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- W4310419225 abstract "Let $mathbb{I!H}subsetmathbb{R}^{3}$, with ${Vol}(mathbb{I!H})sim L^{3}$, contain a fluid of viscosity $nu$ and velocity $mathrm{U}_{i}(x,t)$ with $(x,t)inmathbb{I!H}times[0,infty)$, satisfying the Navier-Stokes equations with some boundary conditions on $partialmathbb{I!H}$ and evolving from initial Cauchy data. Now let $mathscr{B}(x)$ be a Gaussian random field defined for all $xinmathbb{I!H}$ with expectation $mathsf{E}langlemathscr{B}(x)rangle=0$, and a Bargmann-Fock binary correlation $mathsf{E}biglanglemathscr{B}(x)otimes mathscr{B}({y})bigrangle=mathsf{C}exp(-|{x}-{y}|^{2}lambda^{-2})$ with $lambdale {L}$. Define a volume-averaged Reynolds number $mathbf{Re}(mathbb{I!H},t) =(|Vol(mathbb{I!H})|^{-1}int_{mathbb{I!H}}|mathrm{U}_{i}(x,t)|dmu({x}){L}/nu$. The critical Reynolds number is $mathbf{Re}_{c}(mathbb{I!H})$ so that turbulence evolves within $mathbb{I!H}$ for $t$ such that $mathbf{Re}(mathbb{I!H},t)>mathbf{Re}_{c}(mathbb{I!H})$. Let $psi(|mathbf{Re}(mathbb{I!H},t)-mathbf{Re}_{c}(mathbb{I!H})|)$ be an arbitrary monotone-increasing functional. The turbulent flow evolving within $mathbb{I!H}$ is described by the random field $mathscr{U}_{i}(x,t)$ via a 'mixing' ansatz $mathscr{U}_{i}(x,t)=mathrm{U}_{i}(x,t)+betamathrm{U}_{i}(x,t) biglbracepsi(|mathbf{Re}(mathbb{I!H},t)-mathbf{Re}_{c}(mathbb{I!H})|)bigrbrace mathbb{S}_{mathfrak{C}}[mathbf{Re}(mathbb{I!H},t)big]mathscr{B}(x)$ where ${beta}ge 1$ is a constant and $mathbb{S}_{mathfrak{C}}[mathbf{Re}(mathbb{I!H},t)]$ an indicator function. The flow grows increasingly random if $mathbf{Re}(mathbb{I!H},t)$ increases with $t$ so that this is a 'control parameter'. The turbulent flow $mathscr{U}_{i}(x,t)$ is a solution of stochastically averaged N-S equations. Reynolds-type velocity correlations are estimated." @default.
- W4310419225 created "2022-12-10" @default.
- W4310419225 creator A5024292880 @default.
- W4310419225 date "2022-11-27" @default.
- W4310419225 modified "2023-10-16" @default.
- W4310419225 title "A Turbulent Fluid Mechanics via Nonlinear Mixing of Smooth Flows with Bargmann-Fock Random Fields: Stochastically Averaged Navier-Stokes Equations and Velocity Correlations" @default.
- W4310419225 doi "https://doi.org/10.48550/arxiv.2211.14925" @default.
- W4310419225 hasPublicationYear "2022" @default.
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