The velocity perturbations and Reynolds stresses associated with finite-amplitude Holmboe instabilities are investigated using linear stability analysis, numerical simulations, and laboratory experiments. The rightward and leftward propagating Holmboe instabilities are separated, allowing for a direct comparison of the perturbation fields between the numerical simulations and the linear stability analysis. The decomposition and superposition of the perturbation fields provide insights into the structure and origin of Reynolds stresses in Holmboe instabilities. Shear instabilities in stratified flows introduce a directional preference (anisotropy) in velocity perturbation fields, thereby generating Reynolds stresses. Here, we investigate this anisotropy by comparing pairs of horizontal and vertical velocity perturbations (), obtained from the simulations and the laboratory experiment, with predictions from linear stability analysis. For an individual Holmboe mode, both the simulations and linear theory yield elliptical ()-pairs that are oriented toward the second and fourth quadrants (), corresponding to the tilted elliptical trajectories of particle movement. Combining the leftward and rightward Holmboe modes yields () ellipses whose orientation and aspect ratio are phase-dependent. When averaged over a full cycle, the joint probability density functions of () in the linear theory and single wavelength simulations exhibit “steering wheel” structures. This steering wheel is smeared out in multiple wavelength simulations and the laboratory experiment due to varying wavelengths, resulting in an elliptical cloud. All of the approaches adopted in the present study yield Reynolds stresses that are comparable to those reported in previous laboratory and field investigations.
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July 2022
Research Article|
July 08 2022
Velocity perturbations and Reynolds stresses in Holmboe instabilities
Adam J. K. Yang (杨健康)
;
Adam J. K. Yang (杨健康)
a)
(Data curation, Formal analysis, Investigation, Methodology, Writing – original draft, Writing – review & editing)
1
Department of Civil Engineering, University of British Columbia
, Vancouver, British Columbia V6T1Z4, Canada
a)Author to whom correspondence should be addressed: [email protected]
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E. W. Tedford;
E. W. Tedford
(Data curation, Formal analysis, Investigation, Methodology, Writing – original draft, Writing – review & editing)
1
Department of Civil Engineering, University of British Columbia
, Vancouver, British Columbia V6T1Z4, Canada
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J. Olsthoorn
;
J. Olsthoorn
(Data curation, Formal analysis, Investigation, Methodology, Writing – original draft, Writing – review & editing)
1
Department of Civil Engineering, University of British Columbia
, Vancouver, British Columbia V6T1Z4, Canada
2
Department of Civil Engineering, Queen’s University, Kingston
, Ontario K7L 3N6, Canada
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A. Lefauve
;
A. Lefauve
(Data curation, Formal analysis, Investigation, Writing – review & editing)
3
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
, Cambridge CB3 0WA, United Kingdom
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G. A. Lawrence
G. A. Lawrence
(Data curation, Formal analysis, Funding acquisition, Investigation, Methodology, Supervision, Writing – original draft, Writing – review & editing)
1
Department of Civil Engineering, University of British Columbia
, Vancouver, British Columbia V6T1Z4, Canada
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E. W. Tedford
1
J. Olsthoorn
1,2
A. Lefauve
3
G. A. Lawrence
1
1
Department of Civil Engineering, University of British Columbia
, Vancouver, British Columbia V6T1Z4, Canada
2
Department of Civil Engineering, Queen’s University, Kingston
, Ontario K7L 3N6, Canada
3
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
, Cambridge CB3 0WA, United Kingdom
a)Author to whom correspondence should be addressed: [email protected]
Physics of Fluids 34, 074110 (2022)
Article history
Received:
April 30 2022
Accepted:
June 11 2022
Citation
Adam J. K. Yang, E. W. Tedford, J. Olsthoorn, A. Lefauve, G. A. Lawrence; Velocity perturbations and Reynolds stresses in Holmboe instabilities. Physics of Fluids 1 July 2022; 34 (7): 074110. https://doi.org/10.1063/5.0097624
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