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July  2022, 21(7): i-iv. doi: 10.3934/cpaa.2022094

Preface to the special issue on analysis of geophysical phenomena

Adrian Constantin

Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria

Published  July 2022 Early access  May 2022

Citation: Adrian Constantin. Preface to the special issue on analysis of geophysical phenomena. Communications on Pure and Applied Analysis, 2022, 21 (7) : i-iv. doi: 10.3934/cpaa.2022094
References:
[1]

A. Aleman and A. Constantin, Harmonic maps and ideal fluid flows, Arch. Ration. Mech. Anal., 204 (2012), 479-513.  doi: 10.1007/s00205-011-0483-2.

[2]

B. Basu, On the nonlinear three-dimensional models in equatorial ocean flows, Commun. Pure Appl. Anal., this issue.

[3]

J. P. Boyd, Dynamics of the Equatorial Ocean, Springer, Berlin, 2018.

[4]

A. Constantin, Edge waves along a sloping beach, J. Phys. A, 45 (2001), 9723-9731. 

[5]

A. Constantin, Frictional effects in wind-driven ocean currents, Geophys. Astrophys. Fluid Dyn., 115 (2021), 311-358.  doi: 10.1080/03091929.2020.1748614.

[6]

A. Constantin, D. G. Crowdy, V. S. Krishnamurthy and M. H. Wheeler, Stuart-type polar vortices on a rotating sphere, Discrete Cont. Dyn. Syst., 21 (2021), 201-215.  doi: 10.3934/dcds.2020263.

[7]

A. Constantin and P. Germain, Stratospheric planetary flows from the perspective of the Euler equation on a rotating sphere, Arch. Ration. Mech. Anal., to appear.

[8]

A. Constantin and R. I. Ivanov, Equatorial wave-current interactions, Comm. Math. Phys., 370 (2019), 1-48.  doi: 10.1007/s00220-019-03483-8.

[9]

A. Constantin, R. I. Ivanov and C. I. Martin, Hamiltonian formulation for wave-current interactions in stratified rotational flows, Arch. Ration. Mech. Anal., 221 (2016), 1-48.  doi: 10.1007/s00205-016-0990-2.

[10]

A. Constantin and R. S. Johnson, The dynamics of waves interacting with the Equatorial Undercurrent, Geophys. Astrophys. Fluid Dyn., 109 (2015), 311-358.  doi: 10.1080/03091929.2015.1066785.

[11]

A. Constantin and R. S. Johnson, Large gyres as a shallow-water asymptotic solution of Euler's equation in spherical coordinates, Proc. A, 473 (2017), Art. 20170063. doi: 10.1098/rspa.2017.0063.

[12]

A. Constantin and R. S. Johnson, Steady large-scale ocean flows in spherical coordinates, Oceanography, 31 (2018), 42-50. 

[13]

A. Constantin and R. S. Johnson, Atmospheric Ekman flows with variable eddy viscosity, Boundary-Layer Meteorology, 170 (2019), 395-414. 

[14]

A. Constantin and R. S. Johnson, On the modelling of large-scale atmospheric flow, J. Differ. Equ., 285 (2021), 751-798.  doi: 10.1016/j.jde.2021.03.019.

[15]

A. Constantin and R. S. Johnson, On the propagation of waves in the atmosphere, Proc. A, 477 (2021), Art. 20200424.

[16]

A. Constantin and R. S. Johnson, On the propagation of nonlinear waves in the atmosphere, Proc. A, 478 (2022), Art. 20210895. doi: 10.1098/rspa.2021.0895.

[17]

A. Constantin and S. G. Monismith, Gerstner waves in the presence of mean currents and rotation, J. Fluid Mech., 820 (2017), 511-528.  doi: 10.1017/jfm.2017.223.

[18]

O. Constantin and M. J. Martin, A harmonic maps approach to fluid flows, Math. Ann., 369 (2017), 1-16.  doi: 10.1007/s00208-016-1435-9.

[19]

D. G. Crowdy, Stuart vortices on a sphere, J. Fluid Mech., 398 (2004), 381-402.  doi: 10.1017/S0022112003007043.

[20]

J. D. Cullen and R. I. Ivanov, Hamiltonian description of internal ocean waves with Coriolis force, Commun. Pure Appl. Anal., this issue.

[21] B. Cushman-Roisin and J.-M. Beckers, Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects, Academic Press, New York, 2011. 
[22]

A. Geyer and R. Quirchmayr, Weakly nonlinear waves in stratified shear flows, Commun. Pure Appl. Anal., this issue.

[23]

S. Haziot, On the spherical geopotential approximation for Saturn, Commun. Pure Appl. Anal., this issue.

[24]

D. Henry, Energy considerations for nonlinear equatorial water waves, Commun. Pure Appl. Anal., this issue.

[25] J. R. Holton and G. J. Hakim, An introduction to dynamic meteorology, Academic Press, 2013. 
[26]

R. S. Johnson, Some contributions to the theory of edge waves, J. Fluid Mech., 524 (2005), 81-97. 

[27]

R. S. Johnson, The ocean and the atmosphere: an applied mathematician's view, Commun. Pure Appl. Anal., this issue.

[28]

V. S. Krishnamurthy, Liouville links and chains on the plane and associated point vortex equilibria, Commun. Pure Appl. Anal., this issue.

[29] J. Lighthill, Waves in fluids, Cambridge University Press, 2001. 
[30]

T. Lyons, Particle paths in equatorial flows, Commun. Pure Appl. Anal., this issue.

[31]

C. I. Martin, On three-dimensional free surface water flows with constant vorticity, Commun. Pure Appl. Anal., this issue.

[32]

K. Marynets, Stability analysis of the boundary value problem modeling a two-layer ocean, Commun. Pure Appl. Anal., this issue.

[33]

A.-V. Matioc, An exact solution for geophysical equatorial edge waves over a sloping beach, J. Phys. A, 45 (2012), Art. 365501. doi: 10.1088/1751-8113/45/36/365501.

[34]

F. Miao, M. Fečkan and J. Wang, Exact solution and instability for geophysical edge waves, Commun. Pure Appl. Anal., this issue.

[35]

L. Roberti, The surface current of Ekman flows with time-dependent eddy viscosity, Commun. Pure Appl. Anal., this issue.

[36]

Ł. Rudnicki, Geophysics and Stuart vortices on a sphere meet differential geometry, Commun. Pure Appl. Anal., this issue.

[37] G. K. Vallis, Atmosphere and Ocean Fluid Dynamics, Cambridge University Press, Cambridge, 2006. 

show all references

References:
[1]

A. Aleman and A. Constantin, Harmonic maps and ideal fluid flows, Arch. Ration. Mech. Anal., 204 (2012), 479-513.  doi: 10.1007/s00205-011-0483-2.

[2]

B. Basu, On the nonlinear three-dimensional models in equatorial ocean flows, Commun. Pure Appl. Anal., this issue.

[3]

J. P. Boyd, Dynamics of the Equatorial Ocean, Springer, Berlin, 2018.

[4]

A. Constantin, Edge waves along a sloping beach, J. Phys. A, 45 (2001), 9723-9731. 

[5]

A. Constantin, Frictional effects in wind-driven ocean currents, Geophys. Astrophys. Fluid Dyn., 115 (2021), 311-358.  doi: 10.1080/03091929.2020.1748614.

[6]

A. Constantin, D. G. Crowdy, V. S. Krishnamurthy and M. H. Wheeler, Stuart-type polar vortices on a rotating sphere, Discrete Cont. Dyn. Syst., 21 (2021), 201-215.  doi: 10.3934/dcds.2020263.

[7]

A. Constantin and P. Germain, Stratospheric planetary flows from the perspective of the Euler equation on a rotating sphere, Arch. Ration. Mech. Anal., to appear.

[8]

A. Constantin and R. I. Ivanov, Equatorial wave-current interactions, Comm. Math. Phys., 370 (2019), 1-48.  doi: 10.1007/s00220-019-03483-8.

[9]

A. Constantin, R. I. Ivanov and C. I. Martin, Hamiltonian formulation for wave-current interactions in stratified rotational flows, Arch. Ration. Mech. Anal., 221 (2016), 1-48.  doi: 10.1007/s00205-016-0990-2.

[10]

A. Constantin and R. S. Johnson, The dynamics of waves interacting with the Equatorial Undercurrent, Geophys. Astrophys. Fluid Dyn., 109 (2015), 311-358.  doi: 10.1080/03091929.2015.1066785.

[11]

A. Constantin and R. S. Johnson, Large gyres as a shallow-water asymptotic solution of Euler's equation in spherical coordinates, Proc. A, 473 (2017), Art. 20170063. doi: 10.1098/rspa.2017.0063.

[12]

A. Constantin and R. S. Johnson, Steady large-scale ocean flows in spherical coordinates, Oceanography, 31 (2018), 42-50. 

[13]

A. Constantin and R. S. Johnson, Atmospheric Ekman flows with variable eddy viscosity, Boundary-Layer Meteorology, 170 (2019), 395-414. 

[14]

A. Constantin and R. S. Johnson, On the modelling of large-scale atmospheric flow, J. Differ. Equ., 285 (2021), 751-798.  doi: 10.1016/j.jde.2021.03.019.

[15]

A. Constantin and R. S. Johnson, On the propagation of waves in the atmosphere, Proc. A, 477 (2021), Art. 20200424.

[16]

A. Constantin and R. S. Johnson, On the propagation of nonlinear waves in the atmosphere, Proc. A, 478 (2022), Art. 20210895. doi: 10.1098/rspa.2021.0895.

[17]

A. Constantin and S. G. Monismith, Gerstner waves in the presence of mean currents and rotation, J. Fluid Mech., 820 (2017), 511-528.  doi: 10.1017/jfm.2017.223.

[18]

O. Constantin and M. J. Martin, A harmonic maps approach to fluid flows, Math. Ann., 369 (2017), 1-16.  doi: 10.1007/s00208-016-1435-9.

[19]

D. G. Crowdy, Stuart vortices on a sphere, J. Fluid Mech., 398 (2004), 381-402.  doi: 10.1017/S0022112003007043.

[20]

J. D. Cullen and R. I. Ivanov, Hamiltonian description of internal ocean waves with Coriolis force, Commun. Pure Appl. Anal., this issue.

[21] B. Cushman-Roisin and J.-M. Beckers, Introduction to Geophysical Fluid Dynamics: Physical and Numerical Aspects, Academic Press, New York, 2011. 
[22]

A. Geyer and R. Quirchmayr, Weakly nonlinear waves in stratified shear flows, Commun. Pure Appl. Anal., this issue.

[23]

S. Haziot, On the spherical geopotential approximation for Saturn, Commun. Pure Appl. Anal., this issue.

[24]

D. Henry, Energy considerations for nonlinear equatorial water waves, Commun. Pure Appl. Anal., this issue.

[25] J. R. Holton and G. J. Hakim, An introduction to dynamic meteorology, Academic Press, 2013. 
[26]

R. S. Johnson, Some contributions to the theory of edge waves, J. Fluid Mech., 524 (2005), 81-97. 

[27]

R. S. Johnson, The ocean and the atmosphere: an applied mathematician's view, Commun. Pure Appl. Anal., this issue.

[28]

V. S. Krishnamurthy, Liouville links and chains on the plane and associated point vortex equilibria, Commun. Pure Appl. Anal., this issue.

[29] J. Lighthill, Waves in fluids, Cambridge University Press, 2001. 
[30]

T. Lyons, Particle paths in equatorial flows, Commun. Pure Appl. Anal., this issue.

[31]

C. I. Martin, On three-dimensional free surface water flows with constant vorticity, Commun. Pure Appl. Anal., this issue.

[32]

K. Marynets, Stability analysis of the boundary value problem modeling a two-layer ocean, Commun. Pure Appl. Anal., this issue.

[33]

A.-V. Matioc, An exact solution for geophysical equatorial edge waves over a sloping beach, J. Phys. A, 45 (2012), Art. 365501. doi: 10.1088/1751-8113/45/36/365501.

[34]

F. Miao, M. Fečkan and J. Wang, Exact solution and instability for geophysical edge waves, Commun. Pure Appl. Anal., this issue.

[35]

L. Roberti, The surface current of Ekman flows with time-dependent eddy viscosity, Commun. Pure Appl. Anal., this issue.

[36]

Ł. Rudnicki, Geophysics and Stuart vortices on a sphere meet differential geometry, Commun. Pure Appl. Anal., this issue.

[37] G. K. Vallis, Atmosphere and Ocean Fluid Dynamics, Cambridge University Press, Cambridge, 2006. 
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