Research

Dr. Julien's primary areas of research are in the dynamics and instability processes in geophysical and astrophysical fluid dynamics. These include turbulent fluid convection and the effects of stratification, rotation and magnetic fields which are all ubiquitous features of geophysical and astrophysical fluid objects. Particular emphasis has been placed on the development of reduced pde models from the fundamental fluid equations. Further focus has been placed on the characteristics of coherent structures and their transport and organization of large-scale flows. Integral parts of Julien's research include high perfomrance computer simulations, dynamical systems theory, asymptotics and perturbation techniques in applied mathematics.

Publications

REFEREED PUBLICATIONS JOURNAL ARTICLES

1. Julien, K., “Strong spatial interactions with 1:1 resonance: A three-layer convection problem,” Nonlinearity, 7, 1655-1693, (1994).

2. Julien, K., Legg, S., McWilliams J., and J.Werne, “Penetrative convection in rapidly rotating flows: preliminary results from numerical simulation,” Dynamics of Atmospheres and Oceans, 24, 237-249, (1996).

3. Julien, K., Legg, S., McWilliams J., and J.Werne, “Rapidly rotating turbulent RayleighBenard convection,” Journal of Fluid Mechanics, 322, 243-273, (1996).

4. Julien, K., Legg, S., McWilliams J., and J.Werne, “Hard-turbulence in rotating Rayleigh-Benard convection: Preliminary results from numerical simulation,” Physical Review E, 53, R5557-5560, (1996).

5. Bizon, C. A., Werne, J., Predtechensky, A., Julien, K., Mc Cormick, W. D., Swift, J. B., and H. L. Swinney, “Dynamics and scalings in quasi two-dimensional turbulent convection,” Physica A, 239, 204-210, (1997).

6. Bizon, C. A., Predtechensky, A., Werne, J., Julien, K., Mc Cormick, W. D., Swift, J. B., and H. L. Swinney, “Plume dynamics in quasi 2D turbulent convection,” Chaos, 7 (1), 107-123, (1997).

7. Julien, K. and E. Knobloch, “Fully nonlinear oscillatory convection in a rotating layer,” Physics of Fluids, 9, 1906-1913, (1997).

8. Julien, K. and E. Knobloch, “Strongly nonlinear convection cells in a rapidly rotating fluid layer: The tilted f-plane,” Journal of Fluid Mechanics, 360, 141-178, (1998).

9. Julien, K., Knobloch, E., and J. Werne, “A new class of equation for rotationally constrained flows,” Journal of Theoretical and Computational Fluid Dynamics, 11, 251-261, (1998).

10. Balmforth, N., Casti, A., and K. Julien, “Thermohaline convection with nonlinear salt profiles,” Physics of Fluids, 10, 819-828, (1998).

11. Julien, K. and E. Knobloch, “Fully nonlinear three-dimensional convection in a rapidly rotating layer,” Physics of Fluids, 11, 1469-1483, (1999).

12. Julien, K., Legg, S., McWilliams J., and J. Werne, “Plumes in rotating convection. Part ensemble statistics and dynamical balances,” Journal of Fluid Mechanics, 391, 151-187, (1999).

13. Julien K., Knobloch E. and S. M. Tobias, “Strongly nonlinear magnetoconvection in three-dimensions,” Physica D, 128, 105-129, (1999).

14. Julien K., Knobloch E. and S. M. Tobias, “nonlinear magnetoconvection in the presence of strong oblique fields,” Journal of Fluid Mechanics, 410, 285-322, (2000).

15. Rosenthal C.S. and K. Julien , “Numerical Modeling of the absorption and scattering of acoustic radiation by sunspots,” Astrophysical Journal, 532:(2), 1230-1239, Part 1, (2000).

16. Abdulrahman A., Jones C.A., Proctor M.R.E., and K. Julien “Large wavenumber convection in the rotating annulus,” Geophysical and Astrophysical Fluid Dynamics, 93: (3-4), 227- 252, (2000).

17. Legg, S., Julien, K., McWilliams J., and J. Werne, “Vertical transport by convection plumes: Modification by rotation,” Physics and Chemistry of the Earth B, 26, (4), 259-262, (2001).

18. Mullowney, P., Julien, K., and J.D. Meiss “Blinking rolls: Chaotic advection in a threedimensional flow with an invariant,” Siam J. on Applied Dynamical Systems 4, (1), 159- 186 (2005).

19. Ablowitz M. J., Julien, K., Musslimani, Z. H., and M. I. Weinstein “ Wave dynamics in optically modulated waveguide arrays,” Physical Review E,71, (055602) (4 pages) (2005)

20. Knobloch, E., and K. Julien. “Saturation of the Magnetorotational instability” Physics of Fluids, 17 (9): Art. No. 094196 (6 pages) (2005).

21. Petersen, M., Julien, K. and J.B. Weiss. “Vortex cores, strain cells, and filaments in quasi-geostrophic turbulence”, Physics of Fluids, 18 (2): Art. No. 026601(11 pages) (2006).

22. Sprague*, M., Julien, K., Knobloch, E., and J. Werne. “Numerical simulations of an asymptotically reduced system for rotationally constrained convection,” Journal of Fluid Mechanics, 551, 141-174, (2006).

23. Julien, K., Knobloch, E., R. Milliff and J. Werne. “Generalized quasigeostrophy for spatially anisotropic rotationally constrained flows,” Journal of Fluid Mechanics, 555, 233-274, (2006).

24. Martinsen-Burrell, N., Julien, K., Petersen, M.R., and J.B. Weiss. “Merger and alignment in a reduced model for three-dimensional quasigeostrophic ellipsoidal vortices,” Physics of Fluids, 18 (5): Art. No. 057101 (14 pages) (2006).

25. Julien, K. and E. Knobloch, “Saturation of the magnetorotational instability; Asymptotically exact theory,” In Stellar Fluid Dynamics and Numerical Simulations: From the Sun to Neutron Stars, M. Rieutord and B. Dubrulle (eds), EAS Publications Series, 21, 81-104, (2006). Invited article.

26. Petersen, M., Julien, K. and G.R. Stewart. “Baroclinic vorticity production in protoplanetary disks. I. Vortex Formation,” Astrophysical Journal, 658 (2), 1236-1251, Part I (2007).

27. Petersen, M., Stewart, G.R. and K. Julien, “Baroclinic vorticity production in protoplanetary disks. II. Vortex Growth and Longevity,” Astrophysical Journal, 658 (2), 1252-1265, Part I (2007).

28. Julien, K. and E. Knobloch, “Reduced Models for Fluid flows with Strong Constraints,” Journal of Mathematical Physics, 48 (6): Art No. 065405 (34 pages), (2007). Invited article.

29. Vasil G.M., Brummell N.H., and K. Julien, “A new method for fast transforms in paritymixed PDEs: Part II. Application to confined rotating convection,” Journal of Computational Physics, 227, Issue: 1, 8017-8034, (2008).

30. Vasil G.M., Brummell NH, Julien K., “A new method for fast transforms in parity-mixed PDEs: Part I. Numerical techniques and analysis,” Journal of Computational Physics, 227 Issue: 17, 7999-8016, (2008).

31. Jamroz B., Julien K, Knobloch E., “Saturation of the magnetorotational instability at large Elsasser number,” Astronomische Nachrichten, 329 Issue: 7, 675-687, (2008).

32. Mullowney P., Julien K, Meiss JD, “Chaotic advection and the emergence of tori in the Kuppers-Lortz state,” CHAOS, 18 Issue: 3 Art. No. 033104, (2008)

33. Jamroz B., Julien K, Knobloch E., “An asymptotically exact reduced PDE model for the magnetorotational instability: derivation and numerical simulations,” Physica Scripta, T132 Art No. 014027 (2008).

34. Julien K., and M. Watson, “Efficient multi-dimensional solution of PDEs using Chebyshev spectral methods,” Journal of Computational Physics, 228 Issue: 5, 1480-1503, (2009).

35. Chini, G.P., Julien K., and E. Knobloch, “An asymptotically reduced model of turbulent Langmuir circulation,” Geophysical and Astrophysical Fluid Dynamics, 103, Issue: 2-3, 179-197, (2009).

36. Grooms, I., Julien, K., Weiss, J.B. and E. Knobloch, “Models of convective Taylor columns in rotating Rayleigh-Benard convection,” Physical Review Letters, 104, (22), 224501, (2010).

37. Julien, K., and E. Knobloch, “Magnetorotational Instability: Recent developments,” Philosophical Transaction of the Royal Society A: Mathematical, Physical and Engineering Sciences, (368), issue 1916, 1606,1633, (2010)

38. Grooms, I., and Julien, K., “Linearly implicity methods for nonlinear PDE’s with linear dispersion and dissipation,” Journal of Computational Physics, 230 Issue: 9, 3630-3650, (2011).

39. Grooms, I., Julien, K., and B. Fox-Kemper,”On the interaction between planetary geostrophy and mesoscale eddies,” Dynamics of Atmospheres and Oceans, 51, Issue 3, 109-136, (2011).

40. *Calkins, M.A., Aurnou, J.M., Eldridge, J.D. and K. Julien, “The influence of fluid properties on the morphology of core turbulence and the geomagnetic field,” Earth and Planetary Science Letters, 259, 55-60, (2012).

41. Julien, K, *Rubio, .A., Grooms, I., and E. Knobloch, “Statistical and physical balances in low Rossby number Rayleigh-Benard convection.” Geophysical and Astrophysical Fluid Dynamics, 106 (4-5), 392-428, (2012).

42. Julien, K., Knobloch, E., *Rubio, .A., and G. Vasil, “Heat transport in low Rossby number Rayleigh-Benard convection,” Physical Review Letters, 254503 (2012).

43. *Calkins, M.A., Julien, K., and *P. Marti, “Three-dimensional quasi-geostrophic convection in the rotating cylindrical annulus with steeply sloping end walls,” Journal of Fluid Mechanics, 732, (4), 214-244, (2013).

44. *Malecha, Z., Chini, G.P., and K. Julien, “A multiscale algorithms for simulating spatiallyextended Langmuir circulation Dynamics,” Journal of Computational Physics, 271, 131- 150, (2013).

45. Stellmach, S., Lipscher, M., Julien, K., Vasil, G.M., Cheng, J.S., Ribeiro, A., King,. E.M., and J. Aurnou, “Approaching the asymptotic regime of rapidly rotating convection: Boundary layer versus interior dynamics ,” Physical Review Letters, 113, (25), 224501, (2014).

46. *Beaume, C., Knobloch, E., Chini, G., and K. Julien, “Exact coherent structures in an asymptotically reduced description of parallel shear flows.” Fluid Dynamics Research, 47 (1) 015504 (2014).

47. Hamlington, P.E., Van Roekel, L.P., Fox-Kemper, B., Julien, K., and G. Chini, “Langmuirsubmesoscale interactions: descriptive analysis of multiscale frontal spindown simulations,” Journal of Physical Oceanography, 44 (9) 2249-2271 (2014).

48. Nieves, D., *Rubio, A.M., and K. Julien, “Statistical classification of flow morphology in rapidly rotating Rayleigh-Benard convection,” Physics of Fluids, 26, (8), 086602, (2014).

49. *Rubio, A.M., Julien, K., Knobloch, E., and J.B. Weiss, “Upscale energy transfer in threedimensional rapidly rotating turbulent convection,” Physical Review Letters, 112, (14), 144501, (2014).

50. Calkins, M.A., Hale, K., Julien, K., Nieves, D., Driggs, D. and P. Marti, “The asymptotic equivalence of fixed heat flux and fixed temperature thermal boundary conditions for rapidly rotating convection,” Journal of Fluid Mechanics, 784, R2, (2015).

51. Haney, S., Fox-Kemper, B., K., Julien, K., and A. Webb, “Symmetric and geostrophic instabilities in the wave-forced ocean mixed layer,” Journal of Physical Oceanography, 45, (12), 3033-3056, (2015).

52. *Calkins, M.A., Julien, K., Tobias, S.M., and J. Aurnou, “A multiscale dynamo model driven by quasi-geostrophic convection,” Journal of Fluid Mechanics, 780, 143-166, (2015).

53. Aurnou, J., *Calkins, M.A., Cheng, J., Julien, King, E.M., Nieves, D., Soderlund, K.M., and S. Stellmach, “Rotating convective turbulence in Earth and planetary cores,” Physics of the Earth and Planetary Interiors, 246, 52-71, (2015).

54. *Calkins, M.A., Julien, K., and *P. Marti, “Onset of rotating and non-rotating convection in compressible and anelastic ideal gases,” Geophysical and Astrophysical Fluid Dynamics, 109, (4), 422-449, (2015).

55. *Beaume, C., Chini, G.P., Julien, K., and E. Knobloch “Reduced description of exact coherent states in parallel shear flows,” Physical Review E, 91, (4) 043010 (2015).

56. Zhang, Z., Chini, G.P., Julien, K., and E. Knobloch “Dynamics patterns in the reduced Craik-Leibovich equations,” Physical of Fluids, 27, (4), 046605 (2015).

57. *Calkins, M.A., Julien, K., and *P. Marti, “The breakdown of the anelastic approximation in rotating compressible convection: implications for astrophysical systems,” Proc. Roy. Soc. A, 471, (2175), 20140689, (2015).

58. Beaume, C., Knobloch, E., Chini, G., and K. Julien, “Modulated patterns in a reduced model of a transitional shear flow,” Physica Scripta, 91 (2) 024003 (2016).

59. Calkins, M.A., Julien, K., Tobias, S.M., Aurnou, J. and *P. Marti, “Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers: Single-mode solutions.” Physical Review E, 93 (2) 023115 (2016).

60. Julien, K., Aurnou, J., Calkins, M.A., Knobloch, *Marti, P. and S. Stellmach, “A nonlinear model for rotationally constrained convection with Ekman pumping,” Journal of Fluid Mechanics, 798, 50-87, (2016).

61. *Marti, P., Calkins, M.A., and K. Julien, “A computationally efficient spectral method for modeling core dynamics,” Geochemistry, Geophysics and Geosystems, 17, (8), 3031-3053 (2016).

62. Nieves, D., Grooms, I., Julien, K. and J.B. Weiss, “Investigations of non-hydrostatic, stably stratified and rapidly rotating flows,” Journal of Fluid Mechanics, 801, 430-458, (2016).

63. Plumley, M., Julien, K, *Marti, P. and S. Stellmach, “The effect of Ekman pumping on quasigeostrophic Rayleigh-Benard convection,” Journal of Fluid Mechanics, 803, 51-71, (2016).

64. Calkins, M.A., Long, L., Nieves, D., Julien, K., and S.M. Tobias, “Convection-driven kinematic dynamos at low Rossby and magnetic Prandtl numbers.” Physical Review Fluids, 1, (8), 083701 (2016).

65. *Xie, J.H., *Miquel, B., Julien, K., and E. Knobloch, “A reduced model for salt-finger convection in the small diffusivity ratio limit,” Geophysical Fluids, in press, (2017). (Underlined names denote graduate student, * denotes postdoctoral research associate)