ONR logo

HPCMP Frontier Project

HPCMP logo

Multiscale Interactions in Stratified Turbulence


Fluid turbulence subjected to a stabilizing density gradient erupts in spatiotemporally intermittent patches, a phenomenon termed "stratified turbulence,'' with which we are all familiar from riding in airplanes. In addition to being patchy, stratified turbulence involves an enormous range of length scales, which are evident in figure to the right. At larger scales, the turbulence is highly anisotropic and approximately two-dimensional because the buoyancy force strongly suppresses overturning motion. Below some length, called the Ozmidov length scale, three-dimensional turbulence can occur. At an even smaller length, termed the Kolmogorov length scale, turbulent motion is suppressed by viscous forces. The ratio of the Ozmidov to the Kolmogorov lengths scales is related to the buoyancy Reynolds number which characterizes the dynamic range over which three-dimensional turbulence can occur in a stratified flow.

For research simulations to help answer questions about atmospheric and ocean turbulence at engineering length scales, they must have buoyancy Reynolds numbers near the limit of current high performance computers. The U.S. Department of Defense High Performance Computing Modernization Program has provided 750 million core-hours on its largest machine to enable such simulations as part of its Frontier program.


  • Simulate stratified turbulence using 500 billion to 1 trillion grid points so that the buoyancy Reynolds number is high enough to be relevant to the atmosphere and ocean
  • Use simulations to understand stratified turbulence, model it, and improve the assumptions inherent in measuring it with optical sensors
  • Learn from the high-energy physics and other communities how to efficiently share this one-of-a-kind data with researchers around the world
  • Provide undergraduates with hands-on HPC experience and summer internships at computing centers



[1] S. M. de Bruyn Kops. Classical turbulence scaling and intermittency in stably stratified Boussinesq turbulence. J. Fluid Mech., 775:436--463, 2015. [ .pdf ]
[2] S. M. de Bruyn Kops, J. J. Riley, and G. D. Portwood. Toward direct numerical simulations of the stratified turbulence inertial range. In Proceedings of the 8th International Symposium on Stratified Flows, San Diego, CA, 2016. [ http ]
[3] O. Flores, J. J. Riley, and A. R. Horner-Devine. On the dynamics of turbulence near a free surface. J. Fluid Mech., pages 248--265, 2017.
[4] S. M. Joshi, G. N. Thomsen, and P. J. Diamessis. Deflation-accelerated preconditioning of the Poisson-Neumann Schur problem on long domains with a high-order discontinuous element-based collocation method. J. Comput. Phys., 313:209--232, 2016. [ .pdf ]
[5] A. Muschinski and S. M. de Bruyn Kops. Investigation of Hill's optical turbulence model by means of direct numerical simulation. J. Opt. Soc. Am. A, 32:2423--2430, 2015. [ .pdf ]
[6] A. Muschinski. Optical propagation through non-overturning, undulating temperature sheets in the atmosphere. J. Opt. Soc. Am. A, 33(4):793--800, 2016.
[7] A. Muschinski. Temperature variance dissipation equation and its relevance for optical turbulence modeling. J. Opt. Soc. Am. A, 32:2195--2200, 2015. [ .pdf ]
[8] A. Muschinski. Non-Kolmogorov turbulence. In Proceedings of the OSA Imaging and Applied Optics Congress (San Francisco, CA, 26-29 June, 2017), pages PW2D1--1--PW2D1--3, 2017.
[9] G. D. Portwood, S. M. de Bruyn Kops, J. R. Taylor, H. Salehipour, and C. P. Caulfield. Robust identification of dynamically distinct regions in stratified turbulence. J. Fluid Mech., 807:R2 (14 pages), 2016. [ .pdf ]
[10] T. Watanabe, J. J. Riley, S. M. de Bruyn Kops, P. J. Diamessis, and Q. Zhou. Turbulent/non-turbulent interfaces in wakes in stably stratified fluids. J. Fluid Mech., 797:R1 (11 pages), 2016. [ .pdf ]
[11] T. Watanabe, J. J. Riley, and K. Nagata. Effects of stable stratification on turbulent/nonturbulent interfaces in turbulent mixing layers. Phys. Rev. Fluids, 1:044301, 2016. [ .pdf ]
[12] J. J. Riley T. Watanabe, K. Nagata, R. Onishi, and K. Matsuda. A localized turbulent mixing layer in a uniformly stratified environment. J. Fluid Mech., submitted.
[13] Qi Zhou. Far-Field Evolution of Turbulence-Emitted Internal Waves and Reynolds Number Effects on a Localized Stratified Turbulent Flow. PhD thesis, Cornell University, 2015. [ http ]
[14] Q. Zhou and P. J. Diamessis. Lagrangian flows within reflecting internal waves at a horizontal free-slip surface. Phys. Fluids, 27(12):Article no. 126601, 2015. [ .pdf ]
[15] Q. Zhou and P. J. Diamessis. Surface manifestation of internal waves emitted by submerged localized stratified turbulence. J. Fluid Mech., 798:505--539, 2016. [ .pdf ]
[16] Q. Zhou and P. J. Diamessis. Reynolds number effects in stratified turbulent wakes. In Proceedings of the 8th International Symposium on Stratified Flows, San Diego, CA, 2016. [ http ]
Vertical velocity in unstratified turbulence
Vertical velocity in stratified turbulence
(Click on images)
Vertical velocity on a horizontal plane in high resolution simulations of turbulence. Dark color indicates upward flow, light color downward flow. On the top is unstratified turbulence. On the bottom is stratified turbulence that is driven by large-scale horizontal motion; note the intense turbulent patches and the non-turbulent region near the top center of the image. Unless very wide ranges of length and time scales are included, simulations of stratified turbulence can neither replicate individual patches of turbulence nor provide information on their sizes and lifetimes; this is because stratified turbulence is inherently multi-scale and nonlinear due to the presence of a population of such patches.

Return to Turbulence Simulation Laboratory