Related papers: Estimating the Kinetic Energy Spectrum from the Se…
An analytical solution of the perturbed equations is obtained, which exists in all ergodic models of collisionless spherical stellar systems with a single length parameter. This solution corresponds to variations of this parameter, i.e.,…
Most time series observed in practice exhibit time-varying trend (first-order) and autocovariance (second-order) behaviour. Differencing is a commonly-used technique to remove the trend in such series, in order to estimate the time-varying…
The porous medium equation (PME) is a typical nonlinear degenerate parabolic equation. An energetic variational approach has been studied in a recent work [6], in which the trajectory equation is obtained, and a few first order accurate…
Recent work has given a systematic way for studying the kinetics of classical weakly interacting waves beyond leading order, having analogies with renormalization in quantum field theory. An important context is weak wave turbulence,…
Coherent structures in two-dimensional Navier-Stokes turbulence are ubiquitously observed in nature, experiments and numerical simulations. The present study conducts a comparison between several structure detection schemes based on the…
The ensemble Kalman inversion (EKI) for the solution of Bayesian inverse problems of type $y = A u +\varepsilon$, with $u$ being an unknown parameter, $y$ a given datum, and $\varepsilon$ measurement noise, is a powerful tool usually…
In wall-bounded turbulence, a multitude of coexisting turbulence structures form the streamwise velocity energy spectrum from the viscosity- to the inertia-dominated range of scales. Definite scaling-trends for streamwise spectra have…
A prediction model for the turbulent kinetic energy (TKE) induced by tidal-currents is proposed as a function of the barotropic velocity only, along with a robust method evaluating the different parameters involved using Acoustic Doppler…
Equations that follow from the Navier-Stokes equation and incompressibility but with no other approximations are called "exact" here. Exact equations relating 2nd and 3rd-order structure functions are obtained, as is an exact…
Recently, a new connection between density functional theory and kinetic theory has been proposed. In particular, it was shown that the Kohn-Sham (KS) equations can be reformulated as a macroscopic limit of the steady-state solution of a…
Accurate estimation of spatial derivatives from discrete and noisy data is central to scientific machine learning and numerical solutions of PDEs. We extend kinetic-based regularization (KBR), a localized multidimensional kernel regression…
A time-dependent approach for the kinetic energy release (KER) spectrum is developed for a fragmentation of a diatomic molecule after an electronic decay process, e.g. Auger process. It allows one to simulate the time-resolved spectra and…
Stratification can cause turbulence spectra to deviate from Kolmogorov's isotropic -5/3 power-law scaling in the universal equilibrium range at high Reynolds numbers. However, a consensus has not been reached with regard to the exact shape…
Turbulent properties of the quiet Sun represent the basic state of surface conditions, and a background for various processes of solar activity. Therefore understanding of properties and dynamics of this `basic' state is important for…
Variety of statistically steady energy spectra in elastic wave turbulence have been reported in numerical simulations, experiments, and theoretical studies. Focusing on the energy levels of the system, we have performed direct numerical…
The Ensemble Kalman Filter method can be used as an iterative numerical scheme for parameter identification or nonlinear filtering problems. We study the limit of infinitely large ensemble size and derive the corresponding mean-field limit…
A generalization of the kinetic equation is proposed for explaining observed shapes of wind wave spectra. The approach allows to fix a critical uncertainty in modeling wind wave spectra using a condition of equilibrium of nonlinear transfer…
An analytical framework for turbulent channel flow is developed based on the Alexeev hydrodynamic equations, focusing on the coupled behavior of streamwise and transverse velocity components. The mean streamwise velocity is represented as a…
Energy dissipation rate is an important parameter for nearly every experiment on turbulent flow. Mathematically precise relationships between energy dissipation rate and other measurable statistics for the case of anisotropic turbulence are…
In this work we explore the fidelity of numerical approximations to the analytic spectra of hyperbolic partial differential equation systems with variable coefficients. We are particularly interested in the ability of discrete methods to…