Contour surgery: A topological reconnection scheme for extended integrations using contour dynamics

Dritschel, David G.

doi:10.1016/0021-9991(88)90165-9

Cited by 240 publications

(187 citation statements)

References 10 publications

Supporting

Mentioning

187

Contrasting

Order By: Relevance

“…The simulations discussed below in § 3.2 were run with p = 0.005. The contour-dynamics, or contour-surgery method (Zabusky, Hughes & Roberts 1979;Dritschel 1988;see also Kozlov 1983;Pullin 1992) is widely used for highresolution simulations of the dynamics of uniform-vorticity patches. Once the shape and location of the contour bounding a uniform-vorticity patch are known, the flow induced by the patch is calculated by inverting the Laplace operator in the Poisson equation that relates the flow stream function and the vorticity field.…”

Section: Numerical Simulationsmentioning

confidence: 99%

Instabilities of the flow around a cylinder and emission of vortex dipoles

Kizner

Makarov²,

Kamp

et al. 2013

J. Fluid Mech.

View full text Add to dashboard Cite

Instabilities and long-term evolution of two-dimensional circular flows around a rigid circular cylinder (island) are studied analytically and numerically. For that we consider a base flow consisting of two concentric neighbouring rings of uniform but different vorticity, with the inner ring touching the cylinder. We first study the inviscid linear stability of such flows to perturbations of the free edges of the rings. For a given ratio of the vorticity in the rings, the governing parameters of the problem are the radii of the inner and outer rings scaled on the cylinder radius. In this two-dimensional parameter space, we determine analytically the regions of linear stability/instability of each azimuthal mode m = 1, 2, . . . . In the physically most meaningful case of zero net circulation, for each mode m > 1, two regions are identified: a regular instability region where mode m is unstable along with some other modes, and a unique instability region where only mode m is unstable. After the conditions of linear instability are established, inviscid contour-dynamics and high-Reynolds-number finite-element simulations are conducted. In the regular instability regions, simulations of both kinds typically result in the formation of vortical dipoles or multipoles. In the unique instability regions, where the inner vorticity ring is much thinner than the outer ring, the inviscid contour-dynamics simulations do not reveal dipole emission. In the viscous simulation, because viscosity has time to widen the inner ring, the instability develops in the same manner as in the regular instability regions.

show abstract

Section: Numerical Simulationsmentioning

confidence: 99%

Instabilities of the flow around a cylinder and emission of vortex dipoles

Kizner

Makarov²,

Kamp

et al. 2013

J. Fluid Mech.

View full text Add to dashboard Cite

show abstract

“…Another useful measure of eddy growth, particularly suited to the contour representation used here, is the wave activity A, defined as where the sum is over all contours k in a given vertical level, where r e is the radius of the undisturbed circular contour enclosing the same area as k and q k is the vorticity jump on the kth contour. This is a nonlinear pseudo-momentum-based wave activity, second-order in disturbance amplitude, satisfying an exact conservation relation (see Dritschel, 1988 andDritschel &Saravanan, 1994 for more details). The evolution of total wave activity contained in the surface and tropopause potential temperature fields is shown in Figure 5 for the three cases Q = 0, 0.2f 0 , 0.4f 0 .…”

Section: Zonally Symmetric Perturbationmentioning

confidence: 99%

The influence of stratospheric potential vorticity on baroclinic instability

Smy

Scott

2009

Quart J Royal Meteoro Soc

View full text Add to dashboard Cite

This article examines the dynamical coupling between the stratosphere and troposphere by considering the effect of direct perturbations to stratospheric potential vorticity on the evolution of midlatitude baroclinic instability in a simple extension of an Eady model. A simulation in which stratospheric potential vorticity is exactly zero is used as a control case, and both zonally symmetric and asymmetric perturbations to the stratospheric potential vorticity are then considered, the former representative of a strong polar vortex, the latter representative of the stratospheric state following a major sudden warming. Both types of stratospheric perturbation result in significant changes to the synoptic-scale evolution of surface temperature, as well as to zonally and globally averaged tropospheric quantities. In the case of a zonally symmetric perturbation, the linear growth rate of all unstable modes decreases with increasing perturbation amplitude. Initial growth rates in cases with significant asymmetric perturbations are also weaker than those of the control case, but final eddy kinetic energy values are much larger due to the growth of low zonal wavenumbers triggered by the initial stratospheric perturbation. A comparison of the zonally symmetric and asymmetric perturbations gives some insight into the possible influence of pre-or post-sudden-warming conditions on tropospheric evolution.

show abstract

“…By defining the stream function as in (1) and taking the curl of the linear momentum equation, we obtain the vorticity equation ow + o'ljJow _ o'ljJow = 0, ot oy ox Ox oy (2) which expresses conservation of vorticity of a fluid particle. Further, a relation between w and ' ljJ can be derived from their definitions (3) By solving (3) using Green's function, we find an expression for ' ljJ particle ensures that this distribution remains piecewise constant throughout time.…”

Section: The Governing Equationsmentioning

confidence: 99%

“…Contour dynamics is based on the idea that the evolution of a patch of uniform vorticity is fully determined by the evolution of its boundary contour. The method is not limited to just one region of uniform vorticity; indeed, several contours can be nested in order to obtain an approximation of a patch of distributed vorticity (see [1], [2], [11]). Two-dimensional flows of an incompressible, inviscid fluid can be described by Euler's equation, which expresses balance of linear momentum, and the continuity equation, which expresses conservation of mass.…”

Section: Introductionmentioning

confidence: 99%

Contour Dynamics with Symplectic Time Integration

Vosbeek

Mattheij

1997

Journal of Computational Physics

View full text Add to dashboard Cite

In this paper we consider the time evolution of vortices simulated by the method of contour dynamics. Special attention is being paid to the Hamiltonian character of the governing equations and in particular to the conservational properties of numerical time integration for them. We assess symplectic and non-symplectic schemes. For the former methods, we give an implementation which is both efficient and yet effectively explicit. A number of numerical examples sustain the analysis and demonstrate the usefulness of the approach.

show abstract

Contour surgery: A topological reconnection scheme for extended integrations using contour dynamics

Cited by 240 publications

References 10 publications

Instabilities of the flow around a cylinder and emission of vortex dipoles

Instabilities of the flow around a cylinder and emission of vortex dipoles

The influence of stratospheric potential vorticity on baroclinic instability

Contour Dynamics with Symplectic Time Integration

Contact Info

Product

Resources

About