A common assumption concerning vortices in the ocean and atmosphere is that their “aspect ratios”, defined as their characteristic vertical thicknesses divided by their average diameters, are functions only of the vertical stratification (or Rossby deformation radius, or Brunt-Vaisala frequency N) of the surrounding fluid and of the local Coriolis parameter f, and not on any of the properties of the vortices themselves such as their Rossby numbers, diameters, or the internal stratifications within the vortices. In particular, the common assumption is that the aspect ratio is f/N. Our simulations, lab experiments and analyses show that this assumption is false and can be off by factors of 10-100. We have determined the proper scaling law for the aspect ratio. Our results have implications for planetary vortices, where the vertical thickness cannot be directly measured and is often inferred (incorrectly) by the f/N assumption. Understanding the physics that determines the vertical thickness is a needed first step in determining the stability of 3D vortices. In addition, understanding and being able to correctly compute the vertical aspect ratio of vortices is necessary for our current project of determining the secondary (meridional and vertical) circulations within vortices. The latter are important to understand vertical and horizontal transport within a vortex and also within an ocean or atmosphere filled with vortices. For example, a detailed knowledge of the secondary circulations is important to understand color changes in the vortices of Jupiter (i.e., its Great Red Spot), the accumulation and agglomeration of dust into planetesimals in protoplanetary disks and the vertical transport of carbon dioxide from the ocean surface to greater depths.
Published Papers and Abstracts
“Zombie Vortex Instability. A Purely Hydrodynamic Instability to Resurrect The Dead Zones of Protoplanetary Disks”, Philip Marcus, Suyang Pei, Chung-Hsiang Jiang, Joseph Barranco, Pedram Hassanzadeh, Daniel Lecoanet, November 2014, The Astrophysical Journal, 808:87, doi:10.1088/0004-637X/808/1/87. — PDF
“Linear Stability and Nonlinear Evolution of 3D Vortices in Rotating Stratified Flows”, Mani Mahdinia, Pedram Hassanzadeh, Philip Marcus, APS Division of Fluid Dynamics Meeting Abstracts, November 2014. — PDF
“Zombie Vortices: The Dead Zones of Protoplanetary Disks are Not Dead”, Chung-Hsiang Jiang, Philip Marcus, Suyang Pei, Joe Barranco, Pedram Hassanzadeh, Daniel Lecoanet, APS Division of Fluid Dynamics Meeting Abstracts, November 2014. — PDF
“Zombie Vortices: Angular Momentum Transport and Planetesimal Formation”, Joseph Barranco, Philip Marcus, Suyang Pei, Chung-Hsiang Jiang, Pedram Hassanzadeh, Daniel Lecoanet, APS Division of Fluid Dynamics Meeting Abstracts, November 2014. — PDF
”The role of interactions between waves and baroclinic critical layers in zombie vortex self-replication”, Chung-Hsiang Jiang, Suyang Pei, Pedram Hassanzadeh, Aaron Wienkers, Caleb Levy, Philip Marcus, APS Division of Fluid Dynamics Meeting Abstracts, November 2013. — PDF
“Stability of Baroclinic Vortices in Rotating Stratified Flows”, Mani Mahdinia, Pedram Hassanzadeh, Philip Marcus, APS Division of Fluid Dynamics Meeting Abstracts, November 2013. — PDF
“3D Zombie Vortices in Rotating Stratified Shear”, Philip Marcus, Suyang Pei, Chung-Hsiang Jiang, Pedram Hassanzadeh, Joseph Barranco, Daniel Lecoanet, APS Division of Fluid Dynamics Meeting Abstracts, November 2013. — PDF
“Noise and Turbulence Generate 3D Zombie Vortices in Stably Stratified Rotating Shear Flows”, Suyang Pei, Philip S Marcus, Chung-Hsiang Jiang, Pedram Hassanzadeh, Daniel Lecoanet, Joseph A Barranco, APS Division of Fluid Dynamics Meeting Abstracts, November 2013. — PDF
“Three-dimensional vortices generated by self-replication in stably stratified rotating shear flows”, Philip S Marcus, Suyang Pei, Chung-Hsiang Jiang, Pedram Hassanzadeh, Physical Review Letters, vol. 111, August 2013, DOI: 10.1103/PhysRevLett.111.084501. — PDF
“The universal aspect ratio of vortices in rotating stratified flows: experiments and observation”, Oriane Aubert, Michael Le Bars, Patrice Le Gal, Philip S Marcus, Journal of Fluid Mechanics, vol. 706, pp. 34-45, May 2012, doi: 10.1017/jfm.2012.176. — PDF and Supplement
“The universal aspect ratio of vortices in rotating stratified flows: theory and simulation”, Pedram Hassanzadeh, Philip S Marcus, Patrice Le Gal, 2012, Journal of Fluid Mechanics, vol. 706, pp. 46-57, May 2012, doi: 10.1017/jfm.2012.180. — PDF
“Forme et persistance de tourbillons lenticulaires dans les écoulements stratifiés tournants: du laboratoirea à la Tâche Rouge de Jupiter!”, Aubert O., Le Bars M., Le Gal P., Marcus P.S., Résumés des exposés de la 14e Rencontre du Non-Linéaire Paris 2011, pp. 67, September 2011. — PDF
“3D Structure and Internal Circulation of Pancake Vortices in Rotating Stratified Flows”, Pedram Hassanzadeh, Philip Marcus, Oriane Aubert, Michael Le Bars, Patrice Le Gal, APS Division of Fluid Dynamics Meeting Abstracts, vol. 56, November 2011. — PDF
“3D Vortices in Stratified, Rotating Flows – Secondary Circulations and Changes in Aspect Radio Due to Dissipation”, Philip Marcus, Pedram Hassanzadeh, APS Division of Fluid Dynamics Meeting Abstracts, vol. 56, November 2011. — PDF
“Universal scaling law for the aspect ratio of a pancake vortex in a rotating stratified medium”, Oriane Aubert, Michael Le Bars, Patrice Le Gal, Philip S Marcus, APS Division of Fluid Dynamics Meeting Abstracts, vol. 55, November 2010. — PDF
“Inverse Cascades and Zonal Flows on a Beta Plane”, Philip Marcus, Chung-Hsiang Jiang, APS Division of Fluid Dynamics Meeting Abstracts, vol. 54, November 2009. — PDF
“Forward/Inverse Energy Cascade in 2D and QG Turbulence”, Chung-Hsiang Jiang, Philip S Marcus, APS Division of Fluid Dynamics Meeting Abstracts, vol. 54, November 2009. — PDF
“Profound Effects of Boundaries and Weak 3D Motions on Nearly 2D Turbulence”, Philip Marcus, Chung-Hsiaing Jiang, APS Division of Fluid Dynamics Meeting Abstracts, vol. 50, November 2005. — PDF
“3D Vortices in Rotating Stratified Flows”, Xylar Asay-Davis, Sushil Shetty, Philip Marcus, November 2005, APS Division of Fluid Dynamics Meeting Abstracts, vol. 50, November 2005. — PDF
“Dynamics of Vortex Lines in Turbulent 3D Stratified Flows”, Philip Marcus, APS Division of Plasma Physics Meeting Abstracts, October 2005. — PDF
“Three-Dimensional ‘Pancake’ Vortices”, Philip Marcus, Joseph Barranco, Sushil Shetty, Xylar Asay-Davis, , Americal Physical Society Meeting Abstracts, vol. 1, November 2003. — Image
“A Thermal Wind in Pancake Vortices in a Stably Stratified Flow”, D. M. Kidani, P. S. Marcus, APS Division of Fluid Dynamics Meeting Abstracts, November 1997. — Image
“Long time averaged rotating shallow-water equations” Philip S. Marcus, A. Mahalov, in the Proceedings of the First Asian Computational Fluid Dynamics Conference, vol. 3, pp. 1227–1230, (ed. by W. H. Hui, Y.-K. Kwok, and J.R. Chasnov) Hong Kong, 1995.
