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GTP : Geophysical Turbulence Program and TNT : Turbulence Numerics Team IMAGe Advisory board Boulder, January 26, 2009. Geophysical Turbulence Program. GTP has been in existence almost since the beginning of NCAR
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GTP: Geophysical Turbulence Program and TNT: Turbulence Numerics Team IMAGe Advisory boardBoulder, January 26, 2009
Geophysical Turbulence Program • GTP has been in existence almost since the beginning of NCAR (Deardorff, Gilman, Herring, Leith, Lilly, Lorenz, McWilliams, Orszag, Patterson, Thompson, …) History: see Herring, in IUTAM Symposium, Kerr & Kimura Eds, Kluwer (2000) • 40+ members across all divisions and labs at NCAR + a few external universities (CU, Dartmouth, LANL, Nagoya, Penn State, UCLA, Warwick) • GTP, @ $50k, is ~ 10% of the GTP+TNT combined budgets Imperative: cross-cutting research with outreach • Support research on turbulent flows in a variety of contexts, with focused topics drawing on GTP seed funds • Short-term (3-day) visitors, with a ``monthly’’ seminar program • Long-term visitors, for one week [to one year, very rarely possible] • Workshops[and schools, 2 in 20 years] • For the last two years: small partial support for graduate students URGENCY: TO INVOLVE THE YOUNGER GENERATION
``The atmospheric and oceanic boundary layers may be the most crucial ingredients in hurricane dynamics despite their small vertical extent’’ (K. Emanuel, 2004) . . . . . . . Peter Sullivan (ESSL/MMM - GTP): Boundary layers SST Cold water hurricane wake generated by ocean turbulence and surface wave effects Large eddy simulations and modeling of turbulent flows and of boundary layers in complex geophysical flows, with multi-scale dynamics and physical processes. Transition wave - turbulence Storm track High wind atmospheric PBL 25m/s Breaking waves, spray, bubbles, turbulence?
Joe Tribbia (ESSL-CGD & GTP), with Jim McWilliams (UCLA-GTP) Pathway to dissipation in the atmosphere and ocean Thermal / mechanical driving on planetary scale Thin instabilities (baroclinic, frontal) drive inertial cascades to non-rotational scales Further instabilities (K-H, convective) needed to get to 3D isotropic turbulence and dissipation, and transport processes No complete GFD simulation to date. It must span a 2D range from 106 m to 10-100m (3D Turbulence), waves and anisotropy (rotation and/or stratification and/or magnetic fields and/or bottom topography …)
GTP possible mission statement • The Geophysical Turbulence Program at NCAR investigates nonlinear multi-scale eddy-wave interactions for a wide range of geophysical and astrophysical flows. It also develops, analyzes and validates analytical and phenomenological models, numerical methods and experiments as tools for UCAR and for the university community, here and abroad. • Retreat + meeting of GTP to be organized in 2009 (Joe Tribbia) • To be followed by a meeting of a small advisory board (as per the request of the NCAR review panel many years ago …)
GTP seminars in 2007 and/or 2008 J. Baerenzung (NCAR): Spectral modeling of utrbulent fluids G. Boffetta (LANL): Two-dimensional turbulence. C. Bustamante (U. Warwick): Singularities of the Euler equations. P. Hamlington (U. Mich.:, Reynolds stress anisotropy and vorticity alignment. S. Heinz (U. Wyoming): Unified stochastic and deterministic turbulence models (07). J. Liu (CSU): Characteristic methods for fluid transport problems. D. Stanescu (U. Wyoming): Discontinuous Galerkin methods (07). A. Tuck (NOAA): A molecular view of vorticity and turbulence. V. Uritsky (U. Calgary): Self-organized criticality. … …MHD (W-C Müller, W-H Matthaeus, …)
GTP visitors and graduate students - 07 &/or 08 M-E Brachet, ENS-Paris: codes with symmetries in MHD, RK4 and Euler flow with helicity. J.F. Cossette (grad. student, U. Montreal, with Piotr Smolarkiewicz): Semi-Lagrangian schemes. M. Damron (grad. student, U. Arizona, with Larry Winter): a non-Markovian model of rill erosion. J. Finnigan (Commonwealth Scient.): Canopy turbulence in roughness sub-layers D. Jarecka (grad. student, U. Warsaw, with Wojciech Grabowski): Impact of entrainment and mixing on cloud dynamics and microphysics. H. Jonker, U. Delft: A refined view of vertical transport by cumulus convection. P. Ortiz, U. Granada: Coupled dynamics of boundary layers & evolutionary landforms like dunes. Z. Piotrowski, U. Warsaw: Numerical realizability of thermal convection. L-P Wang, U. Delaware: Turbulent collision-coalescence of cloud droplets and impact on warm rain initiation.
Collision-coalescence processes in cloud microphysicsWang, Franklin, Ayama & Grabowski - ESSL/MMM-GTP • PDF of angle of approach of colliding droplets: dominance of inward relative motion due to turbulence • Solid line: model with turbulence black dots: Direct Numerical Simulation (DNS)
GTP/TNT workshops 08 Theme of year: 3-wks Summer School & 3 wkshps (K. Julien @CU, CISL-EOL-ESSL-RAL) * Theory and modelingof Geophysical Turbulence: LANL (B. Wingate) + Wisconsin (L. Smith) * Petascale computing for Geophysical Turbulence: CORA (J. Werne) + UCLA (B. Stevens) * Observations and sensors: RAL (L. Cornman) + EOL (S. Oncley) + ESSL (R. Lenschow) (J. Fernando [AZ] in charge of the Observation week of the summer school) No magnetic field in TOY-08 … 2009?: Turbulent mixing in the upper ocean & boundary layers (W. Large, ESSL-CGD) 2010: Rotating stratified flows (V. Zeitlin, Paris et al.) Past workshops: • Turbulence and Dynamos at Petaspeed (2007) • Turbulence and Scalar Transport in Roughness Sub-layers (2006) • Modeling MHD turbulence with applications to planetary and stellar dynamos (2006) • Theme of the Year (TOY-06) on Multi-scale modeling(one workshop sponsored) • Coherent Structures in the Atmosphere and Ocean (2005) • Atmospheric Turbulence and Mesoscale Meteorology (2005) • Cumulus Parameterization in the Context of Turbulence Studies (2004)
A sample of GTP-supported research [1] • G. Branstator (ESSL-CGD) & J. Berner (now in MMM): distinct signatures of nonlinearity in climate dynamics • W. Grabowski (ESSL-MMM): Parameterization of small-scale and micro-scale processes in models resolving larger scales • J. Herring (ESSL-MMM): Stratified turbulence • R. Lenschow (ESSL-MMM): Analysis of C-HATS experiment (Horizontal Array Turbulence Studies, + Oceans, Canopies, Anisotropy) • C-H Moeng (ESSL-MMM) with J. McWilliams (UCLA), R. Rotunno (MMM), P. Sullivan (MMM) & J. Weil (CIRES/CU) : Evaluation of two-dimensional Planetary Boundary Layer (PBL) models using Large Eddy Simulations (LES)
Peter Sullivan, ESSL-MMM -& GTP:Passive versus active scalar in the dry PBL using LES in a large domain 10002X128 or 502km X 6km(comparable to a field campaign) Passive scalar is at large scales Dynamically active scalar is at the velocity scale (depth of PBL)
A sample of GTP-supported research [2] • M. Rast (CU): Convection + ionisation in the solar convection zone • P. Sullivan (ESSL-MMM) et al.:wind-wave interactions; • J. Tribbia (ESSL-CGD): Multi-scale and climate New! • J. Berner (ESSL-MMM) et al.: stochastic parametrization for numerical weather prediction (NWP) with flow-dependent formulation of unresolved processes
Stream function perturbations with a prescribed kinetic energy spectrum: • Successfully applied to probabilistic NWP (ECMWF pseudo-spectral model) by Shutts (2005), and Berner et al. (2009). • Ongoing: Implementation into WRF limited-area ensemble model using 2D planar Fourier analysis. • Preliminary Result:the Brier score of u is improved (shown is score for events 0 < u < (p), where (p) is climatological standard deviation at pressure p), but more samples are needed. Stochastic parameterization of spectral backscatter for NWP and climate model-errorJ. Berner, A. Fournier, S-Y. Ha, J. Hacker & C. Snyder
Action item for GTP Commonality of issues in fundamental multi-scale dynamics for the Earth’s atmosphere and ocean, and for solar and solar-terrestrial physics • Request for a quadrupling of the funds (50k 200k): • Create a GTP Post-doctoral fellow • Create a GTP Graduate student position • Create a sabbatical GTP visitor The over-arching goal is to investigate and model turbulent flows in weather, climate, solar physics and space weather
Action item for GTP Commonality of issues in fundamental multi-scale dynamics for the Earth’s atmosphere and ocean, and for solar and solar-terrestrial physics • Request for a quadrupling of the funds (50k 200k): • Create a GTP Post-doctoral fellow • Create a GTP Graduate student position • Create a sabbatical GTP visitor Decision making process: annual meeting of GTP members (+) The over-arching goal is to investigate and model turbulent flows in weather, climate, solar physics and space weather
Core of 2.85 FTE + 1 GRA + 1 post-doc Pablo Mininni Scientist 1 @ 0.25 Aimé Fournier Project Sc. @1 FTE AP @ 0.6 Duane Rosenberg, Software Eng. III, @ 1 FTE TNT Team yesterday Julien Baerenzung, Post-doc, 1 FTE (until June 2009) Ed Lee, GRA, 0.5 FTE (until January 22, 2009)
75% at Buenos Aires 40% deputy director of ESSL Core of 2.85 FTE + 1 GRA + 1 post-doc Pablo Mininni Scientist 1 @ 0.25 Aimé Fournier Project Sc. @1 FTE AP @ 0.6 Duane Rosenberg, Software Eng. III, @ 1 FTE TNT Team yesterday Julien Baerenzung, Post-doc (until June 2009) Ed Lee, GRA, 0.5 FTE (until January 22, 2009)
Core of 1.85 FTENo GRA and no post-docTwo NSF gants submitted in 2008 At some point in June 2009:
Imperative • Investigate the basic properties of multi-scale flows • Exploit their commonality-multi-scale interactions, nonlinear phenomena, geophysical turbulence, eddies and waves * Analyze data and implement a variety of turbulence models • Seed theapplications for the Earth and beyond: atmosphere, ocean, PBL, solar physics and space weather • To that effect, develop, test and make availablea suite of tools and data sets @ petascaleand beyond (computing, and also accessing, visualizing, analyzing & sharing the data)
Imperative • Investigate the basic properties of multi-scale flows At the highest possible Reynolds number(s) • Exploit their commonality-multi-scale interactions, nonlinear phenomena, geophysical turbulence, eddies and waves * Analyze data and implement a variety of turbulence models • Seed theapplications for the Earth and beyond: atmosphere, ocean, PBL, solar physics and space weather • To that effect, develop, test and make availablea suite of tools and data sets @ petascaleand beyond (computing, and also accessing, visualizing, analyzing & sharing the data)
Basic research by way of two large runs done at NCAR with GHOST on 15363points,thanks to BTS and ASD allocations I. 2006: Magnetohydrodynamics (MHD), without rotation • First evidence of a dual direct energy cascade:isotropic k-3/2 at large scale, anisotropic k-2weak turbulence at small scale in the highest-ever Reynolds MHD run • First numerical evidence of rolling up of vorticity & current sheets R ~ 1700 GHOST Pablo Mininni et al.
Going beyond, with the help of symmetries • First evidence of lack of universality in decaying MHD without a uniform magnetic field (20483 equiv. grid): Taylor-Green flow, 3 runs, 3 different energy spectra Collision of two current sheets (viz.: VAPOR, CISL) Ed Lee et al. Phys. Rev. E 2008/12 kaleidoscope MAYTAG
Going beyond, with the help of symmetries • First evidence of lack of universality in decaying MHD without a uniform magnetic field (20483 equiv. grid): Taylor-Green flow, 3 runs, 3 different energy spectra Ed Lee et al., in preparation Collision of two current sheets (viz.: VAPOR, CISL) Ed Lee et al. Phys. Rev. E 2008/12 kaleidoscope MAYTAG
Going beyond[2] Developing, testing, or using models for fluid & MHD turbulence: * Chollet-Lesieur model * Lagrangian averaged model (D. Holm, …) * Spectral model based on EDQNM(two-point turbulence closure) ^ with eddy viscosity incorporating helical terms ^ with eddy noise incorporating phase information ^ for any energy spectrum (Julien Baerenzung et al.) Applications to Navier-Stokes (including rotation) and MHD
Second large run at NCAR R ~ 1100 , Ro = 0.05 GHOST II. 2008: Rotation with helical forcing, without magnetic field • First evidence of a non-intermittent and non-Kolmogorovian direct energy cascade at low Rossby number, governed by the direct cascade of helicity (h+e=4), together with an inverse cascade of energy • First evidence of the persistence of strong cyclonic events in rotating turbulence in the presence of helicity, together with strongly turbulent columnar structures Pablo Mininni et al. Vorticity magnitude (zoom), above a threshold
Second large run at NCAR II. In 2009: * Analysis and modeling of the large run with rotation and helical forcing R ~ 1100 , Ro = 0.05 • Parametric study using the model TBD Thanks to a special CISL 5 mo. post-doc allocation for JB Closer look of vorticity magnitude, above a threshold: cohabitation
Going beyond: Modeling of rotating flows Model: Eddy viscosity and eddy noise with variable index energy spectrum Tests on non-helical flows down to Rossby numbers of 0.02 Fig.: Build-up of anisotropy over time Julien Baerenzung et al., in preparation Taylor-Green flow GHOST + X
Adaptive Mesh Refinement2D-Navier-StokesAimé Fournier et al., 2008 • Decay for long times (incompressible) • Formation of dipolar vortex structures • Gain in the number of degrees of freedom (~ 4) with AMR, compared to an equivalent pseudo-spectral code (periodic boundary conditions) GASPAR
Spectral AMR • The need for accuracy in adaptive mesh refinement, when looking at max. norms (Fig.: current in 2D-MHD reconnection) Duane Rosenberg et al (2007) Also: Development of optimized Schwarz preconditioning, in collaboration with Amik St Cyr New: Implementation of a conservative energy scheme (AF +DR) GASPAR
Available TNT tools • GASpAR: High-order adaptive Mesh Refinement code for turbulent flow, and a PDE framework for adaptive mesh solutions * Future: Boussinesq equations, 3D-MHD, Planetary Boundary Layer • GHOST: Primary production pseudo-spectral code for turbulent flows Modular numerics and physics: 2D/ 3D; compressibility; (Hall)-MHD; rotation * Plans: * Stratification, and implementation of (several) LES * Upgrade for petascale and beyond (today: up to ~ 4000 proc.) ^^^^^^^^^^ • Other code: MAYTAG:MAgnetohYdrodynamics TAylor-Green code with enforced symmetries leading to a gain of 32 in CPU / storage Code developed in F’08by M-E Brachet (ENS Paris)
Available high Reynoldsnumber numerical data sets (runs performed at NCAR, NERSC and Pittsburgh) • Navier-Stokes: ^ Taylor-Green (TG) flows, 20483 grids ^ ABC flows, 20483 grids • Navier-Stokes with rotation: ABC, decay,15363 grid • MHD: ^ 10243 forced dynamo runs; ^ 15363 grid, decaying flow; ^ 20483 equivalent grids with imposed TG symmetries Taylor Reynolds numbers of 1100 or above
New research directions 1- Basic research in rotating turbulent flows (in progress): Numerical simulations, phenomenological approach, and spectral modeling (with helicity and with eddy noise) 2 - Stratified turbulent flows (GHOST) (with/without rotation, boundaries, passive tracer; & numerical adaptivity) Potential targeted applications to the stable planetary boundary layer (with Peter Sullivan, ESSL; & Rod Frechlich, RAL) and to aircraft safety(with Larry Cornman, RAL) 3 - Bottom topography using non-uniform mesh (GASPAR)
New needs: Action items for TNT 1- Basic research in rotating turbulent flows (in progress): Numerical simulations, phenomenological approach, and spectral modeling 2 - Stratified turbulent flows (with/without rotation, boundaries, passive tracer; and numerical adaptivity). Potential targeted applications to the stable planetary boundary layer and to aircraft safety (with ESSl and RAL) 3 - Bottom topography, using mesh adaptivity A- Tools for the community (GASPAR, GHOST), going to petascale and beyond B- High-Reynolds number data sets for the community, and how to handle these data sets • A- Sustain the TNT team at its present level • B- Recruit in TNT a Scientist 1 or Scientist 2 in weather/climate turbulence and its modeling C- Obtain substantial computer resources including in the team
TNT collaborations at NCAR, past and present: Tom Bogdan (now at NOAA), Paul Charbonneau (now at Montreal), John Clyne (CISL), Larry Cornman (RAL), Rod Frehlich (RAL and CU), Jack Herring (emeritus, ESSL-M3), Han-Li Liu (ESSL-HAO), Alan Norton (CISL), Amik St Cyr (IMAGE-CISL), Peter Sullivan (ESSL-MMM), Joe Tribbia (ESSL-CGD), … TNT collaborations outside NCAR, past and present: A. Alexakis (Paris), F. Baer (U. Md), A. Bhattacharjee (UNH), M-E Brachet (Paris), B. Breech (U Del.), M. Bustamante (Dublin), V. Carbone (Calabria), C. Cartes (Santiago), S. Cowley (UCLA), P. Dmitruk (Buenos Aires), P. Fisher (Argonne), S. Galtier (Orsay), K. Germaschewski (UNH), J. Graham (Lindau), D. Holm (Imperial, LANL), G. Krstulovic (Paris), D. Lathrop (U. Md), W-H Matthaeus (Bartol), D. Montgomery (Dartmouth), C-S Ng (Alaska), J-F Pinton (Lyon), H. Politano (Nice), Y. Ponty (Nice), J. Toomre (CU), M. Rast (CU), R. Reddy (PSC), J. Riley (U. Washington), M. Taylor (Sandia), L. Turner (Cornell), V. Uristsky (Calgary), H. Wang (U. Md), …
Publications with reviewers, 2007-2009 [1] • Alexakis, A., P. D. Mininni, A. Pouquet, 2007: Turbulent cascades, transfer, and scale interactions in magnetohydrodynamics. New J. Phys., 9, 298, doi: 10.1088/1367-2630/9/8/298. • Baerenzung, J., H. Politano, Y. Ponty, A. G. Pouquet, 2008: Spectral modeling of turbulent flows and the role of helicity. Phys. Rev. E, 77, 046303, doi: 10.1103/PhysRevE.77.0463033 • J. Baerenzung, H. Politano, Y. Ponty and A. Pouquet,, `Spectral Modeling of Magnetohydrodynamic Turbulent Flows,'’ Phys. Rev. E 78, 026310 (2008). • Carbone, V., A. G. Pouquet, 2008: An introduction to fluid and MHD turbulence for astrophysical flows: Theory, observational and numerical data and modeling. Invited set of Lectures EEC School on Astrophysical Plasmas, L Vlahos and P Cargill, Ed., Springer-Verlag, 69-131 • Carlos Cartes, Miguel D. Bustamante, Annick Pouquet, Marc E. Brachet,Generalized Eulerian-Lagrangian description of Navier-Stokes and resistive MHD dynamics,'' Fluid Dyn. Res, 41, 011404 (2009). • Clyne, J., P. Mininni, A. Norton, M. Rast, 2007: Interactive desktop analysis of high resolution simulations: Applications to turbulent plume dynamics and current sheet formation. New J. Phys., 9, 301, doi: 10.1088/1367-2630/9/8/301. • Cowley, S., J.-F. Pinton, A. Pouquet, 2007: Focus on magnetohydrodynamics and the dynamo problem. New J. Phys., 9, E04, doi: 10.1088/1367-2630/9/8/E04 • A. Fournier, D. Rosenberg and A. Pouquet, ``Dynamically adaptive spectral-element simulations of 2D incompressible Navier-Stokes vortex decays,'' to appear, GAFD, Special issue `` Vortex dynamics from quantum to geophysical scales,'’ Guest Editors: C. Barenghi, D. Dritschel and A. Gilbert (2008). • Graham Pietarila, J., D. D. Holm, P. Mininni, A. G. Pouquet, 2008: Three regularization models of the Navier-Stokes equations. Phys. Fluids, 20, 035107, doi: 10.1063/1.2880275. • Graham Pietarila, J., D. Holm, P. Mininni, A. G. Pouquet, 2008: Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes alpha model and their large-eddy-simulation potential. Phys. Rev. E, 75, 056310, doi: 10.1103/PhysRevE.76.056310. • J. Pietarila Graham, P.D. Mininni, and A. Pouquet, The Lagrangian-averaged model for magnetohydrodynamic turbulence and the absence of bottleneck, Phys. Rev. E, to appear (2009). • E. Lee, M.E. Brachet, A. Pouquet, P.D. Mininni and D. Rosenberg,``A paradigmatic flow for small-scale magnetohydrodynamics,'’ Phys. Rev. E 78, 066401 (2008). • Matthaeus, W. H., A. G. Pouquet, P. Mininni, P. Dmitruk, B. Breech, 2008: Rapid directional alignment of velocity and magnetic field in magnetohydrodynamic turbulence. Physical Review Letters, 100, 085003, doi: 10.1103/PhysRevLett.100.085003.
[2] * P.D. Mininni, A. Alexakis and A. Pouquet, Scale interactions and scaling laws in rotating flows at moderate Rossby numbers and large Reynolds numbers,'' Phys. Fluids 21, 015108 (2009). • P.D. Mininni and A. Pouquet, ``Helicity cascades in rotating turbulence,'' to appear, Phys. Fluids (2009), arxiv:0809.0869. • Mininni, P., A. Alexakis, A. G. Pouquet, 2008: Non-local interactions in hydrodynamic turbulence at high Reynolds numbers: The slow emergence of scaling laws. Phys. Rev. E, 77, 036306, doi: 10.1103/PhysRevE.77.036306. • Mininni, P., A. G. Pouquet, 2008: Energy spectra stemming from interactions of Alfven waves and turbulent eddies. Physical Review Letters, 99, 254502, doi: 10.1103/PhysRevLett.99.254502. • Mininni, P. D., D. C. Montgomery, L. Turner, 2007: Hydrodynamic and magnetohydrodynamic computations inside a rotating sphere. New J. Phys., 9, 303, doi: 10.1088/1367-2630/9/8/303 • .Mininni, P. D., 2007: Inverse cascades and alpha effect at a low magnetic Prandtl number. Phys. Rev. E, 76, 026316, doi: 10.1103/PhysRevE.76.026316.1 • Mininni, P., A.. Alexakis, A. Pouquet, 2007: Energy transfer in Hall-MHD turbulence, cascades, backscatter and dynamo action. J. Plasma Phys., 73, 377-401, doi: 10.1017/S0022377806004624.1 • Mininni, P., A. Alexakis, A. G. Pouquet, 2008: Scale interactions in hydrodynamic turbulence at large Reynold numbers. IUTAM Book Series: IUTAM Symp. Comput. Phys. And New Perspectives in Turb., Kaneda, Y, Eds., Springer-Verlag, 4, 125-130, doi: 978 1-4020-6471-5. • P.D. Mininni, E. Lee, A. Norton, and J. Clyne, Flow visualization and field line advection in computational fluid dynamics: application to magnetic fields and turbulent flows, New J. Phys. 10(12), 125007/1-23 (2008). • P. Mininni, P. Sullivan and A. Pouquet,``Two examples from geophysical and astrophysical turbulence on modeling disparate scale interactions,'’ Summer school on mathematics in geophysics, Roger Temam and Joe Tribbia Eds., Springer Verlag, to appear (2009). • C. S. Ng, D. Rosenberg, K. Germaschewski, A. Pouquet and A. Bhattacharjee,``A comparison of spectral element and finite difference simulations with adaptive mesh refinement for the MHD island coalescence instability problem,'’ to appear, Astrophys. J. Suppl. (2009). • Yannick Ponty, Pablo D. Mininni, Jean-Philipe Laval, Alexandros Alexakis, Julien Baerenzung,Francois Daviaud, Berengere Dubrulle, Jean-Fran cois Pinton, Helene Politano and Annick Pouquet, ``Linear and non linear features of the Taylor-Green Dynamos,'’ Comptes Rendus de l'Academie des Sciences (Paris), 9, 749 (2008). • Ponty, Y., P. D. Mininni, J.-F. Pinton, H. Politano, A. Pouquet, 2007: Dynamo action at low magnetic Prandtl numbers: Mean flow versus fully turbulent motions. New J. Phys., 9, 296, doi: 10.1088/1367-2630/9/8/296.3 • Pouquet, A. G., A. Alexakis, P. Mininni, D. Montgomery, 2008: Dynamics of the small scales in magnetohydrodynamic turbulence. IUTAM Book Series: IUTAM Symp. Comput. Phys. And New Perspectives in Turb., Kaneda, Y, Eds., Springer-Verlag, 4, 305-312, doi: 978 1-4020-6471-5. • Rosenberg, D., A. Pouquet, P. D. Mininni, 2007: Adaptive mesh refinement with spectral accuracy for MHD in two space dimensions. New J. Phys., 9, 304, doi: 10.1088/1367-2630/9/8/304 • Wang, H., J. J. Tribbia, F. Baer, A. Fournier, M. A. Taylor, 2007: A spectral element version of CAM2. Mon. Wea. Rev., 135, 3825-3840.
As an example: Summary of the GTP workshop on Turbulence & Scalar Transport in Roughness Sub-layers (RSLs)Jielun Sun et al., ESSL-MMM • Types of roughness elements considered include: • Vegetated canopies • Urban and suburban environments • Underwater plant communities • Ocean waves • Wind farms • Although there are similarities, profound differences in turbulence structures are found among these RSLs depending on rigidity and porosity of roughness elements • Over-ocean RSLs are strongly affected by speed and direction of swell and can impact the entire PBL. • Imprint of urban geometry greatly impacts turbulence structures in RSL due to building shapes and distributions. • Underwater RSLs due to aquatic vegetation can fill entire channel depth. Past, present & future experiments: e.g., HATS, O-HATS, C-HATS, A-HATS (Horizontal Array Turbulence Studies, + Oceans, Canopies, Anisotropy)