arXiv subjects

Bruce R. Fabijonas

Publications and source records attributed to Bruce R. Fabijonas.

6 recordsLinked to original sources

arXiv2006

Intermittency via Self-Similarity -- An Analytic Example

Turbulence is known to show intermittency. That is, statistical properties vary with the length scale in a way not accounted for by statistical similarity where dimensionless ratios of moments are constant. Intermittency occurs even in the inertial range of isotropic turbulence, where physical intuition calls for a self-similar scale dependence. Perceived as a lack of overall scaling invariance, inertial range intermittency has become known as anomalous scaling. We present an analytic example demonstrating how anomalous scaling and self-similarity in the form of global scaling invariance can coexist within the same statistics. Whether we observe anomalous scaling or self-similarity depends on which variables we consider. Our example illustrates consequences of a symmetry, but is not meant as an intermittency model.

physics.flu-dyn↗

arXiv2006

A Theory of Inertial Range Similarity in Isotropic Turbulence

We consider equilibrium statistics for high Reynolds number isotropic turbulence in an incompressible flow driven by steady forcing at the largest scale. Motivated by shell model observations, we develop a similarity theory for the inertial range from clearly stated assumptions. In the right variables, the theory is scaling invariant, but in traditional variables it shows anomalous scaling. We obtain the underlying probability density function, the scaling exponents, and the coefficients for the structure functions. An inertial range length scale also emerges.

physics.flu-dyn↗

arXiv2005

Elliptic instability in the Lagrangian-averaged Euler-Boussinesq-alpha equations

We examine the effects of turbulence on elliptic instability of rotating stratified incompressible flows, in the context of the Lagragian-averaged Euler-Boussinesq-alpha, or \laeba, model of turbulence. We find that the \laeba model alters the instability in a variety of ways for fixed Rossby number and Brunt-Väisälä frequency. First, it alters the location of the instability domains in the $(γ,\cosθ)-$parameter plane, where $θ$ is the angle of incidence the Kelvin wave makes with the axis of rotation and $γ$ is the eccentricity of the elliptic flow, as well as the size of the associated Lyapunov exponent. Second, the model shrinks the width of one instability band while simultaneously increasing another. Third, the model introduces bands of unstable eccentric flows when the Kelvin wave is two-dimensional. We introduce two similarity variables--one is a ratio of the Brunt-Väisälä frequency to the model parameter $Υ_0 = 1+α^2β^2$, and the other is the ratio of the adjusted inverse Rossby number to the same model parameter. Here, $α$ is the turbulence correlation length, and $β$ is the Kelvin wave number. We show that by adjusting the Rossby number and Brunt-Väisälä frequency so that the similarity variables remain constant for a given value of $Υ_0$, turbulence has little effect on elliptic instability for small eccentricities $(γ\ll 1)$. For moderate and large eccentricities, however, we see drastic changes of the unstable Arnold tongues due to the \laeba model.

nlin.CD↗

arXiv2004

Euler-Poincare formulation and elliptic instability for nth-gradient fluids

The energy of an $n^{th}-$gradient fluid depends on its Eulerian velocity gradients of order $n$. A variational principle is introduced for the dynamics of $n^{th}-$gradient fluids and their properties are reviewed in the context of Noether's theorem. The stability properties of Craik-Criminale solutions for first and second gradient fluids are examined.

nlin.CD↗

arXiv2003

Multi-frequency Craik-Criminale solutions of the Navier-Stokes equations

An exact Craik-Criminale (CC) solution to the incompressible Navier-Stokes (NS) equations describes the instability of an elliptical columnar flow interacting with a single Kelvin wave. These CC solutions are extended to allow multi-harmonic Kelvin waves to interact with any exact ``base'' solution of the NS equations. The interaction is evaluated along an arbitrarily chosen flowline of the base solution, so exact nonlinear instability in this context is locally convective, rather than absolute. Furthermore, an iterative method called ``WKB-bootstrapping'' is introduced which successively adds Kelvin waves with incommensurate phases to the extended CC solutions. This is illustrated by constructing an extended CC solution consisting of several Kelvin waves with incommensurate phases interacting with an elliptical columnar flow.

nlin.CD↗

arXiv2002

Mean effects of turbulence on elliptic instability in fluids

Elliptic instability in fluids is discussed in the context of the Lagrangian-averaged Navier-Stokes-alpha (LANS$-α$) turbulence model. This model preserves the Craik-Criminale (CC) family of solutions consisting of a columnar eddy and a Kelvin wave. The LANS$-α$ model is shown to preserve the elliptic instability for the inviscid case. However, the model shifts the critical stability angle. This shift increases (resp. decreases) the maximum growth rate for long (resp. short) waves. It also introduces a band of stable CC solutions for short waves.

nlin.CD↗