相关论文: Resolvent estimates for 2 dimensional perturbation…

In this paper, we consider a resolvent problem arising from the $Q$-tensor model for liquid crystal flows in the half-space. Our purpose is to show the $\mathcal{R}$-boundedness for the solution operator families of the resolvent problem…

Performing global resolvent analysis for high-Reynolds-number turbulent flow calls for the handling of a large discrete operator. Even though such large operator is required in the analysis, most applications of resolvent analysis extracts…

We consider estimation and control of the cylinder wake at low Reynolds numbers. A particular focus is on the development of efficient numerical algorithms to design optimal linear feedback controllers when there are many inputs…

In this paper, we investigate the long-time behavior of solutions to the two-dimensional Navier-Stokes equations with initial data evolving under the influence of the planar Couette flow. We focus on general perturbations, which may be…

We develop a method to estimate space-time flow statistics from a limited set of known data. While previous work has focused on modeling spatial or temporal statistics independently, space-time statistics carry fundamental information about…

Upon decreasing the Reynolds number, plane Couette flow first forms alternately turbulent and laminar oblique bands out of featureless turbulence below some upper threshold R_t. These bands exist down to a global stability threshold R_g…

We propose a novel framework for approximating the statistical properties of turbulent flows by combining variational methods for the search of unstable periodic orbits with resolvent analysis for dimensionality reduction. Traditional…

Numerical simulations of wall-turbulence using the restricted nonlinear (RNL) model generate realistic mean velocity profiles in plane Couette and channel flow at low Reynolds numbers. The results are less accurate at higher Re, and while a…

Equilibrium, traveling wave, and periodic orbit solutions of pipe, channel, and plane Couette flows can now be computed precisely at Reynolds numbers above the onset of turbulence. These invariant solutions capture the complex dynamics of…

Linear stability and the non-modal transient energy growth in compressible plane Couette flow are investigated for two prototype mean flows: (a) the {\it uniform shear} flow with constant viscosity, and (b) the {\it non-uniform shear} flow…

This paper introduces a new operator relevant to input-output analysis of flows in a statistically steady regime far from the steady base flow: the mean resolvent $\mathbf{R}_0$. It is defined as the operator predicting, in the frequency…

In a dissipative system, there exists the (global) attractor which has finite fractal dimensions. The flow on the attractor can be parametrized by a finite number of parameters (Temmam 1987). Using machine learning we demonstrate how to…

A reduced description of shear flows consistent with the Reynolds number scaling of lower-branch exact coherent states in plane Couette flow [J. Wang et al., Phys. Rev. Lett. 98, 204501 (2007)] is constructed. Exact time-independent…

A resolvent-based methodology is employed to obtain spatio--temporal estimates of turbulent pipe flow from probe measurements of wall shear-stress fluctuations. Direct numerical simulations (DNS) and large-eddy simulations (LES) of…

We prove operator-norm resolvent convergence estimates for one-dimensional periodic differential operators with rapidly oscillating coefficients in the non-uniformly elliptic high-contrast setting, which has been out of reach of the…

Plane Couette flow at Re=1200 (based on the channel half-height and half the velocity difference between the top and bottom plates) is investigated with a spatial domain designed to retain only two spanwise integral length scales. In this…

A modelling framework based on the resolvent analysis and machine learning is proposed to predict the turbulent energy in incompressible channel flows. In the framework, the optimal resolvent response modes are selected as the basis…

The ability of linear stochastic response analysis to estimate coherent motions is investigated in turbulent channel flow at friction Reynolds number Re$_\tau$ = 1007. The analysis is performed for spatial scales characteristic of…

A novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow…

Sommerfeld paradox (turbulence paradox) roughly says that mathematically the Couette linear shear flow is linearly stable for all values of the Reynolds number, but experimentally transition from the linear shear to turbulence occurs under…