An exponential solution to the thermocline equations is scaled and calibrated for the intermediate circulation in middle latitudes of the open ocean in accordance with the scaling and results of the more complete numerical models of Bryan and Cox. Evaluation of the average potential vorticity for a number of stations is a main feature of the calibration method. The results of tests on the calib...

We study convection of an incompressible Newtonian fluid heated from below in a two-dimensional domain of height H: the Bénard problem. The lower wall is maintained at a temperature θbottom and the upper wall is maintained at a temperature θtop, where θbottom > θtop . The governing equations are the (2D) Navier–Stokes equations under the Boussinesq approximation, in which all variations in phys...

We consider transport of a solute that undergoes a nonlinear heterogeneous reaction: after reaching a threshold concentration value, it precipitates on the solid matrix to form a crystalline solid. The relative importance of three key pore-scale transport mechanisms (advection, molecular diffusion, and reaction) is quantified by the Péclet (Pe) and Damköhler (Da) numbers. We use multiple-scale ...

We consider absorbing chemical reactions in a fluid flow modeled by the coupled advection-reaction-diffusion equations. In these systems, interplay between diffusion and transportation causes enhanced dissipation phenomenon. show that time scale, together with reaction coupling strength, determines characteristic scale of reaction.

A fractional step numerical method is developed for the nonlinear partial differential equations arising in chemotaxis models, which include density-dependent diffusion terms for chemotaxis, as well as reaction and Fickian diffusion terms. We take the novel approach of viewing the chemotaxis term as an advection term which is possible in the context of fractional steps. This method is applied t...

Dispersion curves to a oscillatory reaction-diffusion system with the selfconsistent flow have obtained by means of numerical calculations. The flow modulates the shape of dispersion curves and characteristics of traveling waves. The point of inflection which separates the dispersion curves into two branches corresponding to trigger and phase waves, moves according to the value of the advection...

This study investigates the viscous term formulation for the newly developed energy stable flux reconstruction (ESFR) scheme, as an extension to the linear advection flux formulation in the original ESFR scheme. The concept of energy stability for the flux reconstruction approach is put forward. This paper also discusses the formulation of inviscid first derivative flux based on flux reconstruc...

Krylov implicit integration factor (IIF) methods were developed in Chen and Zhang (J Comput Phys 230:4336–4352, 2011) for solving stiff reaction–diffusion equations on high dimensional unstructured meshes. The methods were further extended to solve stiff advection–diffusion–reaction equations in Jiang and Zhang (J Comput Phys 253:368–388, 2013). Recently we studied the computational power of Kr...