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Many geophysical and astrophysical phenomena are driven by turbulent fluid dynamics, containing behaviors separated by tens of orders of magnitude in scale. While direct simulations have made large strides toward understanding geophysical…
Implicit time-stepping for advection is applied locally in space and time where Courant numbers are large, but standard explicit time-stepping is used for the remaining solution which is typically the majority. This adaptively implicit…
The propagation of traffic congestion along roads is a commonplace nonlinear phenomenon. When many roads are connected in a network, congestion can spill from one road to others as drivers queue to enter a congested road, creating further…
A nonlinear two-fluid stochastic hydrodynamical description of velocity and concentration fluctuations in sedimenting suspensions is constructed, and analyzed using self-consistent (SC) and renormalization group (RG) methods. The advection…
We explore the fundamental flow structure of inclined gravity currents with direct numerical simulations. A velocity maximum naturally divides the current into inner and outer shear layers, which are weakly coupled by exchange of momentum…
We establish the local and global well-posedness of strong solutions to the two- and three-dimensional anelastic equations of stratified viscous flows. In this model, the interaction of the density profile with the velocity field is taken…
The elastohydrodynamics of slender bodies in a viscous fluid have long been the source of theoretical investigation, being pertinent to the microscale world of ciliates and flagellates as well as to biological and engineered active matter…
A new rotational flamelet model with inward swirling flow through a stretched vortex tube is developed for sub-grid modeling to be coupled with the resolved flow for turbulent combustion. The model has critical new features compared to…
Existing hydrodynamic models of charged fluids consider any external electric field acting on the fluid as either first order in the hydrodynamic derivative expansion and completely arbitrary or zeroth order but constrained by the fluid's…
Recent machine-learning approaches to weather forecasting often employ a monolithic architecture in which distinct physical mechanisms-advection (long-range transport), diffusion-like mixing, thermodynamic processes, and forcing-are…
Even the most simplified models of falling and gliding bodies exhibit rich nonlinear dynamical behavior. Taking a global view of the dynamics of one such model, we find an attracting invariant manifold that acts as the dominant organizing…
We develop a purely hydrodynamic formalism to describe collisional, anisotropic instabilities in a relativistic plasma, that are usually described with kinetic theory tools. Our main motivation is the fact that coarse-grained models of high…
The aim of this paper is to propose a 2D computational algorithm for modeling of the trigger and the propagation of shallow landslides caused by rainfall. We used a Molecular Dynamics (MD) inspired model, similar to discrete element method…
Sediment transport over wave-induced ripples is a very complex phenomenon where available models fail to provide accurate predictions. For coastal engineering applications, the 1-DV advection-diffusion equation could be used with an…
In these lectures, a variety of non-equilibrium transport phenomena are introduced that all involve, in some way, elastic manifolds being driven through random media. A simple class of models is studied focussing on the behavior near to the…
The collision-free velocity model is a microscopic pedestrian model, which despite its simplicity, reproduces fairly well several self-organization phenomena in pedestrian dynamics. The model consists of two components: a direction…
We extend previous conduction-based analogies between ice growth in a lake and cosmological expansion by incorporating buoyancy-driven heat transport. Reformulating the Stefan problem with both conductive and convective fluxes yields an…
Drop impact experiments allow the modelling of a wide variety of natural processes, from raindrop impacts to planetary impact craters. In particular, interpreting the consequences of planetary impacts requires an accurate description of the…
Many immersed boundary methods solve for surface stresses that impose the velocity boundary conditions on an immersed body. These surface stresses may contain spurious oscillations that make them ill-suited for representing the physical…
Artificial viscosity is traditionally interpreted as a positive, spatially acting regularization introduced to stabilize numerical discretizations of hyperbolic conservation laws. In this work, we report a data-driven discovery that…