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Dynamics of Fingering Convection II: The Formation of Thermohaline Staircases
Journal of Fluid Mechanics
  • Stephan Stellmach
  • Adrienne L. Traxler, Wright State University - Main Campus
  • Pascale Garaud
  • N. Brummell
  • T. Radko
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Regions of the ocean's thermocline unstable to salt fingering are often observed to host thermohaline staircases, stacks of deep well-mixed convective layers separated by thin stably stratified interfaces. Decades after their discovery, however, their origin remains controversial. In this paper we use three-dimensional direct numerical simulations to shed light on the problem. We study the evolution of an analogous double-diffusive system, starting from an initial statistically homogeneous fingering state, and find that it spontaneously transforms into a layered state. By analysing our results in the light of the mean-field theory developed in Part 1 (Traxler et al., J. Fluid Mech. doi:10.1017/jfm.2011.98, 2011), a clear picture of the sequence of events resulting in the staircase formation emerges. A collective instability of homogeneous fingering convection first excites a field of gravity waves, with a well-defined vertical wavelength. However, the waves saturate early through regular but localized breaking events and are not directly responsible for the formation of the staircase. Meanwhile, slower-growing, horizontally invariant but vertically quasi-periodic γ-modes are also excited and grow according to the γ-instability mechanism. Our results suggest that the nonlinear interaction between these various mean-field modes of instability leads to the selection of one particular γ-mode as the staircase progenitor. Upon reaching a critical amplitude, this progenitor overturns into a fully formed staircase. We conclude by extending the results of our simulations to real oceanic parameter values and find that the progenitor γ-mode is expected to grow on a time scale of a few hours and leads to the formation of a thermohaline staircase in about one day with an initial spacing in the order of 1–2 m.


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Citation Information
Stephan Stellmach, Adrienne L. Traxler, Pascale Garaud, N. Brummell, et al.. "Dynamics of Fingering Convection II: The Formation of Thermohaline Staircases" Journal of Fluid Mechanics Vol. 677 (2011) p. 554 - 571 ISSN: 00221120
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