skip to main content
OSTI.GOV title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow

Abstract

Stratified shear flows occur in many geophysical contexts, from oceanic overflows and river estuaries to wind-driven thermocline layers. In this study, we explore a turbulent wall-bounded shear flow of lighter miscible fluid into a quiescent fluid of higher density with a range of Richardson numbers $$0.05\lesssim Ri\lesssim 1$$. In order to find a stability parameter that allows close comparison with linear theory and with idealized experiments and numerics, we investigate different definitions of$Ri$$. We find that a gradient Richardson number defined on fluid interface sections where there is no overturning at or adjacent to the maximum density gradient position provides an excellent stability parameter, which captures the Miles–Howard linear stability criterion. For small $$Ri$$ the flow exhibits robust Kelvin–Helmholtz instability, whereas for larger $$Ri$$ interfacial overturning is more intermittent with less frequent Kelvin–Helmholtz events and emerging Holmboe wave instability consistent with a thicker velocity layer compared with the density layer. We compute the perturbed fraction of interface as a quantitative measure of the flow intermittency, which is approximately 1 for the smallest $$Ri$$ but decreases rapidly as $$Ri$ increases, consistent with linear theory. For the perturbed regions, we use the Thorpe scale to characterize the overturning properties of these flows.more » The probability distribution of the non-zero Thorpe length yields a universal exponential form, suggesting that much of the overturning results from increasingly intermittent Kelvin–Helmholtz instability events. Finally, the distribution of turbulent kinetic energy, conditioned on the intermittency fraction, has a similar form, suggesting an explanation for the universal scaling collapse of the Thorpe length distribution.« less

Authors:
 [1]; ORCiD logo [2]
  1. Universite de Lyon, ENS de Lyon, Universite Claude Bernard Lyon 1, CNRS (France)
  2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA); USDOE Laboratory Directed Research and Development (LDRD) Program
OSTI Identifier:
1356145
Report Number(s):
LA-UR-17-20090
Journal ID: ISSN 0022-1120
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Fluid Mechanics
Additional Journal Information:
Journal Volume: 815; Journal ID: ISSN 0022-1120
Publisher:
Cambridge University Press
Country of Publication:
United States
Language:
English
Subject:
58 GEOSCIENCES; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Earth Sciences; Planetary Sciences; turbulence, stratified, instability

Citation Formats

Odier, Philippe, and Ecke, Robert E. Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow. United States: N. p., 2017. Web. doi:10.1017/jfm.2017.48.
Odier, Philippe, & Ecke, Robert E. Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow. United States. https://doi.org/10.1017/jfm.2017.48
Odier, Philippe, and Ecke, Robert E. Tue . "Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow". United States. https://doi.org/10.1017/jfm.2017.48. https://www.osti.gov/servlets/purl/1356145.
@article{osti_1356145,
title = {Stability, intermittency and universal Thorpe length distribution in a laboratory turbulent stratified shear flow},
author = {Odier, Philippe and Ecke, Robert E.},
abstractNote = {Stratified shear flows occur in many geophysical contexts, from oceanic overflows and river estuaries to wind-driven thermocline layers. In this study, we explore a turbulent wall-bounded shear flow of lighter miscible fluid into a quiescent fluid of higher density with a range of Richardson numbers $0.05\lesssim Ri\lesssim 1$. In order to find a stability parameter that allows close comparison with linear theory and with idealized experiments and numerics, we investigate different definitions of$Ri$. We find that a gradient Richardson number defined on fluid interface sections where there is no overturning at or adjacent to the maximum density gradient position provides an excellent stability parameter, which captures the Miles–Howard linear stability criterion. For small $Ri$ the flow exhibits robust Kelvin–Helmholtz instability, whereas for larger $Ri$ interfacial overturning is more intermittent with less frequent Kelvin–Helmholtz events and emerging Holmboe wave instability consistent with a thicker velocity layer compared with the density layer. We compute the perturbed fraction of interface as a quantitative measure of the flow intermittency, which is approximately 1 for the smallest $Ri$ but decreases rapidly as $Ri$ increases, consistent with linear theory. For the perturbed regions, we use the Thorpe scale to characterize the overturning properties of these flows. The probability distribution of the non-zero Thorpe length yields a universal exponential form, suggesting that much of the overturning results from increasingly intermittent Kelvin–Helmholtz instability events. Finally, the distribution of turbulent kinetic energy, conditioned on the intermittency fraction, has a similar form, suggesting an explanation for the universal scaling collapse of the Thorpe length distribution.},
doi = {10.1017/jfm.2017.48},
url = {https://www.osti.gov/biblio/1356145}, journal = {Journal of Fluid Mechanics},
issn = {0022-1120},
number = ,
volume = 815,
place = {United States},
year = {2017},
month = {2}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record

Save / Share:

Works referenced in this record:

Mixing regimes for the flow of dense fluid down slopes into stratified environments
journal, August 2005


Shear instabilities in arrested salt-wedge flows
journal, January 1996


Vertical overturns: A comparison of Thorpe and Ozmidov length scales
journal, January 1982


Marginal Instability?
journal, September 2009


Entrainment and mixing in a laboratory model of oceanic overflow
journal, April 2014


Note on a paper of John W. Miles
journal, June 1961


The Kelvin–Helmholtz to Holmboe instability transition in stratified exchange flows
journal, February 2003


Laboratory observations of shear-layer instability in a stratified fluid
journal, April 1973


Turbulent Mixing in Stratified Fluids
journal, January 1991


Mediterranean Outflow Mixing and Dynamics
journal, February 1993


Fluid Mixing in Stratified Gravity Currents: The Prandtl Mixing Length
journal, April 2009


M IXING E FFICIENCY IN S TRATIFIED S HEAR F LOWS
journal, January 2003


Turbulence and Mixing in a Scottish Loch
journal, July 1977


On the mechanism of shear flow instabilities
journal, October 1994


Density Stratification, Turbulence, but How Much Mixing?
journal, January 2008


Mixing in a density-driven current flowing down a slope in a rotating fluid
journal, May 2008


Holmboe wave fields in simulation and experiment
journal, April 2010


The stability of a sheared density interface
journal, October 1991


Local and Global Instabilities in Spatially Developing Flows
journal, January 1990


Observation and analysis of shear instability in the Fraser River estuary
journal, January 2009


On Holmboe’s instability for smooth shear and density profiles
journal, August 2005


The anatomy of the mixing transition in homogeneous and stratified free shear layers
journal, June 2000


Spatial Holmboe instability
journal, August 2002


On the stability of heterogeneous shear flows
journal, June 1961


Available potential energy and mixing in density-stratified fluids
journal, April 1995


Numerical studies of the stability of inviscid stratified shear flows
journal, January 1972