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We study solutions to the Navier-Stokes equations in the class $L^\infty_t C^\alpha_x$. Landau and Lifshitz [LL87] predicted that the Eulerian and Lagrangian temporal structure functions for turbulence exhibit $1/3$ and $1/2$ scaling laws,…
We investigate numerically the model proposed in Sahoo et al [Phys. Rev. Lett. 118, 164501, (2017)] where a parameter $\lambda$ is introduced in the Navier-Stokes equations such that the weight of homochiral to heterochiral interactions is…
Liquid droplets sliding along solid surfaces are a frequently observed phenomenon in nature, e.g., raindrops on a leaf, and in everyday situations, e.g., drops of water in a drinking glass. To model this situation, we use a phase field…
We consider the numerical approximations for a phase field model consisting of incompressible Navier--Stokes equations with a generalized Navier boundary condition, and the Cahn-Hilliard equation with a dynamic moving contact line boundary…
Vertical thermal convection system exhibits weak turbulence and spatio-temporally chaotic behaviour. In this system, we report seven equilibria and 26 periodic orbits, all new and linearly unstable. These orbits, together with four…
Landfall of a tropical cyclone is the event when it moves over the land after crossing the coast of the ocean. It is important to know the characteristics of the landfall in terms of location and time, well advance in time to take…
In this article, we design and analyze an arbitrary-order stabilized finite element method to approximate the unique continuation problem for laminar steady flow described by the linearized incompressible Navier--Stokes equation. We derive…
Tropical cyclone (TC) intensity forecasts are issued by human forecasters who evaluate spatio-temporal observations (e.g., satellite imagery) and model output (e.g., numerical weather prediction, statistical models) to produce forecasts…
Precipitation from tropical cyclones (TCs) can cause disasters such as flooding, mudslides, and landslides. Predicting such precipitation in advance is crucial, giving people time to prepare and defend against these precipitation-induced…
This paper shows how particle hopping models fit into the context of traffic flow theory. Connections between fluid-dynamical traffic flow models, which derive from the Navier-Stokes-equations, and particle hopping models are shown. In some…
Penalty methods relax the incompressibility condition and uncouple velocity and pressure. Experience with them indicates that the velocity error is sensitive to the choice of penalty parameter $\epsilon$. So far, there is no effective \'a…
In the present work we discuss a possible application of Navier-Stokes-based models to the quantitative description of the circulation of nervous impulses throughout the nervous system. In previous works we have shown that the discharge…
We use a simple yet Earth-like atmospheric model to propose a new framework for understanding the mathematics of blocking events. Analysing error growth rates along a very long model trajectory, we show that blockings are associated with…
Accurate prediction of tropical cyclones remains a major challenge for both numerical weather prediction and emerging artificial intelligence weather prediction systems. While recent global AI models have demonstrated strong skill in…
Equations that follow from the Navier-Stokes equation and incompressibility but with no other approximations are called "exact" here. Exact equations relating 2nd and 3rd-order structure functions are obtained, as is an exact…
Lyman-$\alpha$ transits have been detected from several nearby exoplanets and are one of our best insights into the atmospheric escape process. However, due to ISM absorption, we typically only observe the transit signature in the…
We investigate the behavior of dynamic shape design problems for fluid flow at large time horizon. In particular, we shall compare the shape solutions of a dynamic shape optimization problem with that of a stationary problem and show that…
An obstacle is immersed in an externally driven 2D Stokes or Navier-Stokes fluid. We study the self-equilibration conditions for that obstacle under steady state assumptions on the flow. We then seek to optimize the translational and/or…
The flow of a viscous fluid is perturbed by its internal friction which generates heat and leads to a small temperature change. This does not occur for an ideal fluid. We would like to resolve this picture as a function of the dynamical…
We establish pointwise decay estimates for the velocity field of a steady two-dimensional Stokes flow around a rotating body via a new approach rather than analysis adopted in the previous literature. The novelty is to analyze the singular…