Velocity field and pressure analysis of equatorial flows beneath solitary water waves
Tài liệu tham khảo
J. Scott Russell, Report on waves, in: Fourteenth meeting of the British Association for the Advancement of Science, 1844, pp. 311–390.
Craik, 2004, The origins of water wave theory, Annu. Rev. Fluid Mech., 36, 1, 10.1146/annurev.fluid.36.050802.122118
Friedrichs, 1954, The existence of solitary waves, Comm. Pure Appl. Math., 7, 517, 10.1002/cpa.3160070305
Beale, 1977, The existence of solitary water waves, Comm. Pure Appl. Math., 30, 373, 10.1002/cpa.3160300402
Amick, 1981, On solitary water-waves of finite amplitude, Arch. Ration. Mech. Anal., 76, 9, 10.1007/BF00250799
Amick, 1981, On periodic water-waves and their convergence to solitary waves in the long-wave limit, Philos. Trans. R. Soc. Lond. Ser. A, 303, 633, 10.1098/rsta.1981.0231
Craig, 2002, Non-existence of solitary water waves in three dimensions, R. Soc. Lond. Philos. Trans. Ser. A Math. Phys. Eng. Sci., 360, 2127, 10.1098/rsta.2002.1065
Craig, 1992, Symmetry of free-surface flows, Arch. Ration. Mech. Anal., 118, 1, 10.1007/BF00375690
Craig, 1988, Symmetry of solitary waves, Comm. Partial Differ. Equ., 13, 603, 10.1080/03605308808820554
Hur, 2008, Exact solitary water waves with vorticity, Arch. Ration. Mech. Anal., 188, 213, 10.1007/s00205-007-0064-6
Wheeler, 2013, Large-amplitude solitary water waves with vorticity, SIAM J. Math. Anal., 45, 2937, 10.1137/120891460
Constantin, 2006, The trajectories of particles in Stokes waves, Invent. Math., 166, 523, 10.1007/s00222-006-0002-5
Constantin, 2007, Particle trajectories in solitary water waves, Bull. Amer. Math. Soc., 44, 423, 10.1090/S0273-0979-07-01159-7
Constantin, 2010, On the particle paths in solitary water waves, Quart. Appl. Math., 68, 81, 10.1090/S0033-569X-09-01166-1
Constantin, 2010, Pressure beneath a Stokes wave, Comm. Pure Appl. Math., 63, 533, 10.1002/cpa.20299
Constantin, 2011, Nonlinear water waves with applications to wave-current interactions and tsunamis
Tsai, 2005, On the recovery of surface wave by pressure transfer function, Ocean Eng., 32, 1247, 10.1016/j.oceaneng.2004.10.020
Basu, 2018, Solitary water waves propagating on an underlying uniform current over a finite depth, Nonlinear Anal., 172, 25, 10.1016/j.na.2018.02.003
Constantin, 2011, Pressure beneath a solitary water wave: mathematical theory and experiments, Arch. Ration. Mech. Anal., 201, 251, 10.1007/s00205-011-0396-0
Genoud, 2017, Extrema of the dynamic pressure in a solitary wave, Nonlinear Anal., 155, 65, 10.1016/j.na.2017.01.009
Ehrnström, 2008, On the streamlines and particle paths of gravitational water waves, Nonlinearity, 21, 1141, 10.1088/0951-7715/21/5/012
Basu, 2016, Irrotational two-dimensional free-surface steady water flows over a flat bed with underlying currents, Nonlinear Anal., 147, 110, 10.1016/j.na.2016.08.016
Lyons, 2016, The pressure distribution in extreme Stokes waves, Nonlinear Anal. RWA, 31, 77, 10.1016/j.nonrwa.2016.01.008
Constantin, 2016, Extrema of the dynamic pressure in an irrotational regular wave train, Phys. Fluids, 28, 10.1063/1.4967362
Fan, 2017, Extrema of the dynamic pressure in an irrotational Stokes wave with underlying currents and infinite depth, Nonlinear Anal., 162, 13, 10.1016/j.na.2017.06.006
Martin, 2015, Analyticity of the streamlines and of the free surface for periodic equatorial gravity water flows with vorticity, Nonlinear Anal. RWA, 21, 27, 10.1016/j.nonrwa.2014.06.003
Hsu, 2014, Some nonlinear internal equatorial flows, Nonlinear Anal. RWA, 18, 69, 10.1016/j.nonrwa.2013.12.011
Vallis, 2006
Constantin, 2012, On the modelling of equatorial waves, Geophys. Res. Lett., 39, L05602, 10.1029/2012GL051169
Chu, 2020, Steady periodic waves and formal stability for fixed-depth rotational equatorial flows, J. Differential Equations, 269, 4192, 10.1016/j.jde.2020.03.040
Constantin, 2015, The dynamics of waves interacting with the equatorial undercurrent, Geophys. Astrophys. Fluid Dyn., 109, 311, 10.1080/03091929.2015.1066785
Constantin, 2019, Equatorial wave–current interactions, Comm. Math. Phys., 370, 1, 10.1007/s00220-019-03483-8
Quirchmayr, 2017, On irrotational flows beneath periodic traveling equatorial waves, J. Math. Fluid Mech., 19, 283, 10.1007/s00021-016-0280-7
Wheeler, 2019, On stratified water waves with critical layers and coriolis forces, Discrete Contin. Dyn. Syst., 39, 4747, 10.3934/dcds.2019193
Fedorov, 2009, Equatorial waves, 3679
Chu, 2021, A flow force reformulation of steady periodic fixed-depth irrotational equatorial flows, J. Differential Equations, 292, 220, 10.1016/j.jde.2021.05.029
Chu, 2021, Variational formulations of steady rotational equatorial waves, Adv. Nonlinear Anal., 10, 534, 10.1515/anona-2020-0146
Chu, 2021, Variational formulation of rotational steady water waves in two-layer flows, J. Math. Fluid Mech., 23
Chu, 2019, Steady periodic equatorial water waves with vorticity, Discrete Contin. Dyn. Syst., 39, 4713, 10.3934/dcds.2019191
Fraenkel, 2000
Lighthill, 1978
Jones, 2007, Measuring short-period wind waves in a tidally forced environment with a subsurface pressure gauge, Limnol. Oceanogr. Methods, 5, 317, 10.4319/lom.2007.5.317
Constantin, 2014, Estimating wave heights from pressure data at the bed, J. Fluid Mech., 743, 10.1017/jfm.2014.81
Basu, 2017, Estimation of wave heights from pressure data at the bed in the presence of uniform underlying currents, Nonlinear Anal., 156, 82, 10.1016/j.na.2017.01.016
Basu, 2018, Wave height estimates from pressure and velocity data at an intermediate depth in the presence of uniform currents, Philos. Trans. Roy. Soc. A, 376
Clamond, 2020, Extreme water-wave profile recovery from pressure measurements at the seabed, J. Fluid Mech., 903, 10.1017/jfm.2020.729
Clamond, 2013, Recovery of steady periodic wave profiles from pressure measurements at the bed, J. Fluid Mech., 714, 463, 10.1017/jfm.2012.490
Kogelbauer, 2015, Recovery of the wave profile for irrotational periodic water waves from pressure measurements, Nonlinear Anal. RWA, 22, 219, 10.1016/j.nonrwa.2014.09.003
Hsu, 2014, Recovering surface profiles of solitary waves on a uniform stream from pressure measurements, Discrete Contin. Dyn. Syst., 34, 3035, 10.3934/dcds.2014.34.3035
Constantin, 2012, On the recovery of solitary wave profiles from pressure measurements, J. Fluid Mech., 699, 376, 10.1017/jfm.2012.114
Oliveras, 2012, Recovering the water-wave profile from pressure measurements, SIAM J. Appl. Math., 72, 897, 10.1137/110853285
Henry, 2013, Steady periodic waves bifurcating for fixed-depth rotational flows, Quart. Appl. Math., 71, 455, 10.1090/S0033-569X-2013-01293-8
Constantin, 2004, Exact steady periodic water waves with vorticity, Comm. Pure Appl. Math., 57, 481, 10.1002/cpa.3046
Basu, 2020, A flow force reformulation for steady irrotational water waves, J. Differential Equations, 268, 7417, 10.1016/j.jde.2019.11.057
Amick, 1987, Bounds for water waves, Arch. Ration. Mech. Anal., 99, 91, 10.1007/BF00275873