Overview
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 twodimensional
because the
buoyancy force strongly suppresses overturning motion. Below some
length,
called the Ozmidov length scale, threedimensional 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 threedimensional 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 corehours on its largest machine to enable
such
simulations as part of its Frontier program.
Goals
 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 highenergy physics and other communities
how to efficiently share this oneofakind data with researchers
around the world
 Provide undergraduates with handson HPC experience and
summer
internships at computing centers
Collaborators
Publications
[1]

S. M. de Bruyn Kops.
Classical turbulence scaling and intermittency in stably stratified
Boussinesq turbulence.
J. Fluid Mech., 775:436463, 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. HornerDevine.
On the dynamics of turbulence near a free surface.
J. Fluid Mech., pages 248265, 2017.

[4]

S. M. Joshi, G. N. Thomsen, and P. J. Diamessis.
Deflationaccelerated preconditioning of the PoissonNeumann Schur
problem on long domains with a highorder discontinuous elementbased
collocation method.
J. Comput. Phys., 313:209232, 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, 32:24232430, 2015.
[ .pdf ]

[6]

A. Muschinski.
Optical propagation through nonoverturning, undulating temperature
sheets in the atmosphere.
J. Opt. Soc. Am. A, 33(4):793800, 2016.

[7]

A. Muschinski.
Temperature variance dissipation equation and its relevance for
optical turbulence modeling.
J. Opt. Soc. Am. A, 32:21952200, 2015.
[ .pdf ]

[8]

A. Muschinski.
NonKolmogorov turbulence.
In Proceedings of the OSA Imaging and Applied Optics Congress
(San Francisco, CA, 2629 June, 2017), pages PW2D11PW2D13, 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/nonturbulent 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.
FarField Evolution of TurbulenceEmitted 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
freeslip 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., 798:505539, 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 ]


(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 largescale horizontal motion; note the intense turbulent
patches and the nonturbulent 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
multiscale and nonlinear due to the presence of a population of such
patches.
