Abstract. Application of the Brown-Samelson theorem, which shows that particle motion is integrable in a class of vorticity-conserving, two-dimensional incompressible flows, is extended here to a class of explicit time dependent dynamically balanced flows in multilayered systems. Particle motion for nonsteady two-dimensional flows with discontinuities in the vorticity or potential vorticity fields (modon solutions) is shown to be integrable. An example of a two-layer modon solution constrained by observations of a Gulf Stream ring system is discussed.
The lattice-Bhatnagar-Gross-Krook (BGK) method has been used to simulate fluid flow in the nearly incompressible limit. But for the completely incompressible flows, two special approaches should be applied to the general model, for the steady and unsteady cases, respectively. Introduced by Zou et al.,1 the method for steady incompressible flows will be described briefly in this paper. For the unsteady case, we will show, using a simple numerical example, the need to solve a Poisson equation for pressure.
Smoothed Particle Hydrodynamics (SPH) is a mesh-free numerical method that can simulate metal cutting problems efficiently. The thermal modeling of such processes with SPH, nevertheless, is not straightforward. The difficulty is rooted in the computationally demanding procedures regarding convergence properties and boundary treatments, both known as SPH Grand Challenges. This paper, therefore, intends to rectify these issues in SPH cutting models by proposing two improvements: (1) Implementing a higher-order Laplacian formulation to solve the heat equation more accurately. (2) Introducing a more realistic thermal boundary condition using a robust surface detection algorithm. We employ the proposed framework to simulate an orthogonal cutting process and validate the numerical results against the available experimental measurements.
Integrable unsteady motion with an application to ocean eddies
