Related papers: Direct Statistical Simulation Using Generalised Cu…
It is widely believed that statistical closure theories for dynamical systems provide statistics equivalent to those of the governing dynamical equations from which the former are derived. Here, we demonstrate counterexamples in the context…
We examine the effectiveness of the Generalised Quasilinear (GQL) Approximation introduced by Marston et al (2016). This approximation splits the variables into large and small scales in directions where there is a translational symmetry…
We present a Direct Statistical Simulation (DSS) of jet formation on a \beta-plane, solving for the statistics of a fluid flow via an expansion in cumulants. Here we compare an expansion truncated at second order (CE2) to statistics…
Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. In this paper we present a generalization of quasilinear theory to include dynamic mode…
We consider direct statistical simulation (DSS) of a paradigm system of convection interacting with mean flows. In the Busse Annulus model zonal jets are generated through the interaction of convectively driven turbulence and rotation;…
We review progress that has been made in utilizing one form of Direct Statistical Simulation (DSS) to describe geophysical and astrophysical flows that are anisotropic and inhomogeneous. We first explain the approach, which is based upon a…
In this paper, we study estimation of nonlinear models with cross sectional data using two-step generalized estimating equations (GEE) in the quasi-maximum likelihood estimation (QMLE) framework. In the interest of improving efficiency, we…
We study generalised quasilinear (GQL) approximations applied to turbulent plane Couette flow. The GQL framework is explored in conjunction with a Galerkin reduced-order model (ROM) recently developed by Cavalieri & Nogueira (Phys. Rev.…
A generalised quasilinear (GQL) approximation (Marston \emph{et al.}, \emph{Phys. Rev. Lett.}, vol. 116, 104502, 2016) is applied to turbulent channel flow at $Re_\tau \simeq 1700$ ($Re_\tau$ is the friction Reynolds number), with emphasis…
Large-scale atmospheric flows may not be so nonlinear as to preclude their statistical description by systematic expansions in cumulants. I extend previous work by examining a two-layer baroclinic model of the general circulation. The fixed…
The existence of generalized steady states (GSSs) in nonlinear mechanical systems under moderate temporally aperiodic forcing has only been shown recently. Here we derive systematic expansions for such GSSs and construct a numerical…
The general pressure equation (GPE) is a new method proposed recently by Toutant (J. Comput. Phys., 374:822-842 (2018)) for incompressible flow simulation. It circumvents the Poisson equation for the pressure and performs better than the…
Continuing from Part 1 (Hern\'andez \emph{et al.}, \emph{arXiv:2108.12395}, 2021), a generalized quasilinear (GQL) approximation is studied in turbulent channel flow using a flow decomposition defined with spanwise Fourier modes: the flow…
Zonal flows have been observed to appear spontaneously from turbulence in a number of physical settings. A complete theory for their behavior is still lacking. Recently, a number of studies have investigated the dynamics of zonal flows…
Data assimilation (DA) integrates observational data with numerical models to improve the prediction of complex physical systems. However, traditional DA methods often struggle with nonlinear dynamics and multi-scale variability,…
Solutions to many partial differential equations satisfy certain bounds or constraints. For example, the density and pressure are positive for equations of fluid dynamics, and in the relativistic case the fluid velocity is upper bounded by…
Direct statistical simulation (DSS) of nonlinear dynamical systems bypasses the traditional route of accumulating statistics by lengthy direct numerical simulations (DNS) by solving the equations that govern the statistics themselves. DSS…
Hamiltonians of a wide-spread class of strongly coupled quantum system models are expressed as nonlinear functions of $sl(2)$ generators. It enables us to use the $sl(2)$ formalism, in particular, $sl(2)$ generalized coherent states (GCS)…
In recent years, coupled with traditional turbulence models, the second-order gas-kinetic scheme (GKS) has been used in the turbulent flow simulations. At the same time, high-order GKS has been developed, such as the two-stage fourth-order…
The direct Gaussian copula model with discrete marginal distributions is an appealing data-analytic tool but poses difficult computational challenges due to its intractable likelihood. A number of approximations/surrogates for the…