Mechanics of merging events for a series of layers in a stratified turbulent fluid
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Authors
Radko, Timour
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2007
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Abstract
This study attempts to explain the evolutionary pattern of a series of well-mixed
layers separated by thin high-gradient interfaces frequently observed in stratified
fluids. Such layered structures form as a result of the instability of the equilibrium
with uniform stratification, and their subsequent evolution is characterized by a
sequence of merging events which systematically increase the average layer thickness.
The coarsening of layers can take one of two forms, depending on the realized
vertical buoyancy flux law. Layers merge either when the high-gradient interfaces
drift and collide, or when some interfaces gradually erode without moving vertically.
The selection of a preferred pattern of coarsening is rationalized by the analytical
theory – the merging theorem – which is based on linear stability analysis for a series
of identical layers and strongly stratified interfaces. The merging theorem suggests
that the merger by erosion of weak interfaces occurs when the vertical buoyancy flux
decreases with the buoyancy variation across the step. If the buoyancy flux increases
with step height, then coarsening of a staircase may result from drift and collision
of the adjacent interfaces. Our model also quantifies the time scale of merging events
and makes it possible to predict whether the layer merging continues indefinitely
or whether the coarsening is ultimately arrested. The merging theorem is applied to
extant one-dimensional models of turbulent mixing and successfully tested against
the corresponding fully nonlinear numerical simulations. It is hypothesized that the
upscale cascade of buoyancy variance associated with merging events may be one of
the significant sources of the fine-scale (∼10 m) variability in the ocean.
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Article
Description
The article of record as published may be found at http://dx.doi.org/10.1017/S0022112007004703
Series/Report No
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Oceanography
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Citation
J. Fluid Mech. (2007), vol. 577, pp. 251–273.
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This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.