Related papers: Diffusion of passive scalar in a finite-scale rand…
We study the evolution of a passive scalar subject to molecular diffusion and advected by an incompressible velocity field on a 2D bounded domain. The velocity field is $u = \nabla^\perp H$, where H is an autonomous Hamiltonian whose level…
We consider a passive scalar that is advected by a prescribed mean zero divergence-free velocity field, diffuses, and reacts according to a KPP-type nonlinear reaction. We introduce a quantity, the bulk burning rate, that makes both…
The dispersion of a passive scalar in a fluid through the combined action of advection and molecular diffusion is often described as a diffusive process, with an effective diffusivity that is enhanced compared to the molecular value.…
Spatio-temporal deterministic chaos at small Taylor-Reynolds numbers $Re_{\lambda} \lesssim 40$ and distributed chaos at turbulent $Re_{\lambda} \gtrsim 40$ in passive scalar dynamics have been studied using results of direct numerical…
We analyze multi-point correlation functions of a tracer in an incompressible flow at scales far exceeding the scale $L$ at which fluctuations are generated (quasi-equilibrium domain) and compare them with the correlation functions at…
The paper studies the behavior of the trajectories of fluid particles in a compressible generalization of the Kraichnan ensemble of turbulent velocities. We show that, depending on the degree of compressibility, the trajectories either…
In this paper we investigate the properties of rapidly rotating decaying turbulence using numerical simulations and phenomenological modelling. We find that as the turbulent flow evolves in time, the Rossby number decreases to $\sim…
We show that the decay of a passive scalar $\theta$ advected by a random incompressible flow with zero correlation time in Batchelor limit can be mapped exactly to a certain quantum-mechanical system with a finite number of degrees of…
Considering the action for the theory $\lambda\phi^{4}$ for a massive scalar bosonic field as an entropy functional on the space of coupling constants and on the space of fields, we determine the gradient flows for the scalar field, the…
In this paper, we investigated the statistical differences between active and passive scalars in isotropic compressible turbulence. In the inertial range, the kinetic energy and scalar have the Kolmogorov spectra, and the Kolmogorov and…
Similarities and differences between Kolmogorov scale-by-scale equilibria/non-equilibria for velocity and scalar fields are investigated in the intermediate layer of a fully developed turbulent channel flow with a passive scalar/temperature…
The advection and diffusion of a passive scalar is investigated for a map of the 2-torus. The map is chaotic, and the limit of almost-uniform stretching is considered. This allows an analytic understanding of the transition from a phase of…
A turbulent flow is characterized by velocity fluctuations excited in an extremely broad interval of wave numbers $k> \Lambda_{f}$ where $\Lambda_{f}$ is a relatively small set of the wave-vectors where energy is pumped into fluid by…
We report on the modification of the spectrum of a passive scalar inside a turbulent flow by the injection of large bubbles. While the spectral modification through bubbles is well known and well analyzed for the velocity fluctuations,…
In a forced three-dimensional turbulent flow the scales larger than the forcing scale have been conjectured to reach a thermal equilibrium state forming a $k^2$ energy spectrum. In this work we examine the properties of these large scales…
The asymptotic decay of passive scalar fields is solved analytically for the Kraichnan model, where the velocity has a short correlation time. At long times, two universality classes are found, both characterized by a distribution of the…
We establish exact inequalities for the structure-function scaling exponents of a passively advected scalar in both the inertial-convective and viscous-convective ranges. These inequalities involve the scaling exponents of the velocity…
We provide the leading behavior at large wavenumbers of the two-point correlation function of a scalar field passively advected by a turbulent flow. We first consider the Kraichnan model, in which the turbulent carrier flow is modeled by a…
Polymeric turbulence, flows of fluids with dilute polymer additives at high Reynolds numbers, exhibits striking deviations from the Kolmogorovean behaviour of Newtonian turbulence. Recent experiments as well as simulations have uncovered a…
We study the decay of superflow of a one-dimensional (1D) superfluid in the presence of a periodic potential. In 1D, superflow at zero temperature can decay via quantum nucleation of phase slips even when the flow velocity is much smaller…