Self-similarity and vanishing diffusion in fluvial landscapes.

Complex topographies exhibit universal properties when fluvial erosion dominates landscape evolution over other geomorphological processes. Similarly, we show that the solutions of a minimalist landscape evolution model display invariant behavior as the impact of soil diffusion diminishes compared to fluvial erosion at the landscape scale, yielding complete self-similarity with respect to a dimensionless channelization index. Approaching its zero limit, soil diffusion becomes confined to a region of vanishing area and large concavity or convexity, corresponding to the locus of the ridge and valley network.

Self-regularization in turbulence from the Kolmogorov 4/5-law and alignment.

A defining feature of three-dimensional hydrodynamic turbulence is that the rate of energy dissipation is bounded away from zero as viscosity is decreased (Reynolds number increased). This phenomenon-anomalous dissipation-is sometimes called the 'zeroth law of turbulence' as it underpins many celebrated theoretical predictions. Another robust feature observed in turbulence is that velocity structure functions [Formula: see text] exhibit persistent power-law scaling in the inertial range, namely [Formula: see text] for exponents [Formula: see text] over an ever increasing (with Reynolds) range of scales.

Bounds on heat flux for Rayleigh-Bénard convection between Navier-slip fixed-temperature boundaries.

We study two-dimensional Rayleigh-Bénard convection with Navier-slip, fixed temperature boundary conditions and establish bounds on the Nusselt number. As the slip-length varies with Rayleigh number [Formula: see text], this estimate interpolates between the Whitehead-Doering bound by [Formula: see text] for free-slip conditions (Whitehead & Doering. 2011 Ultimate state of two-dimensional Rayleigh-Bénard convection between free-slip fixed-temperature boundaries.

The statistical geometry of material loops in turbulence.

Material elements - which are lines, surfaces, or volumes behaving as passive, non-diffusive markers - provide an inherently geometric window into the intricate dynamics of chaotic flows. Their stretching and folding dynamics has immediate implications for mixing in the oceans or the atmosphere, as well as the emergence of self-sustained dynamos in astrophysical settings. Here, we uncover robust statistical properties of an ensemble of material loops in a turbulent environment.

Inertial-Range Reconnection in Magnetohydrodynamic Turbulence and in the Solar Wind.

In situ spacecraft data on the solar wind show events identified as magnetic reconnection with wide outflows and extended "X lines," 10(3)-10(4) times ion scales. To understand the role of turbulence at these scales, we make a case study of an inertial-range reconnection event in a magnetohydrodynamic simulation. We observe stochastic wandering of field lines in space, breakdown of standard magnetic flux freezing due to Richardson dispersion, and a broadened reconnection zone containing many current sheets.

Asymptotic results for backwards two-particle dispersion in a turbulent flow.

We derive an exact equation governing two-particle backwards mean-squared dispersion for both deterministic and stochastic tracer particles in turbulent flows. For the deterministic trajectories, we probe the consequences of our formula for short times and arrive at approximate expressions for the mean-squared dispersion which involve second order structure functions of the velocity and acceleration fields. For the stochastic trajectories, we analytically compute an exact t3 contribution to the squared separation of stochastic paths.