38 research outputs found
Warm turbulence in the Boltzmann equation
We study the single-particle distributions of three-dimensional hard sphere
gas described by the Boltzmann equation. We focus on the steady homogeneous
isotropic solutions in thermodynamically open conditions, i.e. in the presence
of forcing and dissipation. We observe nonequilibrium steady state solution
characterized by a warm turbulence, that is an energy and particle cascade
superimposed on the Maxwell-Boltzmann distribution. We use a dimensional
analysis approach to relate the thermodynamic quantities of the steady state
with the characteristics of the forcing and dissipation terms. In particular,
we present an analytical prediction for the temperature of the system which we
show to be dependent only on the forcing and dissipative scales. Numerical
simulations of the Boltzmann equation support our analytical predictions.Comment: 4 pages, 5 figure
Helicity conservation by flow across scales in reconnecting vortex links and knots
The conjecture that helicity (or knottedness) is a fundamental conserved quantity has a rich history in fluid mechanics, but the nature of this conservation in the presence of dissipation has proven difficult to resolve. Making use of recent advances, we create vortex knots and links in viscous fluids and simulated superfluids and track their geometry through topology-changing reconnections. We find that the reassociation of vortex lines through a reconnection enables the transfer of helicity from links and knots to helical coils. This process is remarkably efficient, owing to the antiparallel orientation spontaneously adopted by the reconnecting vortices. Using a new method for quantifying the spatial helicity spectrum, we find that the reconnection process can be viewed as transferring helicity between scales, rather than dissipating it. We also infer the presence of geometric deformations that convert helical coils into even smaller scale twist, where it may ultimately be dissipated. Our results suggest that helicity conservation plays an important role in fluids and related fields, even in the presence of dissipation
Equilibrium and nonequilibrium description of negative temperature states in a one-dimensional lattice using a wave kinetic approach
We predict negative temperature states in the discrete nonlinear Schödinger (DNLS) equation as exact solutions of the associated wave kinetic equation. Within the wave kinetic approach, we define an entropy that results monotonic in time and reaches a stationary state, that is consistent with classical equilibrium statistical mechanics. We also perform a detailed analysis of the fluctuations of the actions at fixed wave numbers around their mean values. We give evidence that such fluctuations relax to their equilibrium behavior on a shorter timescale than the one needed for the spectrum to reach the equilibrium state. Numerical simulations of the DNLS equation are shown to be in agreement with our theoretical results. The key ingredient for observing negative temperatures in lattices characterized by two invariants is the boundedness of the dispersion relation
Rogue Waves: From Nonlinear Schrödinger Breather Solutions to Sea-Keeping Test
Under suitable assumptions, the nonlinear dynamics of surface gravity waves can be modeled by the one-dimensional nonlinear Schrödinger equation. Besides traveling wave solutions like solitons, this model admits also breather solutions that are now considered as prototypes of rogue waves in ocean. We propose a novel technique to study the interaction between waves and ships/structures during extreme ocean conditions using such breather solutions. In particular, we discuss a state of the art sea-keeping test in a 90-meter long wave tank by creating a Peregrine breather solution hitting a scaled chemical tanker and we discuss its potential devastating effects on the ship
Scattering of Line-Ring Vortices in a Superfluid
We study the scattering of vortex rings by a superfluid line vortex using the Gross-Pitaevskii equation in a parameter regime where a hydrodynamic description based on a vortex filament approximation is applicable. By using a vortex extraction algorithm, we are able to track the location of the vortex ring as a function of time. Using this, we show that the scattering of the vortex ring in our Gross-Pitaevskii simulations is well captured by the local induction approximation of a vortex filament model for a wide range of impact parameters. The scattering of a vortex ring by a line vortex is characterised by the initial offset of the centre of the ring from the axis of the vortex. We find that a strong asymmetry exists in the scattering of a ring as a function of this initial scattering parameter
Wind generated rogue waves in an annular wave flume
We investigate experimentally the statistical properties of a wind-generated wave field and the spontaneous formation of rogue waves in an annular flume. Unlike many experiments on rogue waves, where waves are mechanically generated, here the wave field is forced naturally by wind as it is in the ocean. What is unique about the present experiment is that the annular geometry of the tank makes waves propagating circularly in an {\it unlimited-fetch} condition. Within this peculiar framework, we discuss the temporal evolution of the statistical properties of the surface elevation. We show that rogue waves and heavy-tail statistics may develop naturally during the growth of the waves just before the wave height reaches a stationary condition. Our results shed new light on the formation of rogue waves in a natural environment
Kolmogorov turbulence, Anderson localization and KAM integrability
The conditions for emergence of Kolmogorov turbulence, and related weak wave
turbulence, in finite size systems are analyzed by analytical methods and
numerical simulations of simple models. The analogy between Kolmogorov energy
flow from large to small spacial scales and conductivity in disordered solid
state systems is proposed. It is argued that the Anderson localization can stop
such an energy flow. The effects of nonlinear wave interactions on such a
localization are analyzed. The results obtained for finite size system models
show the existence of an effective chaos border between the
Kolmogorov-Arnold-Moser (KAM) integrability at weak nonlinearity, when energy
does not flow to small scales, and developed chaos regime emerging above this
border with the Kolmogorov turbulent energy flow from large to small scales.Comment: 8 pages, 6 figs, EPJB style
Helicity within the vortex filament model
Kinetic helicity is one of the invariants of the Euler equations that is associated with the topology of vortex lines within the fluid. In superfluids, the vorticity is concentrated along vortex filaments. In this setting, helicity would be expected to acquire its simplest form. However, the lack of a core structure for vortex filaments appears to result in a helicity that does not retain its key attribute as a quadratic invariant. By defining a spanwise vector to the vortex through the use of a Seifert framing, we are able to introduce twist and henceforth recover the key properties of helicity. We present several examples for calculating internal twist to illustrate why the centreline helicity alone will lead to ambiguous results if a twist contribution is not introduced. Our choice of the spanwise vector can be expressed in terms of the tangential component of velocity along the filament. Since the tangential velocity does not alter the configuration of the vortex at later times, we are able to recover a similar equation for the internal twist angle to that of classical vortex tubes. Our results allow us to explain how a quasi-classical limit of helicity emerges from helicity considerations for individual superfluid vortex filaments
Nonlinearity and Topology
The interplay of nonlinearity and topology results in many novel and emergent
properties across a number of physical systems such as chiral magnets, nematic
liquid crystals, Bose-Einstein condensates, photonics, high energy physics,
etc. It also results in a wide variety of topological defects such as solitons,
vortices, skyrmions, merons, hopfions, monopoles to name just a few.
Interaction among and collision of these nontrivial defects itself is a topic
of great interest. Curvature and underlying geometry also affect the shape,
interaction and behavior of these defects. Such properties can be studied using
techniques such as, e.g. the Bogomolnyi decomposition. Some applications of
this interplay, e.g. in nonreciprocal photonics as well as topological
materials such as Dirac and Weyl semimetals, are also elucidated
Mixed flux-equipartition solutions of a diffusion model of nonlinear cascades
We present a parametric study of a nonlinear diffusion equation which generalises Leith's model of a turbulent cascade to an arbitrary cascade having a single conserved quantity. There are three stationary regimes depending on whether the Kolmogorov exponent is greater than, less than or equal to the equilibrium exponent. In the first regime, the large-scale spectrum scales with the Kolmogorov exponent. In the second regime, the large-scale spectrum scales with the equilibrium exponent so the system appears to be at equilibrium at large scales. Furthermore, in this equilibrium-like regime, the amplitude of the large-scale spectrum depends on the small-scale cut-off. This is interpreted as an analogue of cascade nonlocality. In the third regime, the equilibrium spectrum acquires a logarithmic correction. An exact analysis of the self-similar, nonstationary problem shows that time-evolving cascades have direct analogues of these three regimes