Profile of a two-dimensional vortex condensate beyond the universal limit

Area of Science:

• Fluid Dynamics
• Turbulence Studies
• Computational Physics

Background:

• Inverse turbulent cascades in 2D systems generate large-scale coherent vortex dipoles.
• Previous research established a power-law vorticity profile for small-scale forcing (Ω(r) ∝ r⁻¹).

Purpose of the Study:

• Investigate the spatial vorticity profile within coherent vortices under different forcing conditions.
• Determine how forcing correlation length and spatial distribution affect vorticity distribution.

Main Methods:

• Numerical hyperviscous simulations in a 2D periodic domain.
• Utilized time-shortly correlated, spatially random forcing with varying correlation lengths (k_f).
• Performed simulations with spatially localized forcing for comparison.

Main Results:

• Spatially homogeneous forcing with finite correlation length leads to steeper vorticity profiles compared to the asymptotic limit.
• Profile steepness increases with forcing scale but decreases with Reynolds number at the forcing scale.
• Spatially localized forcing results in flatter vorticity profiles, with pumping increasing with distance from the vortex center.

Conclusions:

• The spatial distribution and scale of forcing significantly alter the vorticity profile of coherent vortices.
• The observed changes in vorticity profiles are linked to variations in the effective pumping of the vortex.
• Results challenge the universal applicability of the asymptotic power-law profile under realistic forcing conditions.