- Editors' Suggestion
- Access by Xinjiang University
Stratified shear instability in the cabbeling regime
Phys. Rev. Fluids 6, 084802 – Published 5 August, 2021
DOI: https://doi.org/10.1103/PhysRevFluids.6.084802
Abstract
The shear instability of stratified fluids is a well-studied problem in transition to turbulence. In temperate lakes, early springs typically lead to a weak thermal stratification involving water both above and below the temperature at which the density maximum occurs. This implies that mixing of two parcels with the same density, but different temperature, can lead to the creation of denser fluid, a phenomenon known as cabbeling. We report on simulations of shear instability in the cabbeling regime. We find that the initial stages of instability are dominated by shear instability, yielding billows. However, these billows are systematically located below the centerline of the shear layer. Three-dimensionalization occurs through Rayleigh-Taylor-like instabilities, and cabbeling efficiency is greatly increased in the fully three-dimensionalized state. By contrasting with initial states that have the same density profile, but a temperature well outside of the cabbeling regime, we demonstrate that the fully three-dimensional state of the density field is fundamentally different in the cabbeling regime.
Physics Subject Headings (PhySH)
Article Text
References (31)
- P. Hazel, Numerical studies of the stability of inviscid stratified shear flows, J. Fluid Mech. 51, 39 (1972).
- G. P. Klaassen and W. R. Peltier, The influence of stratification on secondary instability in free shear layers, J. Fluid Mech. 227, 71 (1991).
- R. T. Pierrehumbert and S. E. Widnall, The two- and three-dimensional instabilities of a spatially periodic shear layer, J. Fluid Mech. 114, 59 (1982).
- A. Mashayek and W. R. Peltier, The zoo of secondary instabilities precursory to stratified shear flow transition. Part 2. The influence of stratification, J. Fluid Mech. 708, 45 (2012).
- A. Lefauve, J. L. Partridge, Q. Zhou, S. B. Dalziel, C. P. Caulfield, and P. F. Linden, The structure and origin of confined Holmboe waves, J. Fluid Mech. 848, 508 (2018).
- A. K. Kaminski and W. D. Smyth, Stratified shear instability in a field of pre-existing turbulence, J. Fluid Mech. 862, 639 (2019).
- E. W. Tedford, R. Pieters, and G. A. Lawrence, Symmetric Holmboe instabilities in a laboratory exchange flow, J. Fluid Mech. 636, 137 (2009).
- H. Salehipour, C. P. Caulfield, and W. R. Peltier, Turbulent mixing due to the Holmboe wave instability at high Reynolds number, J. Fluid Mech. 803, 591 (2016).
- H. Van Haren and L. Gostiaux, A deep-ocean Kelvin-Helmholtz billow train, Geophys. Res. Lett. 37, L03605 (2010).
- E. W. Tedford, J. R. Carpenter, R. Pawlowicz, R. Pieters, and G. A. Lawrence, Observation and analysis of shear instability in the Fraser River estuary, J. Geophys. Res.: Oceans 114, C11006 (2009).
- W. D. Smyth, J. D. Nash, and J. N. Moum, Self-organized criticality in geophysical turbulence, Sci. Rep. 9, 3747 (2019).
- S. Groeskamp, R. P. Abernathey, and A. Klocker, Water mass transformation by cabbeling and thermobaricity, Geophys. Res. Lett. 43, 10,835 (2016).
- M. J. Andrews and S. B. Dalziel, Small Atwood number Rayleigh-Taylor experiments, Philos. Trans. R. Soc. A 368, 1663 (2010).
- G. Kirillin, M. Leppäranta, A. Terzhevik, N. Granin, J. Bernhardt, C. Engelhardt, T. Efremova, S. Golosov, N. Palshin, P. Sherstyankin, G. Zdorovennova, and R. Zdorovennov, Physics of seasonally ice-covered lakes: A review, Aquatic Sci. 74, 659 (2012).
- B. Yang, J. Young, L. Brown, and M. Wells, High-frequency observations of temperature and dissolved oxygen reveal under-ice convection in a large lake, Geophys. Res. Lett. 44, 12,218 (2017).
- J. W. Cooper, Natural convection in a horizontal layer of water cooled from above to near freezing, J. Heat Transf. 97, 47 (1975).
- P. Vasseur and L. Robillard, Transient natural convection heat transfer in a mass of water cooled through , Int. J. Heat Mass Transfer 23, 1195 (1980).
- D. S. Lin and M. W. Nansteel, Natural convection heat transfer in a square enclosure containing water near its density maximum, Int. J. Heat Mass Transf. 30, 2319 (1987).
- H. N. Ulloa, K. B. Winters, A. Wüest, and D. Bouffard, Differential heating drives downslope flows that accelerate mixed-layer warming in ice-covered waters, Geophys. Res. Lett. 46, 13872 (2019).
- C. P. Caulfield and W. R. Peltier, The anatomy of the mixing transition in homogeneous and stratified free shear layers, J. Fluid Mech. 413, 1 (2000).
- L. N. Thomas and C. J. Shakespeare, A new mechanism for mode water formation involving cabbeling and frontogenetic strain at thermohaline fronts, J. Phys. Oceanogr. 45, 2444 (2015).
- B. Akula, P. Suchandra, M. Mikhaeil, and D. Ranjan, Dynamics of unstably stratified free shear flows: An experimental investigation of coupled Kelvin–Helmholtz and Rayleigh–Taylor instability, J. Fluid Mech. 816, 619 (2017).
- B. J. Olson, J. Larsson, S. K. Lele, and A. W. Cook, Nonlinear effects in the combined Rayleigh-Taylor/Kelvin-Helmholtz instability, Phys. Fluids (1994) 23, 114107 (2011).
- P. K. Kundu, I. M. Cohen, and H. H. Hu, Fluid Mechanics (Academic Press, New York, 2002), p. 730.
- D. Brydon, S. Sun, and R. Bleck, A new approximation of the equation of state for seawater, suitable for numerical ocean models, J. Geophys. Res. 104, 1537 (1999).
- C. J. Subich, K. G. Lamb, and M. Stastna, Simulation of the Navier-Stokes equations in three dimensions with a spectral collocation method, Int. J. Numer. Methods Fluids 73, 103 (2013).
- Q. Lian, W. D. Smyth, and Z. Liu, Numerical computation of instabilities and internal waves from in situ measurements via the viscous Taylor–Goldstein problem, J. Atmos. Ocean. Technol. 37, 759 (2020).
- L. N. Trefethen, Spectral Methods in MatLab (Society for Industrial and Applied Mathematics, Philadelphia, PA, 2000).
- J. Olsthoorn, E. W. Tedford, and G. A. Lawrence, Diffused-interface Rayleigh-Taylor instability with a nonlinear equation of state, Phys. Rev. Fluids 4, 094501 (2019).
- W. D. Smyth and K. B. Winters, Turbulence and mixing in Holmboe waves, J. Phys. Oceanogr. 33, 694 (2003).
- S. Khani and M. L. Waite, Large eddy simulations of stratified turbulence: The dynamic Smagorinsky model, J. Fluid Mech. 773, 327 (2015).