TY - JOUR

T1 - Vortex merger in rotating stratified flows

AU - Dritschel, David Gerard

N1 - This work extended prior two-dimensional studies of vortex merger to a three-dimensional quasi-geostrophic (rapidly rotating and stably stratified) fluid. It was shown that tall vortices do not behave like two-dimensional vortices, and instead tall vortices break up as a result of a tall-column instability investigated by the author in earlier weeks.

PY - 2002/3/25

Y1 - 2002/3/25

N2 - This paper describes the interaction of symmetric vortices in a three-dimensional quasi-geostrophic fluid. The initial vortices are taken to be uniform-potential-vorticity ellipsoids, of height 2h and width 2R, and with centres at ( +/-d/2, 0, 0), embedded within a background flow having constant background rotational and buoyancy frequencies, f/2 and N respectively. This problem was previously studied by von Hardenburg et al. (2000), who determined the dimensionless critical merger distance d/R as a function of the height-to-width aspect ratio h/R (scaled by f/N). Their study, however, was limited to small to moderate values of h/R, as it was anticipated that merger at large h/R would reduce to that for two columnar two-dimensional vortices, i.e. d/R approximate to 3.31. Here, it is shown that no such two-dimensional limit exists; merger is found to occur at any aspect ratio, with d similar to h for h/R much greater than 1.New results are also found for small to moderate values of h/R. In particular, our numerical simulations reveal that asymmetric merger is predominant, despite the initial conditions, if one includes a small amount of random noise. For small to moderate h/R, decreasing the initial separation distance d first results in a weak exchange of material, with one vortex growing at the expense of the other. As d decreases further, this exchange increases and leads to two dominant but strongly asymmetric vortices. Finally, for yet smaller d, rapid merger into a single dominant vortex occurs-in effect the initial vortices exchange nearly all of their material with one another in a nearly symmetrical fashion.

AB - This paper describes the interaction of symmetric vortices in a three-dimensional quasi-geostrophic fluid. The initial vortices are taken to be uniform-potential-vorticity ellipsoids, of height 2h and width 2R, and with centres at ( +/-d/2, 0, 0), embedded within a background flow having constant background rotational and buoyancy frequencies, f/2 and N respectively. This problem was previously studied by von Hardenburg et al. (2000), who determined the dimensionless critical merger distance d/R as a function of the height-to-width aspect ratio h/R (scaled by f/N). Their study, however, was limited to small to moderate values of h/R, as it was anticipated that merger at large h/R would reduce to that for two columnar two-dimensional vortices, i.e. d/R approximate to 3.31. Here, it is shown that no such two-dimensional limit exists; merger is found to occur at any aspect ratio, with d similar to h for h/R much greater than 1.New results are also found for small to moderate values of h/R. In particular, our numerical simulations reveal that asymmetric merger is predominant, despite the initial conditions, if one includes a small amount of random noise. For small to moderate h/R, decreasing the initial separation distance d first results in a weak exchange of material, with one vortex growing at the expense of the other. As d decreases further, this exchange increases and leads to two dominant but strongly asymmetric vortices. Finally, for yet smaller d, rapid merger into a single dominant vortex occurs-in effect the initial vortices exchange nearly all of their material with one another in a nearly symmetrical fashion.

KW - GEOSTROPHIC TURBULENCE

KW - CONTOUR DYNAMICS

KW - VORTICES

KW - INSTABILITY

KW - MODELS

KW - FLUID

UR - http://www.scopus.com/inward/record.url?scp=0037171425&partnerID=8YFLogxK

U2 - 10.1017/S0022112001007364

DO - 10.1017/S0022112001007364

M3 - Article

SN - 0022-1120

VL - 455

SP - 83

EP - 101

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

ER -