Jared Whitehead


Email:

jaredwh@umich.edu

Phone:

(734) 763-5273

Office (north campus):

SRB 2531

Office (central campus):

East Hall 2860

 

Current Status:

PhD Applied and Interdisciplinary Mathematics

 

Curriculum Vitae

Research Interests

Research Statement (work in progress)

  • Geophysical Fluid Dynamics
  • Rayleigh Benard Convection
  • Quantifying the effect of diffusion and filters in General Circulation Models
  • Upper Bound Theory (the Background Method of Hopf, Doering and Constantin)
  • Scaling laws in Turbulent Flow
  • Rotating, stratified fluids
  • Computational Fluid Dynamics (DNS)
Publications
In preparation:
  • A stability analysis of advection and diffusion in the Comunity Atmosphere Model Spectral Element (CAM-SE) model. (with P. A. Ullrich, C. Jablonowski, and M. A. Taylor).
  • Downscale Cascades in Tracer Transport Test-Cases. (with J. Kent, C. Jablonowski, and R. B. Rood).
  • The logarithm persists: infinite Prandtl number convection with mixed thermal boundary conditions. (with C. R. Doering and R. Wittenberg).
  • Rigid rigorous bounds on heat transport in a slippery container. (with C. R. Doering).
  • Potential vorticity: a diagnostic tool for general circulation models. (with C. Jablonowski, J. Kent, and R. B. Rood).
  • Assessing tracer transport algorithms and the impact of vertical resolution in a finite-volume dynamica core. (in revision for publication at Monthly Weather Review, with J. Kent, C. Jablonowski, and R. B. Rood).

Published:
  • The ultimate regime of two-dimensional Rayleigh-Benard convection with stress-free boundaries. (with C. R. Doering) Physics Review Letters, Vol. 106, 244501, p1-p4 (2011).
  • Internal heating driven convection at infinite Prandtl number. (with C. R. Doering) Journal of Mathematical Physics, Vol. 52, 093101, 11 pages (2011).
  • A stability analysis of divergence damping on a latitude-longitude grid. (with C. Jablonowski, R. B. Rood, and P. H. Lauritzen) Monthly Weather Review, Vol. 139, No. 9, 2976--2993 (2011).
  • Asymptotic values, pre-poles, and periodic points. (with L. Bakker) International Journal of Bifurcations and Chaos, Vol. 20, No. 4 (2010).
Other Publications
  • Topics in Geophysical Fluid Dynamics. Phd Dissertation, University of Michigan (January 2012).
  • Topological bifurcations of Julia sets. Undergraduate Honors Thesis, Brigham Young University (April 2006).
RB Movies
Selected Presentations
  • The Ultimate State of Two-dimensional Rayleigh Benard Convection between Free-Slip Fixed-Temperature Boundaries, APS Division of Fluid Dynamics Meeting, Baltimore, MD, USA (November 2011).
  • Bounds on Heat Transport of Fixed Flux Thermal Boundary Conditions at Infinite Prandtl Number, SIAM Partial Differential Equations Meeting, San Diego, CA, USA (November 2011).
  • The Ultimate State of Two-dimensional Rayleigh Benard Convection between Free-Slip Fixed-Temperature Boundaries, Los Alamos National Laboratories Center for Nonlinear Studies Invited Speaker, Los Alamos, NM, USA (October 2011).
  • Internal heating driven convection at Infinite Prandtl Number, Incompressible Fluids, Turbulence and Mixing, Carnegie Mellon University, Pittsburgh, PA, USA (October 2011).
  • Bounds on the turbulent transport of heat driven by an internal heat source, International Congress on Industrial and Applied Mathematics, Vancouver, BC, Canada (July 2011).
  • Bounds on the turbulent transport of heat at infinite Prandtl number with no-slip boundaries, 67th Midwest Partial Differential Equations, University of Illinois Urbana-Champaign, USA (March 2011).
  • A generalized Hardy-Rellich inequality and improved bounds for convection driven by internal heating, University of Michigan SIAM student conference, Ann Arbor, MI, USA (November 2010).
  • A stability analysis of divergence damping on a latitude-longitude grid, Partial Differential Equations on the Sphere, Pottsdam, Germany (August 2010).
  • The Mathematics of climate change, Applied and Interdisciplinary Mathematics Student Seminar, Ann Arbor, MI, USA (October 2008, 2009).
  • Functional representation of families of minimal surfaces, Intermountain Section Meeting of the Mathematical Association of America, Pocatello, ID, USA (March 2005).
  • topological bifurcations of Julia sets, Spring Research Conference, Brigham Young University, Provo, UT, USA (March 2005, 2006).
Posters (1st author only)
  • Evaluating the impact of dissipative subgrid-scale mixing processes in the dynamical cores of NCAR's Community Atmosphere Model, DOE-BER PI meeting, Washington D.C., USA (September 2011).
  • Potential Vorticity: a diagnostic tool for General Circulation Models, Michigan Geophysical Union student poster competition, Ann Arbor, MI, USA (March 2011).
  • Divergence damping: is additional diffusion good for stability? Michigan Geophysical Union student poster competition, Ann Arbor, MI, USA (March 2010).
Awards
  • IDEAS-IGERT fellow (January-December 2011).
  • 2nd place Michigan Geophysical Union student poster competition (March 2010).
  • Orson Pratt Award, outstanding senior in Mathematics dept, BYU (April 2005).
Grants/ Proposals
  • Co-PI "Numerical Simulation of 2D and 3D Turbulent Convection at Finite and Infinite Prandtl Numbers". Allocation NSF TeraGrid resources.
Advisors/ Collaborators
Other

Latest update: Feb 24th, 2011