Chang Liu, University of California, Berkeley

Staircase solutions and stability in bounded salt-finger convection

This work performs bifurcation analysis of bounded salt-finger convection using single-mode equations obtained from a severely truncated Fourier expansion in the horizontal. We find staircase-like solutions having respectively one, two, and three well-mixed mean salinity regions (S1, S2, and S3) in the vertical direction. Tilted fingers (TF1) and traveling waves (TW1) break horizontal reflection symmetry with spontaneous formations of large-scale shear. Solutions that break vertical reflection symmetry are also found. S1 solution shows a trend closely matching the DNS results for Sherwood number, mean salinity and temperature profiles over density ratio. The single-mode solutions close to high wavenumber onset are in excellent agreement with 2D DNS within a small horizontal domain.