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We develop and analyze a highly efficient, second-order time-marching scheme for infinite-dimensional nonlinear geophysical fluid models, designed to accurately approximate invariant measures-that is, the stationary statistical properties…
To improve models of the structure and evolution of stellar and planetary interiors, it is important to quantify transport by strongly stratified turbulence in low Prandtl number fluids. Recent numerical studies have shown evidence for…
In this paper, we propose a variationally consistent technique for decreasing the maximum eigenfrequencies of structural dynamics related finite element formulations. Our approach is based on adding a symmetric positive-definite term to the…
Attempts to disentangle shear-flow turbulence often focus on identifying relatively simple solutions, such as travelling waves or periodic orbits. We show, however, that capturing multiscale features requires considering states at least as…
This paper discusses the effect of sequential conflict resolution maneuvers of an infinite aircraft flow through a finite control volume. Aircraft flow models are utilized to simulate traffic flows and determine stability. Pseudo-random…
The temporal and spatiotemporal linear stability analyses of viscoelastic, subdiffusive, plane Poiseuille and Couette flows obeying the Fractional Upper Convected Maxwell (FUCM) equation in the limit of low to moderate Reynolds number…
The sequential nature of autoregressive next-token prediction imposes a fundamental speed limit on large language models. While continuous flow models offer a path to parallel generation, they traditionally demand expensive iterative…
In this stub article, we show that laminar quasi-periodically developed flow is characterized by velocity and pressure modes which decay exponentially along the main flow direction. As the amplitudes of these modes exhibit streamwise…
We propose a multiscale computational method for thin-layer flows of complex fluids, termed the synchronized molecular dynamics (SMD) method, which directly couples local molecular dynamics (MD) simulations with a macroscopic lubrication…
We present an explicit scheme for a two-dimensional multilayer shallow water model with density stratification, for general meshes and collocated variables. The proposed strategy is based on a regularized model where the transport velocity…
This paper develops a spatial input-output approach to investigate the dynamics of a turbulent boundary layer subject to a localized single frequency excitation. This method uses one-way spatial integration to reformulate the problem in…
Resolvent analysis is a powerful tool for modeling and analyzing turbulent flows and in particular provides an approximation of coherent flow structures. Despite recent algorithmic advances, computing resolvent modes for flows with more…
Low Reynolds number turbulence in wall-bounded shear flows \emph{en route} to laminar flow takes the form of oblique, spatially-intermittent turbulent structures. In plane Couette flow, these emerge from uniform turbulence via a…
It is well-known that stable and unstable manifolds strongly influence fluid motion in unsteady flows. These emanate from hyperbolic trajectories, with the structures moving nonautonomously in time. The local directions of emanation at each…
Cross-streamline non-inertial migration of a vesicle in a bounded Poiseuille flow is investigated experimentally and numerically. The combined effects of the walls and of the curvature of the velocity profile induce a movement towards the…
This paper concerns spectral instability of shear flows in the incompressible Navier-Stokes equations with sufficiently large Reynolds number: $R\to \infty$. It is well-documented in the physical literature, going back to Heisenberg, C.C.…
A well-developed method to induce mixing on microscopic scales is to exploit flows generated by steady streaming. Steady streaming is a classical fluid dynamics phenomenon whereby a time-periodic forcing in the bulk or along a boundary is…
Self-consistent chaotic transport is studied in a Hamiltonian mean-field model. The model provides a simplified description of transport in marginally stable systems including vorticity mixing in strong shear flows and electron dynamics in…
This work presents a model reduction approach for problems with coherent structures that propagate over time such as convection-dominated flows and wave-type phenomena. Traditional model reduction methods have difficulties with these…
We propose a new class of univariate nonstationary time series models, using the framework of modulated time series, which is appropriate for the analysis of rapidly-evolving time series as well as time series observations with missing…