Evolution of a Point Plume in a Rotating Unstratified Fluid Overlain by a Stratified Layer: Scaling and Implications for Icy Satellites.

(Wang, S., Kang, W., and Marshall, J.), JGR Planets, vol. 131, no. 7, 2026.

Abstract

Plumes that rise through an unstratified layer and penetrate into an adjacent stably stratified layer are ubiquitous in geophysical and planetary environments, including the subsurface oceans of icy satellites such as Europa, Enceladus, and Titan. In this study, we investigate the evolution of such plumes from isolated buoyant sources, both in non-rotating and rotating systems, with particular emphasis on their penetration height. Non-rotating plumes evolve into a classical “mushroom” structure, whereas rotating plumes evolve into baroclinic cones or can not reach the stratified layer, depending on the interface height h i . A scaling law for the penetration height z p is derived in terms of h i and two characteristic length scales, L N ≡ F 0 / N 3 1 / 4 and L r o t ≡ F 0 / f 3 1 / 4 , where F 0 is the buoyancy flux of the source, N is the buoyancy frequency, and f = 2 Ω is the Coriolis parameter ( Ω is the rotation rate). In the non-rotating regime, the scaling recovers the classical relation z p ∝ L N when the unstratified layer is thin and predicts z p / L N ∝ h i / L N − 1 / 3 when the layer is thick. In the rapid-rotating regime, z p remains constant for small h i , followed by a decrease toward zero as h i increases, due to the lateral mixing by baroclinic eddies. Under weak stratification, plumes typically arrest at about 50 L r o t , independent of h i . Applying these scalings to icy-ocean worlds suggests that on Europa, plumes could reach the ice shell, whereas on Enceladus and Titan, they are likely arrested in the mid-ocean.

doi = 10.1029/2026JE009649