We develop an optimization-based approach for additive decomposition and reconnection of algebraic problems arising from discretization of partial differential equations (PDEs). Application to a scalar advection-diffusion PDE illustrates the new approach. In particular, we obtain a robust iterative solver for advection-dominated problems using standard multi-level solvers for the Poisson equation.

We show that in a reaction diffusion system on a two-dimensional substrate with advection in the confined direction, the drift (advection) induced instability occurs through a Hopf bifurcation, which can become a double Hopf bifurcation. The box size in the direction of the drift is a vital parameter. Our analysis involves reduction to a low dimensional dynamical system and constructing amplitu...

Simulations of vortex tube dynamics reveal that the non-Gaussian nature of turbulent fluctuation originates in the effect of random advection. A similar non-Gaussian distribution is found numerically in a simplified statistical model of random advection. An analytical solution is obtained in the mean-field case.

5 The authors analyze the column-integrated moist static energy budget over the region of 6 the tropical Indian ocean covered by the sounding array during the CINDY/DYNAMO field 7 experiment in late 2011. The analysis is performed using data from the the sounding array 8 complemented by the Objectively Analyzed air-sea Fluxes for the Global Oceans (OAflux) 9 and Clouds and the Earth’s Radiant E...

This note addresses the subject of advection around the theme of applying Characteristic Maps as a method of constructing solvers. Typically the accuracy of solvers is characterized as an asymptotic function of a short time step, short usually defined by restricting the value of the CFL parameter. Within the range of the CFL limit the asymptotic function is expressed as a formula in terms of a ...

Aircraft, radiosonde, surface-flux, and boundary-layer wind profiler data from the Cooperative Atmosphere Surface Exchange Study’s 1997 field project, CASES-97, are combined with synoptic data to study the evolution of the vertically-averaged mixed-layer potential temperature [ ] and mixing-ratio [Q] on three nearly-cloudless days from 1000 CST to 1200 CST (local noon is approximately 1230 CST)...