arXiv subjects

Anna Frishman

Publications and source records attributed to Anna Frishman.

23 records · Page 2Linked to original sources

arXiv2015

Time-irreversibility of the statistics of a single particle in a compressible turbulence

We investigate time-irreversibility from the point of view of a single particle in Burgers turbulence. Inspired by the recent work for incompressible flows [Xu et al., PNAS 111.21 (2014) 7558], we analyze the evolution of the kinetic energy for fluid markers and use the fluctuations of the instantaneous power as a measure of time irreversibility. For short times, starting from a uniform distribution of markers, we find the scaling $\left<[E(t)-E(0)]^n\right>\propto t$ and $\left \propto \textrm{Re}^{n-1}$ for the power as a function of the Reynolds number. Both observations can be explained using the "flight-crash" model, suggested by Xu et al. Furthermore, we use a simple model for shocks which reproduces the moments of the energy difference including the pre-factor for $\left $. To complete the single particle picture for Burgers we compute the moments of the Lagrangian velocity difference and show that they are bi-fractal. This arises in a similar manner to the bi-fractality of Eulerian velocity differences. In the above setting time irreversibility is directly manifest as particles eventually end up in shocks. We additionally investigate time irreversibility in the long-time limit when all particles are located inside shocks and the Lagrangian velocity statistics are stationary. We find the same scalings for the power and energy differences as at short times and argue that this is also a consequence of rare "flight-crash" events related to shock collisions.

physics.flu-dyn↗

arXiv2014

New type of anomaly in turbulence

The turbulent energy flux through scales, $\barε$, remains constant and non vanishing in the limit of zero viscosity, which results in the fundamental anomaly of time irreversibility. It was considered straightforward to deduce from this the Lagrangian velocity anomaly, $\left< d u^2/dt\right>=-4 \barε$ at $t=0$, where $\vec{u}$ is the velocity difference of a pair of particles, initially separated by a fixed distance. In this letter we demonstrate that this derivation assumed first taking the limit $t \to 0$ and then $ν\to 0$, while the true anomaly requires taking viscosity to zero first. For compressible turbulence we find that the limits $t \to 0$ and $ν\to 0$ do not commute and the Lagrangian anomaly is completely altered: $\left< d u^2/dt\right>$ has different values forward and backward in time. We show that this new anomaly is related to the particles entering/exiting shocks forward/backward in time. For incompressible flows, on the other hand, we show that the limits can be interchanged and the Lagrangian anomaly is still induced by the flux law, apparently due to a homogeneous distribution of fluid particles at all times.

nlin.CD↗

arXiv2013

Stability of rapidly-rotating charged black holes in $AdS_5 \times S^5$

We study the stability of charged rotating black holes in a consistent truncation of Type $IIB$ Supergravity on $AdS_5 \times S^5$ that degenerate to extremal black holes with zero entropy. These black holes have scaling properties between charge and angular momentum similar to those of Fermi surface-like operators in a subsector of ${\cal N}=4$ SYM. By solving the equation of motion for a massless scalar field in this background, using matched asymptotic expansion followed by a numerical solution scheme, we are able to compute its Quasi-Normal modes, and analyze it's regime of (in)stability. We find that the black hole is unstable when its angular velocity with respect to the horizon exceeds 1 (in units of $1/l_{AdS}$). A study of the relevant thermodynamic Hessian reveals a local thermodynamic instability which occurs at the same region of parameter space. We comment on the endpoints of this instability.

hep-th↗

arXiv2013

What a single snapshot reveals about the future and the past of turbulent flow

We develop an analytic formalism and derive new exact relations that express the short-time dispersion of fluid particles via the single-time velocity correlation functions in homogeneous isotropic and incompressible turbulence. The formalism establishes a bridge between single-time Eulerian and long-time Lagrangian pictures of turbulent flows. In particular, we derive an exact formula for a short-term analog of the long-time Richardson law, and we identify a conservation law of turbulent dispersion which is true even in non-stationary turbulence.

nlin.CD↗

arXiv2012

Degenerate Rotating Black Holes, Chiral CFTs and Fermi Surfaces I - Analytic Results for Quasinormal Modes

In this work we discuss charged rotating black holes in $AdS_5 \times S^5$ that degenerate to extremal black holes with zero entropy. These black holes have scaling properties between charge and angular momentum similar to those of Fermi surface operators in a subsector of $\mathcal{N}=4$ SYM. We add a massless uncharged scalar to the five dimensional supergravity theory, such that it still forms a consistent truncation of the type IIB ten dimensional supergravity and analyze its quasinormal modes. Separating the equation of motion to a radial and angular part, we proceed to solve the radial equation using the asymptotic matching expansion method applied to a Heun equation with two nearby singularities. We use the continued fraction method for the angular Heun equation and obtain numerical results for the quasinormal modes. In the case of the supersymmetric black hole we present some analytic results for the decay rates of the scalar perturbations. The spectrum of quasinormal modes obtained is similar to that of a chiral 1+1 CFT, which is consistent with the conjectured field-theoretic dual. In addition, some of the modes can be found analytically.

hep-th↗