9129767 SE97LMEN items 1 0 date desc year Ierley 18 https://gierley.scrippsprofiles.ucsd.edu/wp-content/plugins/zotpress/
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Ierley, G., & Kostinski, A. (2022). Signals as departures from random walks. Physical Review E, 105(6), 13. https://doi.org/10.1103/PhysRevE.105.064114
Durbach, I. N., Harris, C. M., Martin, C., Helble, T. A., Henderson, E. E., Ierley, G., Thomas, L., & Martin, S. W. (2021). Changes in the movement and calling behavior of Minke whales (Balaenoptera acutorostrata) in response to navy training. Frontiers in Marine Science, 8. https://doi.org/10.3389/fmars.2021.660122
Ierley, G., & Kostinski, A. (2021). Extraction of unknown signals in arbitrary noise. Physical Review E, 103(2). https://doi.org/10.1103/PhysRevE.103.022130
Ierley, G., & Kostinski, A. (2020). Detection of unknown signals in arbitrary noise. Physical Review E, 102(3). https://doi.org/10.1103/PhysRevE.102.032221
Ierley, G., & Kostinski, A. (2019). Universal rank-order transform to extract signals from noisy data. Physical Review X, 9(3). https://doi.org/10.1103/PhysRevX.9.031039
Helble, T. A., Henderson, E. E., Ierley, G. R., & Martin, S. W. (2016). Swim track kinematics and calling behavior attributed to Bryde’s whales on the Navy’s Pacific Missile Range Facility. Journal of the Acoustical Society of America, 140(6), 4170–4177. https://doi.org/10.1121/1.4967754
Helble, T. A., Ierley, G. R., D’Spain, G. L., & Martin, S. W. (2015). Automated acoustic localization and call association for vocalizing humpback whales on the Navy’s Pacific Missile Range Facility. Journal of the Acoustical Society of America, 137(1), 11–21. https://doi.org/10.1121/1.4904505
Landuyt, W., & Ierley, G. (2012). Linear stability analysis of the onset of sublithospheric convection. Geophysical Journal International, 189(1), 19–28. https://doi.org/10.1111/j.1365-246X.2011.05341.x
Helble, T. A., Ierley, G. R., D’Spain, G. L., Roch, M. A., & Hildebrand, J. A. (2012). A generalized power-law detection algorithm for humpback whale vocalizations. Journal of the Acoustical Society of America, 131(4), 2682–2699. https://doi.org/10.1121/1.3685790
Livermore, P. W., Ierley, G., & Jackson, A. (2011). The evolution of a magnetic field subject to Taylor’s constraint using a projection operator. Geophysical Journal International, 187(2), 690–704. https://doi.org/10.1111/j.1365-246X.2011.05187.x
Jackson, A., Livermore, P. W., & Ierley, G. (2011). On Ohmic heating in the Earth’s core II: Poloidal magnetic fields obeying Taylor’s constraint. Physics of the Earth and Planetary Interiors, 187(3–4), 322–327. https://doi.org/10.1016/j.pepi.2011.06.003
Livermore, P. W., & Ierley, G. R. (2010). Quasi-L (p) norm orthogonal Galerkin expansions in sums of Jacobi polynomials. Numerical Algorithms, 54(4), 533–569. https://doi.org/10.1007/s11075-009-9353-5
Livermore, P. W., Ierley, G. R., & Jackson, A. (2010). The construction of exact Taylor states. II: The influence of an inner core. Physics of the Earth and Planetary Interiors, 178(1–2), 16–26. https://doi.org/10.1016/j.pepi.2009.07.015
Livermore, P. W., Ierley, G., & Jackson, A. (2009). The construction of exact Taylor states. I: The full sphere. Geophysical Journal International, 179(2), 923–928. https://doi.org/10.1111/j.1365-246X.2009.04340.x
Livermore, P. W., & Ierley, G. R. (2009). A new hypergeometric identity linking coefficients of a certain class of homogeneous polynomials motivated from magneto hydrodynamics. Advances in Applied Mathematics, 43(4), 390–393. https://doi.org/10.1016/j.aam.2009.06.001
Livermore, P. W., Ierley, G., & Jackson, A. (2008). The structure of Taylor’s constraint in three dimensions. Proceedings of the Royal Society A-Mathematical Physical and Engineering Sciences, 464(2100), 3149–3174. https://doi.org/10.1098/rspa.2008.0091
Ierley, G. R., Kerswell, R. R., & Plasting, S. C. (2006). Infinite-Prandtl-number convection. Part 2. A singular limit of upper bound theory. Journal of Fluid Mechanics, 560, 159–227. https://doi.org/10.1017/s0022112006000450
Plasting, S. C., & Ierley, G. R. (2005). Infinite-Prandtl-number convection. Part 1. Conservative bounds. Journal of Fluid Mechanics, 542, 343–363. https://doi.org/10.1017/s0022112005006555
Balmforth, N. J., Ierley, G. R., & Young, W. R. (2002). Tidal conversion by subcritical topography. Journal of Physical Oceanography, 32(10), 2900–2914. https://doi.org/10.1175/1520-0485(2002)032<2900:tcbst>2.0.co;2
Ierley, G. R., & Worthing, R. A. (2001). Bound to improve: a variational approach to convective heat transport. Journal of Fluid Mechanics, 441, 223–253.
Ierley, G., & Miles, J. (2001). On Townsend’s rapid-distortion model of the turbulent-wind-wave problem. Journal of Fluid Mechanics, 435, 175–189.
Ierley, G. R., & Ruehr, O. G. (1997). A combinatorial expression from oceanography. Siam Review, 39(4), 772–774.
Balmforth, N. J., Ierley, G. R., & Worthing, R. (1997). Pulse dynamics in an unstable medium. Siam Journal on Applied Mathematics, 57(1), 205–251.
Sheremet, V. A., Ierley, G. R., & Kamenkovich, V. M. (1997). Eigenanalysis of the two-dimensional wind-driven ocean circulation problem. Journal of Marine Research, 55(1), 57–92. https://doi.org/10.1357/0022240973224463
Ierley, G. R., & Sheremet, V. A. (1995). Multiple Solutions and Advection-Dominated Flows in the Wind-Driven Circulation .1. Slip. Journal of Marine Research, 53(5), 703–737. https://doi.org/10.1357/0022240953213052
Cessi, P., & Ierley, G. R. (1995). Symmetry-breaking multiple equilibria in quasi-geostrophic, wind-driven flows. Journal of Physical Oceanography, 25(6), 1196–1205. https://doi.org/10.1175/1520-0485(1995)025<1196:sbmeiq>2.0.co;2
Balmforth, N. J., Ierley, G. R., & Spiegel, E. A. (1994). Chaotic Pulse Trains. Siam Journal on Applied Mathematics, 54(5), 1291–1334. https://doi.org/10.1137/s0036139993247422
Cessi, P., & Ierley, G. R. (1993). Nonlinear disturbances of western boundary currents. Journal of Physical Oceanography, 23(8), 1727–1735. https://doi.org/10.1175/1520-0485(1993)023<1727:ndowbc>2.0.co;2
Balmforth, N. J., Cvitanovic, P., Ierley, G. R., Spiegel, E. A., & Vattay, G. (1993). Advection of Vector-Fields by Chaotic Flows. In J. R. Buchler & H. E. Kandrup (Eds.), Stochastic Processes in Astrophysics (Vol. 706, pp. 148–160). New York Acad Sciences.
Ierley, G., Spencer, B., & Worthing, R. (1992). Spectral Methods in Time for a Class of Parabolic Partial-Differential Equations. Journal of Computational Physics, 102(1), 88–97. https://doi.org/10.1016/s0021-9991(05)80008-7
Ierley, G. R., & Young, W. R. (1991). Viscous instabilities in the western boundary layer. Journal of Physical Oceanography, 21(9), 1323–1332. https://doi.org/10.1175/1520-0485(1991)021<1323:viitwb>2.0.co;2
Elphick, C., Ierley, G. R., Regev, O., & Spiegel, E. A. (1991). Interacting Localized Structures with Galilean Invariance. Physical Review A, 44(2), 1110–1122. https://doi.org/10.1103/PhysRevA.44.1110
Hollerbach, R., & Ierley, G. R. (1991). A Modal Alpha-2-Dynamo in the Limit of Asymptotically Small Viscosity. Geophysical and Astrophysical Fluid Dynamics, 56(1–4), 133–158. https://doi.org/10.1080/03091929108219515
Ierley, G. R. (1990). Boundary-Layers in the General Ocean Circulation. Annual Review of Fluid Mechanics, 22, 111–142. https://doi.org/10.1146/annurev.fl.22.010190.000551
Kolkka, R. W., & Ierley, G. R. (1989). Phase-Space Analysis of the Spurt Phenomenon for the Giesekus Viscoelastic Fluid Model. Journal of Non-Newtonian Fluid Mechanics, 33(3), 305–323. https://doi.org/10.1016/0377-0257(89)80004-7
Childress, S., Ierley, G. R., Spiegel, E. A., & Young, W. R. (1989). Blow-up of unsteady two-dimensional Euler and Navier-Stokes solutions having stagnation-point form. Journal of Fluid Mechanics, 203, 1–22. https://doi.org/10.1017/s0022112089001357
Kolkka, R. W., Malkus, D. S., Hansen, M. G., Ierley, G. R., & Worthing, R. A. (1988). Spurt Phenomena of the Johnson Segalman Fluid and Related Models. Journal of Non-Newtonian Fluid Mechanics, 29(1–3), 303–335. https://doi.org/10.1016/0377-0257(88)85059-6
Ierley, G. R., & Young, W. R. (1988). Inertial recirculation in a beta-plane corner. Journal of Physical Oceanography, 18(4), 683–689. https://doi.org/10.1175/1520-0485(1988)018<0683:iriapc>2.0.co;2
Ierley, G. R., & Malkus, W. V. R. (1988). Stability Bounds on Turbulent Poiseuille Flow. Journal of Fluid Mechanics, 187, 435–449. https://doi.org/10.1017/s0022112088000503
Ierley, G. R. (1987). On the Onset of Inertial Recirculation in Barotropic General-Circulation Models. Journal of Physical Oceanography, 17(12), 2366–2374. https://doi.org/10.1175/1520-0485(1987)017<2366:otooir>2.0.co;2
Cessi, P., Ierley, G., & Young, W. (1987). A model of the inertial recirculation driven by potential vorticity anomalies. Journal of Physical Oceanography, 17(10), 1640–1652. https://doi.org/10.1175/1520-0485(1987)017<1640:amotir>2.0.co;2
Kolkka, R. W., & Ierley, G. R. (1987). On the Convected Linear-Stability of a Viscoelastic Oldroyd-B Fluid Heated from Below. Journal of Non-Newtonian Fluid Mechanics, 25(2), 209–237. https://doi.org/10.1016/0377-0257(87)85044-9
Young, W. R., & Ierley, G. R. (1986). Eastern boundary conditions and weak solutions of the ideal thermocline equations. Journal of Physical Oceanography, 16(11), 1884–1900. https://doi.org/10.1175/1520-0485(1986)016<1884:ebcaws>2.0.co;2
Ierley, G. R. (1986). Spectral Methods for the Solution of Nonlinear Boundary-Value-Problems, a Case-Study. Applied Mathematics and Computation, 20(1–2), 21–21. https://doi.org/10.1016/0096-3003(86)90119-0
Ierley, G. R., & Ruehr, O. G. (1986). Analytic and Numerical-Solutions of a Nonlinear Boundary-Layer Problem. Studies in Applied Mathematics, 75(1), 1–36.
Ierley, G. R. (1985). Macrodynamics of alpha(2) dynamos. Geophysical and Astrophysical Fluid Dynamics, 34(1–4), 143–173. https://doi.org/10.1080/03091928508245441
Ierley, G. R. (1984). Theoretical Estimates of the Westward Drift. Physics of the Earth and Planetary Interiors, 36, 43–48. https://doi.org/10.1016/0031-9201(84)90097-9
Ierley, G. R., & Young, W. R. (1983). Can the western boundary layer affect the potential vorticity distribution in the Sverdrup interior of a wind gyre. Journal of Physical Oceanography, 13(10), 1753–1763. https://doi.org/10.1175/1520-0485(1983)013<1753:ctwbla>2.0.co;2