Vortex Interactions Subjected to Deformation Flows: A Review

Round 1

Reviewer 1 Report

Review of Vortex interaction subjected to deformation flows: a review

 by K.V. Koshel, E.A. Ryzhov and X. J. Carton

     Dynamics of vortex and vortex system embedded into deformation flows is considered. The paper consists of two parts. In the first one (Sections 2-5) regular and chaotic dynamics of simple vortex systems on the deformation flows are analyzed. The following problems are discussed: motion of vorticity centre of an ensemble of singular vortex in M-layer flow; relative motion of two singular vortices in barotropic and two-layer fluids; three-vortex problem when one vortex is fixed in the upper layer and two others in the lower layer; distributed vortices (elliptical and ellipsoidal).  In the second part of the manuscript, the scalar fluid particle advection induced by the models considered in the first part is explored.

     The review is very informative and interesting and can be published in Fluids after a minor revision; comments are in Attachment.

Comments for author File: Comments.rtf

Author Response

Response to the reviewer comments.

First, we would like to thank the reviewer for the comments that lead to a significant improvement of the manuscript. 

Second, we have corrected all the typos and added explanations to the constants g', \omega_0, \tilde g. The figure references have been also corrected. 

Reviewer 2 Report

This paper summarizes the progress in analytical/numerical understanding of the motion of quasigeostrophic point vortices and elliptical/ellipsoidal vortices in the background deformation flows on an f-plane. The first part is devoted to the analysis of the systems of two and three point vortices, as well as the single ellipsoidal vortex, including steady states and transition to chaos. The second part concentrates on the analysis of regular and chaotic advection of scalar fields by the vortices considered in the first part. These analyses were argued to be relevant for applications in planetary sciences, as well as in oceanography, although this was not the focus of the review.

In my estimation, this review paper would be most useful for the scientists specializing in the theoretical geophysical fluid dynamics (gauged, for example, by a huge number of the studies in this field reviewed in this paper), whereas its broader impacts (e.g., in the field of oceanography and atmospheric or planetary sciences) are less clear. My moderate rating of the paper significance, yet the recommendation of acceptance is a reflection of this statement. 

One thing that, I believe, the author could at least comment on in the paper is the lack of beta-effect in their model. The motion of the singular vortices on the beta-plane, for example, would be fundamentally different (and, arguably, much more complex) from the f-plane case, due to radiation of Rossby waves etc. Are there motion regimes in real world that could still be well described, even if approximately, by the f-plane dynamics?

Author Response

Response to the reviewer comments.

First, we would like to thank the reviewer for the suggestions. 

Second, we have added a few sentences about the importance of the beta-effect in the Problem formulation section (the second paragraph) :

It is worth noting that the dynamics of oceanic mesoscale features (like the vortices studied in the paper) may be affected by the the beta-effect, that is the change of the Coriolis frequency with the latitude, if the size and strength of the vortices do not comply with the f-plane approximation, that is beta L / f ~ O(1) and U / (beta L^2) ~ O(1), where L is the characteristic length-scale of the features. This implies essentially that L ~ f/beta and L ~ sqrt(U/beta), the second one being stricter than the first one. Orders of magnitude of both are respectively 5000 km and 225 km for U=1m/s, f=10^-4 s^-1 and beta =2 10^-11
m^-1 s^-1. The smaller value effectively indicates the typical size of structures that can be reasonably studied by the f-plane approximation. Otherwise, the evolution of the vortices becomes much more complicated including the possibility of a self-induced drift of isolated vortices due to the beta-effect. This, in turn, will produce much more complicated vortex evolution patterns compared to the ones reviewed in the paper.