in this volume illustrate how much can be said about Ennius' poem and its place in literary history independent of any commitment to inevitably speculative totalizing interpretations.
The fourteen papers in this volume take advantage of advances in the study of Ennius’ Annales that have occurred in the generation since Otto Skutsch published his monumental edition and commentary on the poem, while also taking advantage of Jackie Elliott's recent provocation to question the most basic assumptions that underlie Skutsch’s work. The result is a collection of essays as diverse in their individual interests and objectives as we believe Ennius and his Annals also were. The essays are organized under four rubrics, namely (1) Innovation, (2) Authority, (3) Influence, and (4) Interpretation. An afterword reflects on the findings of the volume as a whole, with equal emphasis on new questions that the individual papers raise and on solutions that they propose, while raising additional points that should provoke further research.
Horizontal density layers are commonly observed in stratified turbulence. Recent work (e.g. Taylor & Zhou, J. Fluid Mech., vol. 823, 2017, R5) has reinvigorated interest in the Phillips instability (PI), by which density layers form via negative diffusion if the turbulent buoyancy flux weakens as stratification increases. Theoretical understanding of PI is incomplete, in part because it remains unclear whether and by what mechanism the flux-gradient relationship for a given example of turbulence has the required negative-diffusion property. Furthermore, the difficulty of analysing the flux-gradient relation in evolving turbulence obscures the operating mechanism when layering is observed. These considerations motivate the search for an example of PI that can be analysed clearly. Here PI is shown to occur in two-dimensional Boussinesq sheared stratified turbulence maintained by stochastic excitation. PI is analysed using the second-order S3T closure of statistical state dynamics, in which the dynamics is written directly for statistical variables of the turbulence. The predictions of S3T are verified using nonlinear simulations. This analysis provides theoretical underpinning of PI based on the fundamental equations of motion that complements previous analyses based on phenomenological models of turbulence.
Simulations of strongly stratified turbulence often exhibit coherent large-scale structures called vertically sheared horizontal flows (VSHFs). VSHFs emerge in both two-dimensional (2D) and three-dimensional (3D) stratified turbulence with similar vertical structure. The mechanism responsible for VSHF formation is not fully understood. In this work, the formation and equilibration of VSHFs in a 2D Boussinesq model of stratified turbulence is studied using statistical state dynamics (SSD). In SSD, equations of motion are expressed directly in the statistical variables of the turbulent state. Restriction to 2D turbulence facilitates application of an analytically and computationally attractive implementation of SSD referred to as S3T, in which the SSD is expressed by coupling the equation for the horizontal mean structure with the equation for the ensemble mean perturbation covariance. This second-order SSD produces accurate statistics, through second order, when compared with fully nonlinear simulations. In particular, S3T captures the spontaneous emergence of the VSHF and associated density layers seen in simulations of turbulence maintained by homogeneous large-scale stochastic excitation. An advantage of the S3T system is that the VSHF formation mechanism, which is wave–mean flow interaction between the emergent VSHF and the stochastically excited large-scale gravity waves, is analytically understood in the S3T system. Comparison with fully nonlinear simulations verifies that S3T solutions accurately predict the scale selection, dependence on stochastic excitation strength, and nonlinear equilibrium structure of the VSHF. These results constitute a theory for VSHF formation applicable to interpreting simulations and observations of geophysical examples of turbulent jets such as the ocean’s equatorial deep jets.