Statistical analysis of high-Rayleigh

Statistical analysis of high-Rayleigh-number
turbulent convection data (SBDA003)
Ambrish Pandey1,3, Janet D. Scheel2 and Jörg Schumacher1
1Institute
of Thermodynamics and Fluid Mechanics,Technische Universität Ilmenau, Germany
2Department of Physics, Occidental College, Los Angeles, USA
3Department of Physics, Indian Institute of Technology, Kanpur, India
Motivation
2. Extreme thermal dissipation events
1.  Analysis of the large-scale circulation in the closed convection cell by
means of Proper Orthogonal Decomposition
Full cell
2.  Analysis of the evolution of extreme events of thermal dissipation and
kinetic energy dissipation
Bulk volume
Level 0
Track 4th-order moment of
thermal dissipation rate
Original production run
3.  Analysis of energy spectra in the bulk of convection cell and comparison with Kolmogorov spectra in isotropic turbulence of ref. [2]
(0)
tout ⇡ 0.72Tf
Rayleigh-Bénard (RB) Simulation Model
@~u
1
+ (~u · r)~u =
rp + ⌫r2 ~u + g↵(T
@t
⇢0
r · ~u = 0
@T
+ (~u · r)T = r2 T
@t
Level 1
Formation of the temperature
front between two colliding
plumes
1st rerun with finer data output
T0 )~ez
(1)
tout =
Level 2
Detailed analysis of the
production terms in the
gradient balance equations
2nd rerun with finest output
Spectral element method (nek5000) with polynomials of order N=13 [1]. Production jobs on up to 131,072 BG/Q cores for small-scale structure studies.
(2)
tout =
•  Total amount of simulation data (9 parameter sets): approx. 45 Tbyte
1 (0)
t
5 out
1
(1)
t
10 out
Extreme
Dissipation
Event
•  One simulation snapshot for the biggest simulation for RB convection in a
liquid metal flow = 130 GByte
Thermal
Plume
Collision
•  Data in subvolumes of the original unstructured element mesh have been
spectrally interpolated onto a uniform Cartesian or cylindrical grids.
•  Support by JSC personel for improvement of parallel IO.
•  Analysis of different
temperature and
velocity gradient
production terms shows
that energy dissipation
lags behind thermal
dissipation
1. Proper Orthogonal Decomposition of data
•  Extreme event is
caused by cessastion
of large-scale flow
References
•  Expansion of velocity and temperature data into a basis of empirical
orthogonal modes which are sorted with respect to their kinetic energy
(see left panel) and/or scalar variance
•  Subtraction of large-scale velocity and temperature fields from original
data
•  Analysis of derivative moments of the remaining fields (see right panel)
does not change the scaling results which were reported in [3].
[1] J. D. Scheel, M.S. Emran and J. Schumacher, Resolving the fine-scale structures
in turbulent Rayleigh-Bénard convection, New. J. Phys.15, 113063 (2013).
[2] A. Kumar, A. G. Chatterjee and M. K. Verma, Energy spectrum of buoyancydriven turbulence, Phys. Rev. E 90, 023016 (2014).
[3] J. Schumacher, J. D. Scheel, D. Krasnov, D. A. Donzis, V. Yakhot and K. R.
Sreenivasan, Small-scale universality in fluid turbulence, Proc. Natl. Acad. Sci.
USA 111, 10961-10965 (2014).