An official website of the United States government
Abstract The mixing of tracers by mesoscale eddies, parameterized in many ocean general circulation models (OGCMs) as a diffusive‐advective process, contributes significantly to the distribution of tracers in the ocean. In the ocean interior, diffusive contribution occurs mostly along the direction parallel to local neutral density surfaces. However, near the surface of the ocean, small‐scale turbulence and the presence of the boundary itself break this constraint and the mesoscale transport occurs mostly along a plane parallel to the ocean surface (horizontal). Although this process is easily represented in OGCMs with geopotential vertical coordinates, the representation is more challenging in OGCMs that use a general vertical coordinate, where surfaces can be tilted with respect to the horizontal. We propose a method for representing the diffusive horizontal mesoscale fluxes within the surface boundary layer of general vertical coordinate OGCMs. The method relies on regridding/remapping techniques to represent tracers in a geopotential grid. Horizontal fluxes are calculated on this grid and then remapped back to the native grid, where fluxes are applied. The algorithm is implemented in an ocean model and tested in idealized and realistic settings. Horizontal diffusion can account for up to 10% of the total northward heat transport in the Southern Ocean and Western boundary current regions of the Northern Hemisphere. It also reduces the vertical stratification of the upper ocean, which results in an overall deepening of the surface boundary layer depth. Finally, enabling horizontal diffusion leads to meaningful reductions in the near‐surface global bias of potential temperature and salinity.
more »
« less
This content will become publicly available on February 1, 2026
Kinetic Monte Carlo methods for three-dimensional diffusive capture problems in exterior domains
Cellular scale decision-making is modulated by the dynamics of signalling molecules and their diffusive trajectories from a source to small absorbing sites on the cellular surface. Diffusive capture problems which model this process are computationally challenging due to their complex geometry and mixed boundary conditions together with intrinsically long transients that occur before a particle is captured. This paper reports on a particle-based kinetic Monte Carlo (KMC) method that provides rapid accurate simulation of arrival statistics for (i) a half-space bounded by a surface with a finite collection of absorbing traps and (ii) the domain exterior to a convex cell, again with absorbing traps. We validate our method by replicating classical results and verifying some newly developed boundary homogenization theories and matched asymptotic expansions on capture rates. In the case of non-spherical domains, we describe a new shielding effect in which geometry can play a role in sharpening cellular estimates on the directionality of diffusive sources.
more »
« less
- Award ID(s):
- 2052636
- PAR ID:
- 10630835
- Publisher / Repository:
- Royal society.
- Date Published:
- Journal Name:
- Royal Society Open Science
- Volume:
- 12
- Issue:
- 2
- ISSN:
- 2054-5703
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Abstract Particles are injected into a large planar domain through the boundary and perform a random or sufficiently chaotic deterministic motion inside the domain. Our main example is the Sinai billiard, which periodically extended to our large planar domain, is referred to as the Lorentz process. Assuming that the particles move independently from one another and the boundary is also absorbing, we prove the emergence of local equilibrium of the particle density in the diffusive scaling limit in two scenarios. One scenario is an arbitrary domain with piece-wise smooth boundary and a carefully chosen injection rule; the other scenario is a rectangular domain and a much more general injection mechanism. We study the latter scenario in an abstract framework that includes Lorentz processes and random walks and hopefully allows for more applications in the future.more » « less
-
The diffusive tortuosity factor of a porous media quantifies the material’s resistance to diffusion, an important component of modeling flows in porous structures at the macroscale. Advances in X-ray micro-computed tomography (-CT) imaging provide the geometry of the material at the microscale (microstructure) thus enabling direct numerical simulation (DNS) of transport at the microscale. The data from these DNS are then used to close material’s macroscale transport models, which rely on effective material properties. In this work, we present numerical methods suitable for large scale simulations of diffusive transport through complex microstructures for the full range of Knudsen regimes. These numerical methods include a finite-volume method for continuum conditions, a random walk method for all regimes from continuum to rarefied, and the direct simulation Monte Carlo method. We show that for particle methods, the surface representation significantly affects the accuracy of the simulation for high Knudsen numbers, but not for continuum conditions. We discuss the upscaling of pore-resolved simulations to single species and multi-species volume-averaged models. Finally, diffusive tortuosities of a fibrous material are computed by applying the discussed numerical methods to 3D images of the actual microstructure obtained from X-ray computed micro-tomography.more » « less
-
null (Ed.)In this paper, we introduce a geometry-based structural design method as an alternative approach for designing low-density structures applicable to material science and mechanical engineering. This method will provide control over internal force-flow, boundary condition, and applied loads. The methodology starts with an introduction to the principles of geometric equilibrium and continues by introducing multiple design techniques to generate truss cellular, polyhedron cellular, and shell cellular (or Shellular) materials by manipulating the geometry of the equilibrium of force. The research concludes by evaluating the mechanical performance of a range of cellular structures designed by this approach.more » « less
-
Trapping diffusive particles at surfaces is a key step in many systems in chemical and biological physics. Trapping often occurs via reactive patches on the surface and/or the particle. The theory of boundary homogenization has been used in many prior works to estimate the effective trapping rate for such a system in the case that either (i) the surface is patchy and the particle is uniformly reactive or (ii) the particle is patchy and the surface is uniformly reactive. In this paper, we estimate the trapping rate for the case that the surface and the particle are both patchy. In particular, the particle diffuses translationally and rotationally and reacts with the surface when a patch on the particle contacts a patch on the surface. We first formulate a stochastic model and derive a five-dimensional partial differential equation describing the reaction time. We then use matched asymptotic analysis to derive the effective trapping rate, assuming that the patches are roughly evenly distributed and occupy a small fraction of the surface and the particle. This trapping rate involves the electrostatic capacitance of a four-dimensional duocylinder, which we compute using a kinetic Monte Carlo algorithm. We further use Brownian local time theory to derive a simple heuristic estimate of the trapping rate and show that it is remarkably close to the asymptotic estimate. Finally, we develop a kinetic Monte Carlo algorithm to simulate the full stochastic system and then use these simulations to confirm the accuracy of our trapping rate estimates and homogenization theory.more » « less
