Profile of a twodimensional vortex condensate beyond the universal limit
Abstract
It is well known that an inverse turbulent cascade in a finite (2 π ×2 π ) twodimensional periodic domain leads to the emergence of a systemsized coherent vortex dipole. We report a numerical hyperviscous study of the spatial vorticity profile inside one of the vortices. The exciting force was shortly correlated in time, random in space, and had a correlation length l_{f}=2 π /k_{f} with k_{f} ranging from 100 to 12.5. Previously, it was found that in the asymptotic limit of smallscale forcing, the vorticity exhibits the powerlaw behavior Ω (r ) =(3^{ε /α ) 1 /2}r^{−1} , where r is the distance to the vortex center, α is the bottom friction coefficient, and ε is the inverse energy flux. Now we show that for a spatially homogeneous forcing with finite k_{f} the vorticity profile becomes steeper, with the difference increasing with the pumping scale but decreasing with the Reynolds number at the forcing scale. Qualitatively, this behavior is related to a decrease in the effective pumping of the coherent vortex with distance from its center. To support this statement, we perform an additional simulation with spatially localized forcing, in which the effective pumping of the coherent vortex, on the contrary, increases with r , and show that in this case the vorticity profile can be flatter than the asymptotic limit.
 Publication:

Physical Review E
 Pub Date:
 August 2022
 DOI:
 10.1103/PhysRevE.106.025102
 arXiv:
 arXiv:2208.01959
 Bibcode:
 2022PhRvE.106b5102P
 Keywords:

 Physics  Fluid Dynamics
 EPrint:
 doi:10.1103/PhysRevE.106.025102