I am a physicist and specialize in geophysical fluid dynamics. Currently I do research at NWRA studying inertial oscillations and eddies.


Numerical Models – Movies and code for a number of geophysical fluid dynamics models, including the a quasigeostrophic eddy, forced-dissipative turbulence, an unstable shear flow, surface gravity waves, Poincare waves, linear internal waves, and many others.

Inertial Oscillations – A brief introduction to inertial oscillations, both theoretical and observational. This also includes a Matlab script for computing inertial paths, velocities, and periods from the exact solutions.

Quasigeostrophic Eddies – Movies of the sea-surface height as observed from satellite altimetry and the sea-surface height of a quasigeostrophic model attempting to reproduce the observations. This also include a number of animations from the monopole study, where a quasigeostrophic eddy was allowed to evolve in isolation.

Internal Modes – A collection of Matlab classes to quickly and accurately compute the vertical modes and SQG modes from arbitrary stratification.

Garrett-Munk Spectrum – Matlab classes to compute both the exact, and approximated versions of the Garrett-Munk spectrum.



A. Sykulski, S. Olhede, A. Guillaumin, J. M. Lilly, and J. Early. The De-Biased Whittle Likelihood. Biometrika. 2018. (pdf, doi, supplemental material)

J. M. Lilly, A. Sykulski, J. Early, and S. Olhede. Fractional Brownian motion, the Matern process, and stochastic modeling of turbulent dispersion. Nonlinear Processes in Geophysics. 2017. (pdf, doi, supplemental material)

A. Guillamin, A. Sykulski, S. Olhede, J. Early, and J. M. Lilly. Analysis of nonstationary modulated time series with applications to oceanographic surface flow measurements. Journal of Time Series Analysis. 2017. (pdf, doi, supplemental material)

A. Sykulski, S. Olhede, J. M. Lilly, and J. Early. Frequency-domain stochastic modeling of stationary bivariate or complex-valued signals. IEEE Transactions on Signal Processing. 2017. (pdf, doi, supplemental material)

S. Elipot, R. Lumpkin, R. C. Perez, J. M. Lilly, J. J. Early, and A. M. Sykulski. A global surface drifter data set at hourly resolution. Journal of Geophysical Research: Oceans. 2016. (pdf, doi, supplemental material)

T. Bartlett, A. Sykulski, S. Olhede, J. M. Lilly, J. Early. A power variance test for nonstationarity in complex-valued signals. Proceedings of the 14th International Conference on Machine Learning and Applications. 2015. (pdf, doi, supplemental material)

Shcherbina, et al. The LatMix summer campaign: submesoscale stirring in the upper ocean. Bulletin of the American Meteorological Society. 2015. (pdf, doi, supplemental material)

J. Early The forces of inertial oscillations. Quarterly Journal of the Royal Meteorological Society. 2012. (pdfdoisupplemental material)

D. Chelton, P. Gaube, M. Schlax, J. Early, R. Samelson. The influence of nonlinear mesoscale eddies on near-surface oceanic chlorophyll. Science. 2011. (doi)

J. Early, R. Samelson, D. Chelton. Long-term evolution of quasi-geostrophic eddies. Journal of Physical Oceanography. August 2011.  (pdfdoisupplemental material)

J. Early, J. Pohjanpelto, R. Samelson. Group foliation of equations in geophysical fluid dynamics. Discrete and Continuous Dynamical Systems, Series A. March 2010. (pdfdoi)

Unpublished Notes

2011 – Stokes drift of Rossby waves (pdf)

Unpublished computation of the Stokes drift due to Rossby waves. A single plane wave does not induce stokes drift, but two plane waves can.