Turbulence is a fundamental and ubiquitous phenomenon in nature, occurring from astrophysical to biophysical scales. At the same time, it is widely recognized as one of the key unsolved problems in modern physics, representing a paradigmatic example of nonlinear dynamics far from thermodynamic equilibrium. Whereas in the past, most theoretical work in this area has been devoted to NavierStokes flows, there is now a growing awareness of the need to extend the research focus to systems with more general patterns of energy injection and dissipation. These include various types of complex fluids and plasmas, as well as active systems consisting of self-propelled particles, like dense bacterial suspensions. Recently, a continuum model has been proposed for such "living fluids" that is based on the Navier-Stokes equations, but extends them to include some of the most general terms admitted by the symmetry of the problem [Wensink HH, et al. (2012) Proc Natl Acad Sci USA 109:14308-14313]. This introduces a cubic nonlinearity, related to the Toner-Tu theory of flocking, which can interact with the quadratic Navier-Stokes nonlinearity. We show that as a result of the subtle interaction between these two terms, the energy spectra at large spatial scales exhibit power laws that are not universal, but depend on both finite-size effects and physical parameters. Our combined numerical and analytical analysis reveals the origin of this effect and even provides a way to understand it quantitatively. Turbulence in active fluids, characterized by this kind of nonlinear self-organization, defines a new class of turbulent flows.D espite several decades of intensive research, turbulence-the irregular motion of a fluid or plasma-still defies a thorough understanding. It is a paradigmatic example of nonlinear dynamics and self-organization far from thermodynamic equilibrium also closely linked to fundamental questions about irreversibility (1) and mixing (2). The classical example of a turbulent system is a Navier-Stokes flow, with a single quadratic nonlinearity, wellseparated drive and dissipation ranges, and an extended intermediate range of purely conservative scale-to-scale energy transfer (3). However, many turbulent systems of scientific interest involve more general patterns of energy injection, transfer, and dissipation. A fascinating example of these kinds of generalized turbulent dynamics can be observed in dense bacterial suspensions (4). Although the motion of the individual swimmers in the background fluid takes place at Reynolds numbers well below unity, the coarse-grained dynamics of these self-propelled particles display spatiotemporal chaos, i.e., turbulence (5-7). Nevertheless, the correlation functions of the velocity and vorticity fields display some essential differences compared with their counterparts in classical fluid turbulence (8, 9). Moreover, the collective motion of bacteria in such suspensions exhibits long-range correlations (10), appears to be driven by internal instabilities (11), and depends strongly...

A reduced four-dimensional (integrated over perpendicular velocity) gyrokinetic model of slab ion temperature gradient-driven turbulence is used to study the phase-space scales of free energy dissipation in a turbulent kinetic system over a broad range of background gradients and collision frequencies. Parallel velocity is expressed in terms of Hermite polynomials, allowing for a detailed study of the scales of free energy dynamics over the four-dimensional phase space. A fully spectral code – the DNA code – that solves this system is described. Hermite free energy spectra are significantly steeper than would be expected linearly, causing collisional dissipation to peak at large scales in velocity space even for arbitrarily small collisionality. A key cause of the steep Hermite spectra is acritical balance– an equilibration of the parallel streaming time and the nonlinear correlation time – that extends to high Hermite numbern. Although dissipation always peaks at large scales in all phase space dimensions, small-scale dissipation becomes important in an integrated sense when collisionality is low enough and/or nonlinear energy transfer is strong enough. Toroidal full-gyrokinetic simulations using theGenecode are used to verify results from the reduced model. Collision frequencies typically found in present-day experiments correspond to turbulence regimes slightly favoring large-scale dissipation, while turbulence in low-collisionality systems like ITER and space and astrophysical plasmas is expected to rely increasingly on small-scale dissipation mechanisms. This work is expected to inform gyrokinetic reduced modeling efforts like Large Eddy Simulation and gyrofluid techniques.

A gyrokinetic model of ion temperature gradient driven turbulence in magnetized plasmas is used to study the injection, nonlinear redistribution, and collisional dissipation of free energy in the saturated turbulent state over a broad range of driving gradients and collision frequencies. The dimensionless parameter L(T)/L(C), where L(T) is the ion temperature gradient scale length and L(C) is the collisional mean free path, is shown to parametrize a transition between a saturation regime dominated by nonlinear transfer of free energy to small perpendicular (to the magnetic field) scales and a regime dominated by dissipation at large scales in all phase space dimensions.

Discrete kinetic eigenmode spectra of electron plasma oscillations in weakly collisional plasma: A numerical study Phys. Plasmas 20, 012125 (2013) Non-planar ion-acoustic solitary waves and their head-on collision in a plasma with nonthermal electrons and warm adiabatic ions Phys. Plasmas 20, 012122 (2013) The incomplete plasma dispersion function: Properties and application to waves in bounded plasmas Phys. Plasmas 20, 012118 (2013) Effect of ion temperature on ion-acoustic solitary waves in a magnetized plasma in presence of superthermal electrons Phys. Plasmas 20, 012306 (2013) Additional information on Phys. Plasmas Basic linear eigenmode spectra for electrostatic Langmuir waves and drift-kinetic slab ion temperature gradient modes are examined in a series of scenarios. Collisions are modeled via a Lenard-Bernstein collision operator which fundamentally alters the linear spectrum even for infinitesimal collisionality [Ng et al., Phys. Rev. Lett. 83, 1974(1999. A comparison between different discretization schemes reveals that a Hermite representation is superior for accurately resolving the spectra compared to a finite differences scheme using an equidistant velocity grid. Additionally, it is shown analytically that any even power of velocity space hyperdiffusion also produces a Case-Van Kampen spectrum which, in the limit of zero hyperdiffusivity, matches the collisionless Landau solutions. V C 2013 American Institute of Physics. [http://dx

A notable feature of plasma turbulence is its propensity to retain features of the underlying linear eigenmodes in a strongly turbulent state-a property that can be exploited to predict various aspects of the turbulence using only linear information. In this context, this work examines gradient-driven gyrokinetic plasma turbulence through three lenses-linear eigenvalue spectra, pseudospectra, and singular value decomposition (SVD). We study a reduced gyrokinetic model whose linear eigenvalue spectra include ion temperature gradient driven modes, stable drift waves, and kinetic modes representing Landau damping. The goal is to characterize in which ways, if any, these familiar ingredients are manifest in the nonlinear turbulent state. This pursuit is aided by the use of pseudospectra, which provide a more nuanced view of the linear operator by characterizing its response to perturbations. We introduce a new technique whereby the nonlinearly evolved phase space structures extracted with SVD are linked to the linear operator using concepts motivated by pseudospectra. Using this technique, we identify nonlinear structures that have connections to not only the most unstable eigenmode but also subdominant modes that are nonlinearly excited. The general picture that emerges is a system in which signatures of the linear physics persist in the turbulence, albeit in ways that cannot be fully explained by the linear eigenvalue approach; a nonmodal treatment is necessary to understand key features of the turbulence.