Related papers: A universal equation for calculating the energy gr…
In this paper, the physics of flow instability and turbulent transition in shear flows is studied by analyzing the energy variation of fluid particles under the interaction of base flow with a disturbance. For the first time, a model…
The energy method, also known as the Reynolds-Orr equation, is widely utilized in predicting the unconditional stability threshold of shear flows owing to the zero contribution of nonlinear terms to the time derivative of perturbation…
A new universal theory for flow instability and turbulent transition is proposed in this study. Flow instability and turbulence transition have been challenging subjects for fluid dynamics for a century. The critical condition of turbulent…
Based on the energy gradient method, criteria for turbulent transition are proposed for pressure driven flow and shear driven flow, respectively. For pressure driven flow, the necessary and sufficient condition for turbulent transition is…
Flow instability and turbulent transition can be well explained using a new proposed theory--Energy gradient theory [1]. In this theory, the stability of a flow depends on the relative magnitude of energy gradient in streamwise direction…
The energy gradient theory is used to study the instability of Taylor-Couette flow between concentric rotating cylinders. This theory has been proposed in our previous works. In our previous studies, the energy gradient theory was…
We present rigorous estimates for some physical quantities related to turbulent and non-turbulent channel flows driven by a uniform pressure gradient. Such results are based on the concept of stationary statistical solution, which is…
This paper provides a pedagogical introduction to the classical nonlinear stability analysis of the plane Poiseuille and Couette flows. The whole procedure is kept as simple as possible by presenting all the logical steps involved in the…
Scale-space energy density function, $E(\mathbf{x}, \mathbf{r})$, is defined as the derivative of the two-point velocity correlation. The function E describes the turbulent kinetic energy density of scale r at a location x and can be…
This paper addresses the integral energy fluxes in natural and controlled turbulent channel flows, where active skin-friction drag reduction techniques allow a more efficient use of the available power. We study whether the increased…
We present a new rigorous method for estimating statistical quantities in fluid dynamics such as the (average) energy dissipation rate directly from the equations of motion. The method is tested on shear flow, channel flow,…
An approximate method to compute mean velocity profiles in turbulent flows is developed. This approach is based on the equation connecting the Reynolds stress and mean velocity. By using the measured values of pressure drop and average…
The new proposed "energy gradient theory," which physically explains the phenomena of flow instability and turbulent transition in shear flows and has been shown to be valid for parallel flows, is extended to curved flows in this study.…
Transition to turbulence is due to the instability of a laminar flow subject to a disturbance. This complicated problem can be explained using a new proposed energy gradient theory in our previous study. This theory is extended to the…
The flow of the laminar boundary layer on a flat plate is studied with simulation of Navier-Stokes equations. The mechanisms of flow instability at external edge of the boundary layer and near the wall are analyzed using the energy gradient…
The competition between the drive and stabilization of plasma microinstabilities by sheared flow is investigated, focusing on the ion temperature gradient mode. Using a twisting mode representation in sheared slab geometry, the…
The possibility to derive an equation for the mean velocity field in turbulent flow by using classical statistical mechanics is investigated. An application of projection operator technique available in the literature is used for this…
Using the Lagrangian transport of momentum, the Reynolds shear stress can be expressed in terms of basic turbulence parameters. In this view, the Reynolds stress gradient represents the lateral transport of streamwise momentum, balanced by…
We introduce and implement a method to compute stationary states of nonlinear Schr\''odinger equations on metric graphs. Stationary states are obtained as local minimizers of the nonlinear Schr\''odinger energy at fixed mass. Our method is…
In this paper, we investigate the relations between global and local energy transfers in a turbulent von K\'arm\'an flow. The goal is to understand how and where energy is dissipated in such a flow and to reconstruct the energy cycle in an…