Related papers: Dynamical Fractional and Multifractal Fields
Motivated by the modeling of the spatial structure of the velocity field of three-dimensional turbulent flows, and the phenomenology of cascade phenomena, a linear dynamics has been recently proposed able to generate high velocity gradients…
Turbulent cascades characterize the transfer of energy injected by a random force at large scales towards the small scales. In hydrodynamic turbulence, when the Reynolds number is large, the velocity field of the fluid becomes irregular and…
This paper develops a fractional stochastic partial differential equation (SPDE) to model the evolution of a random tangent vector field on the unit sphere. The SPDE is governed by a fractional diffusion operator to model the L\'{e}vy-type…
A framework to establish response theory for a class of nonlinear stochastic partial differential equations (SPDEs) is provided. More specifically, it is shown that for a certain class of observables, the averages of those observables…
In this chapter we provide an introduction to fractional dissipative partial differential equations (PDEs) with a focus on trying to understand their dynamics. The class of PDEs we focus on are reaction-diffusion equations but we also…
Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and…
This paper presents a class of turbulence models written in terms of fractional partial differential equations (FPDEs) with stochastic loads. Every solution of these FPDE models is an incompressible velocity field and the distribution of…
Stochastic partial differential equations (SPDEs) represent a very active research field with numerous recent developments and breakthrough results. There are several well-established approaches and methods used to construct solutions for…
Multiplicative cascades have been introduced in turbulence to generate random or deterministic fields having intermittent values and long-range power-law correlations. Generally this is done using discrete construction rules leading to…
Stochastic dynamics has emerged as one of the key themes ranging from models in applications to theoretical foundations in mathematics. One class of stochastic dynamics problems that has received considerable attention recently are…
We propose a simple stochastic model of cascading transport in wave number space to clarify the origin of intermittent behavior of fully-developed fluid turbulence. In spite of lack of nonlinearity and viscosity the model gives non-Gaussian…
Many systems in physics, engineering, and biology exhibit multiscale stochastic dynamics, where low-dimensional slow variables evolve under the influence of high-dimensional fast processes. In practice, observations are often limited to a…
Obtaining accurate field statistics continues to be one of the major challenges in turbulence theory and modeling. From the various existing modeling approaches, multifractal models have been successful in capturing intermittency in…
We investigate the statistical properties, based on numerical simulations and analytical calculations, of a recently proposed stochastic model for the velocity field of an incompressible, homogeneous, isotropic and fully developed turbulent…
We develop numerical methods for reaction-diffusion systems based on the equations of fluctuating hydrodynamics (FHD). While the FHD formulation is formally described by stochastic partial differential equations (SPDEs), it becomes similar…
In this paper, we introduce a class of stochastic partial differential equations (SPDEs) with fractional time-derivatives, and study the $L_2$-theory of the equations. This class of SPDEs can be used to describe random effects on transport…
Geometrical random multiplicative cascade processes are often used to model positive-valued multifractal fields such as the energy dissipation in fully developed turbulence. We propose a dynamical generalization describing the energy…
In this article we expand and develop the authors' recent proposed methodology for efficient stochastic superparameterization (SP) algorithms for geophysical turbulence. Geophysical turbulence is characterized by significant intermittent…
This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial…
Periodically forced turbulence is used as a test case to evaluate the predictions of two-equation and multiple-scale turbulence models in unsteady flows. The limitations of the two-equation model are shown to originate in the basic…