TY - JOUR

T1 - The elliptical model of two-dimensional vortex dynamics. II

T2 - Disturbance equations

AU - Dritschel, David G.

AU - Legras, Bernard

PY - 1991/1/1

Y1 - 1991/1/1

N2 - In Part I [Phys. Fluids A 3, 845 (1991)] approximate equations were developed that describe the basic evolution of vortices in a general strain field. These equations take the form of a set of coupled, nonlinear ordinary differential equations describing the time evolution of the centroids, aspect ratios, and orientations of a nested set of elliptical contours representing each vortex. Here, in Part II, the model is extended to include disturbances to the elliptical shape of each contour, disturbances that are excited naturally by the interaction with other vortices. This interaction is worked out explicitly for the first time. The final equations obtained decouple into sets of equations for each mode symmetry, allowing for a very simple description of the disturbance evolution. Numerical tests show remarkable agreement between the elliptical model and the full equations of motion in four problems: (1) the equilibrium contour shapes of a multicontour family of vortices, (2) the linear stability of this family, (3) the equilibrium, nonelliptical shapes of two corotating vortex patches, and (4) the interaction between two symmetrical vortex patches, including merging.

AB - In Part I [Phys. Fluids A 3, 845 (1991)] approximate equations were developed that describe the basic evolution of vortices in a general strain field. These equations take the form of a set of coupled, nonlinear ordinary differential equations describing the time evolution of the centroids, aspect ratios, and orientations of a nested set of elliptical contours representing each vortex. Here, in Part II, the model is extended to include disturbances to the elliptical shape of each contour, disturbances that are excited naturally by the interaction with other vortices. This interaction is worked out explicitly for the first time. The final equations obtained decouple into sets of equations for each mode symmetry, allowing for a very simple description of the disturbance evolution. Numerical tests show remarkable agreement between the elliptical model and the full equations of motion in four problems: (1) the equilibrium contour shapes of a multicontour family of vortices, (2) the linear stability of this family, (3) the equilibrium, nonelliptical shapes of two corotating vortex patches, and (4) the interaction between two symmetrical vortex patches, including merging.

UR - http://www.scopus.com/inward/record.url?scp=36449000962&partnerID=8YFLogxK

U2 - 10.1063/1.858016

DO - 10.1063/1.858016

M3 - Article

AN - SCOPUS:36449000962

SN - 0899-8213

VL - 3

SP - 855

EP - 869

JO - Physics of Fluids A

JF - Physics of Fluids A

IS - 5

ER -