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Register a new userStatistical theory of reversals in two-dimensional confined turbulent flows
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It is shown that the Truncated Euler Equations, i.e. a finite set of ordinary differential equations for the amplitude of the large-scale modes, can correctly describe the complex transitional dynamics that occur within the turbulent regime of a confined 2D Navier-Stokes flow with bottom friction and a spatially periodic forcing. In particular, the random reversals of the large scale circulation on the turbulent background involve bifurcations of the probability distribution function of the large-scale circulation velocity that are described by the related microcanonical distribution which displays transitions from gaussian to bimodal and broken ergodicity. A minimal 13-mode model reproduces these results.
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We use momentum transfer arguments to predict the friction factor $f$ in two-dimensional turbulent soap-film flows with rough boundaries (an analogue of three-dimensional pipe flow) as a function of Reynolds number Re and roughness $r$, considering separately the inverse energy cascade and the forward enstrophy cascade. At intermediate Re, we predict a Blasius-like friction factor scaling of $fproptotextrm{Re}^{-1/2}$ in flows dominated by the enstrophy cascade, distinct from the energy cascade scaling of $textrm{Re}^{-1/4}$. For large Re, $f sim r$ in the enstrophy-dominated case. We use conformal map techniques to perform direct numerical simulations that are in satisfactory agreement with theory, and exhibit data collapse scaling of roughness-induced criticality, previously shown to arise in the 3D pipe data of Nikuradse.
Starting from the action-angle variables and using a standard asymptotic expansion, here we present a new derivation of the Wave Kinetic Equation for resonant process of the type $2leftrightarrow 2$. Despite not offering new physical results and despite not being more rigorous than others, our procedure has the merit of being straightforward; it allows for a direct control of the random phase and random amplitude hypothesis of the initial wave field. We show that the Wave Kinetic Equation can be derived assuming only initial random phases. The random amplitude approximation has to be taken only at the end, after taking the weak nonlinearity and large box limits. This is because the $delta$-function over frequencies contains the amplitude-dependent nonlinear correction which should be dropped before the random amplitude approximation applies. If $epsilon$ is the small parameter in front of the anharmonic part of the Hamiltonian, the time scale associated with the Wave Kinetic equation is shown to be $1/epsilon^2$. We give evidence that random phase and amplitude hypotheses persist up to a time of the order $1/epsilon$.
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The shear-induced reversible self-organization of active rotors into strip-like aggregates is studied by carrying out computational simulations. The numerical and theoretical results demonstrate that the average width of the strips is linearly dependent on the relative intensity of active torque to the shear rate of the imposed flow. In the particle strips, edge flows are observed to be against the imposed flow and play a crucial role to maintain the stability of the strips. Additionally, the rheological result shows the dependence of shear and rotational viscosities on the active torque direction and the oddness of normal stress response. By exhibiting a novel collective phenomenon of active rotors, our study paves the way of understanding the chiral active matter.
A detailed comparison between data from experimental measurements and numerical simulations of Lagrangian velocity structure functions in turbulence is presented. By integrating information from experiments and numerics, a quantitative understanding of the velocity scaling properties over a wide range of time scales and Reynolds numbers is achieved. The local scaling properties of the Lagrangian velocity increments for the experimental and numerical data are in good quantitative agreement for all time lags. The degree of intermittency changes when measured close to the Kolmogorov time scales or at larger time lags. This study resolves apparent disagreements between experiment and numerics.
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