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Deep learning of mixing by two ‘atoms’ of stratified turbulence

Published online by Cambridge University Press:  04 January 2019

Hesam Salehipour Open the ORCID record for Hesam Salehipour [Opens in a new window]  and
W. R. Peltier
Hesam Salehipour*
Affiliation:
Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada Autodesk Research, MaRS Discovery District, 661 University Ave, Toronto, ON M5G 1M1, Canada
W. R. Peltier
Affiliation:
Department of Physics, University of Toronto, Toronto, ON M5S 1A7, Canada
*
†Email address for correspondence: [email protected]
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Abstract

Current global ocean models rely on ad hoc parameterizations of diapycnal mixing, in which the efficiency of mixing is globally assumed to be fixed at 20 %, despite increasing evidence that this assumption is questionable. As an ansatz for small-scale ocean turbulence, we may focus on stratified shear flows susceptible to either Kelvin–Helmholtz (KHI) or Holmboe wave (HWI) instability. Recently, an unprecedented volume of data has been generated through direct numerical simulation (DNS) of these flows. In this paper, we describe the application of deep learning methods to the discovery of a generic parameterization of diapycnal mixing using the available DNS dataset. We furthermore demonstrate that the proposed model is far more universal compared to recently published parameterizations. We show that a neural network appropriately trained on KHI- and HWI-induced turbulence is capable of predicting mixing efficiency associated with unseen regions of the parameter space well beyond the range of the training data. Strikingly, the high-level patterns learned based on the KHI and weakly stratified HWI are ‘transferable’ to predict HWI-induced mixing efficiency under much more strongly stratified conditions, suggesting that through the application of appropriate networks, significant universal abstractions of density-stratified turbulent mixing have been recognized.

JFM classification

Geophysical and Geological Flows: Ocean processes Turbulent Flows: Stratified turbulence Mixing: Turbulent mixing
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 861 , 25 February 2019 , R4
Copyright
© 2019 Cambridge University Press 

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References

Arthur, R. S., Venayagamoorthy, S. K., Koseff, J. R. & Fringer, O. B. 2017 How we compute N matters to estimates of mixing in stratified flows. J. Fluid Mech. 831, R2.Google Scholar
Goodfellow, I., Bengio, Y. & Courville, A. 2016 Deep Learning. MIT Press.Google Scholar
Gregg, M. C., D’Asaro, E. A., Riley, J. J. & Kunze, E. 2018 Mixing efficiency in the ocean. Annu. Rev. Mar. Sci. 10, 443–473.Google Scholar
Hinton, G. E, Srivastava, N., Krizhevsky, A., Sutskever, I. & Salakhutdinov, R. R.2012 Improving neural networks by preventing co-adaptation of feature detectors. arXiv:1207.0580.Google Scholar
Ioffe, S. & Szegedy, C.2015 Batch normalization: accelerating deep network training by reducing internal covariate shift. arXiv:1502.03167.Google Scholar
Kingma, D. P. & Ba, J.2014 Adam: a method for stochastic optimization. arXiv:1412.6980.Google Scholar
Krizhevsky, A., Sutskever, I. & Hinton, G. E. 2012 Imagenet classification with deep convolutional neural networks. In Advances in Neural Information Processing Systems, pp. 1097–1105.Google Scholar
LeCun, Y., Bengio, Y. & Hinton, G. I. 2015 Deep learning. Nature 521 (7553), 436–444.Google Scholar
Maffioli, A., Brethouwer, G. & Lindborg, E. 2016 Mixing efficiency in stratified turbulence. J. Fluid Mech. 794, R3.Google Scholar
Mashayek, A., Salehipour, H., Bouffard, D., Caulfield, C. P., Ferrari, R., Nikurashin, M., Peltier, W. R. & Smyth, W. D. 2017 Efficiency of turbulent mixing in the abyssal ocean circulation. Geophys. Res. Lett. 44 (12), 6296–6306.Google Scholar
Mater, B. D. & Venayagamoorthy, S. K. 2014 The quest for an unambiguous parameterization of mixing efficiency in stably stratified geophysical flows. Geophys. Res. Lett. 41 (13), 4646–4653.Google Scholar
Monismith, S. G., Koseff, J. R. & White, B. L. 2018 Mixing efficiency in the presence of stratification: when is it constant? Geophys. Res. Lett. 45 (11), 5627–5634.Google Scholar
Osborn, T. R. & Cox, C. S. 1972 Oceanic fine structure. Geophys. Astrophys. Fluid Dyn. 3 (1), 321–345.Google Scholar
Peltier, W. R. & Caulfield, C. P. 2003 Mixing efficiency in stratified shear flows. Annu. Rev. Fluid Mech. 35, 135–167.Google Scholar
Portwood, G. D., de Bruyn Kops, S. M., Taylor, J. R., Salehipour, H. & Caulfield, C. P. 2016 Robust identification of dynamically distinct regions in stratified turbulence. J. Fluid Mech. 807, R2.Google Scholar
Salehipour, H., Caulfield, C. P. & Peltier, W. R. 2016a Turbulent mixing due to the Holmboe wave instability at high Reynolds number. J. Fluid Mech. 803, 591–621.Google Scholar
Salehipour, H. & Peltier, W. R. 2015 Diapycnal diffusivity, turbulent Prandtl number and mixing efficiency in Boussinesq stratified turbulence. J. Fluid Mech. 775, 464–500.Google Scholar
Salehipour, H., Peltier, W. R. & Caulfield, C. P. 2018 Self-organized criticality of turbulence in strongly stratified mixing layers. J. Fluid Mech. 856, 228–256.Google Scholar
Salehipour, H., Peltier, W. R. & Mashayek, A. 2015 Turbulent diapycnal mixing in stratified shear flows: the influence of Prandtl number on mixing efficiency and transition at high Reynolds number. J. Fluid Mech. 773, 178–223.Google Scholar
Salehipour, H., Peltier, W. R., Whalen, C. B. & MacKinnon, J. A. 2016b A new characterization of the turbulent diapycnal diffusivities of mass and momentum in the ocean. Geophys. Res. Lett. 43 (7), 3370–3379.Google Scholar
Schneider, T., Lan, S., Stuart, A. & Teixeira, J. 2017 Earth System Modeling 2.0: a blueprint for models that learn from observations and targeted high-resolution simulations. Geophys. Res. Lett. 44, 12396–12417.Google Scholar
Smyth, W. D., Moum, J. & Caldwell, D. 2001 The efficiency of mixing in turbulent patches: inferences from direct simulations and microstructure observations. J. Phys. Oceanogr. 31, 1969–1992.Google Scholar
Winters, K. B., Lombard, P. N., Riley, J. J. & D’Asaro, E. A. 1995 Available potential energy and mixing in density-stratified fluids. J. Fluid Mech. 289, 115–128.Google Scholar
Wunsch, C. & Ferrari, R. 2004 Vertical mixing, energy, and the general circulation of the oceans. Annu. Rev. Fluid Mech. 36, 281–314.Google Scholar