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Forcing and friction effects on vertically propagating waves in the equatorial oceans
520
A. PhysicalOceanography
to include interactions up to an arbitrary order in wave steepness. A large number of free wave modes are typically used whose amplitude evolutions are determined through a pseudospectral treatment of the nonlinear free-surface conditions. Method efficiency and accuracy are demonstrated by comparisons to fully nonlinear semi-Lagrangian computations; calculations of long-time evolution of wavetrains using the modified Zakharov equations; and experimental measurements of a travelling wave packet. Nonlinear interactions between two colliding wave envelopes of different carrier frequencies are also considered. Dept. of Ocean Engng, MIT, Cambridge, M A 02139, USA. 88:3257 Fenton, J.D. and R.J. Sobey (comments), 1988. Discussion of 'Nonuniqneness in stream function wave theoD',' by R.A. Dalrymple and Pedro Solara. J. WatWay Port coast. Ocean Engng, Am. Soc. civ. Engrs, 114(1):110-114. 88:3258 Gent, P.R., 1987. Forcing and friction effects on vertically propagating waves in the equatorial oceans. J. phys. Oceanogr., 17(11):1897-1908. A new projection onto the meridional eigenfunctions of the pressure equation, derived for a single Fourier wave component, demonstrates that the solution is regular and not singular at the inertial latitudes, and is more convenient to use than the corresponding projection onto the meridional velocity equation. The wavenumber spectrum from the resulting forced vertical structure equation, found for four choices of vertical profile for the body force, is insensitive to the particular profile chosen. The projection is used to study the effects of forcing and linear damping on the vertical propagation of space-time transformed energy in three wave modes: Kelvin, first Rossby and mixed Rossby-gravity waves. With constant buoyancy frequency, energy decay is exponential in depth with the coefficient proportional to the damping magnitude. Linear damping effects are very different on each wave. Thus, it is fallacious to make deductions about meridional phase changes in the total solution to a general forced problem from the phase changes of each wave component. NCAR, Boulder, CO 80307, USA. 88:3259 Hudspeth, R.T., J.H, Nath and P. Khare, 1988. Wave phase/amplitude effects on force coefficients. J. Wat Way Port coast. Ocean Engng, A m. Soc. cir. Engrs, 114(1):34-49. An algorithm to compute force coefficients for the two-term Morison equation for a cylinder in waves
OLR (1988)35 (6)
illustrates the parametric dependence of force coefficient estimates on the Dean eccentricity parameter and their sensitivity to phase/amplitude measurements of the ambient wave. The algorithm is based on linear regression analysis of error in the computed force assuming that the Morison equation and linear wave theory represent the 'true' force and wave kinematics exactly. Ocean Engng Prog., Dept. of Civ. Engng, Oregon State Univ., Corvallis, OR 97331, USA. (emm) 88:3260 Janssen, P.A.E.M., 1987. The initial evolution of gravity--capillary waves. J. Fluid Mech., 184: 581 597. Discussed here is the initial evolution of windgenerated, gravity-capillary waves by means of a dynamical model that includes the effects of wind input, viscous dissipation and three-wave interactions. Studies of the generation of the initial wavelets by wind reveal that under certain conditions a sudden migration of the peak wavenumber is found, related to the phenomenon of second-harmonic resonance. During the generation of the initial wavelets by wind, nonlinear three-wave interactions may be important. Therefore, the experimental determination of the growth rate of the waves by wind by just analysing the time series of the surface elevation might be in error. ECMWF, Shinfield Park, Reading, UK. 88:3261 Kirby, J.T. (comment), 1988. Discussion of 'Refraction--diffraction model for linear water waves,' by B,A. Ebersole. J. WatWay Port coast. Ocean Engng, Am. Soc. civ. Engrs, l l4(1):101-103. 88:3262 McCalpin, J.D., 1987. A note on the reflection of low-frequency equatorial Rosshy waves from realistic western boundaries. J. phys. Oceanogr., 17(11): 1944-1949. The analytic theory of Cane and Gent on the reflection of low frequency equatorial waves from arbitrary boundaries is applied to the reflection of long Rossby waves from realistic approximations to the western boundaries of the Atlantic, Pacific, and Indian oceans. Results show that low-frequency, first meridional mode, first baroclinic mode reflection is close to that of a straight north-south boundary in all three basins. Increasing the frequency, meridional mode number, a n d / o r vertical mode number causes drastic changes in the energy flux reflection coefficients. Corresponding to the general slope and complexity of the coastline, effects are greatest for the Pacific Ocean and least for the Indian Ocean.
A. PhysicalOceanography
to include interactions up to an arbitrary order in wave steepness. A large number of free wave modes are typically used whose amplitude evolutions are determined through a pseudospectral treatment of the nonlinear free-surface conditions. Method efficiency and accuracy are demonstrated by comparisons to fully nonlinear semi-Lagrangian computations; calculations of long-time evolution of wavetrains using the modified Zakharov equations; and experimental measurements of a travelling wave packet. Nonlinear interactions between two colliding wave envelopes of different carrier frequencies are also considered. Dept. of Ocean Engng, MIT, Cambridge, M A 02139, USA. 88:3257 Fenton, J.D. and R.J. Sobey (comments), 1988. Discussion of 'Nonuniqneness in stream function wave theoD',' by R.A. Dalrymple and Pedro Solara. J. WatWay Port coast. Ocean Engng, Am. Soc. civ. Engrs, 114(1):110-114. 88:3258 Gent, P.R., 1987. Forcing and friction effects on vertically propagating waves in the equatorial oceans. J. phys. Oceanogr., 17(11):1897-1908. A new projection onto the meridional eigenfunctions of the pressure equation, derived for a single Fourier wave component, demonstrates that the solution is regular and not singular at the inertial latitudes, and is more convenient to use than the corresponding projection onto the meridional velocity equation. The wavenumber spectrum from the resulting forced vertical structure equation, found for four choices of vertical profile for the body force, is insensitive to the particular profile chosen. The projection is used to study the effects of forcing and linear damping on the vertical propagation of space-time transformed energy in three wave modes: Kelvin, first Rossby and mixed Rossby-gravity waves. With constant buoyancy frequency, energy decay is exponential in depth with the coefficient proportional to the damping magnitude. Linear damping effects are very different on each wave. Thus, it is fallacious to make deductions about meridional phase changes in the total solution to a general forced problem from the phase changes of each wave component. NCAR, Boulder, CO 80307, USA. 88:3259 Hudspeth, R.T., J.H, Nath and P. Khare, 1988. Wave phase/amplitude effects on force coefficients. J. Wat Way Port coast. Ocean Engng, A m. Soc. cir. Engrs, 114(1):34-49. An algorithm to compute force coefficients for the two-term Morison equation for a cylinder in waves
OLR (1988)35 (6)
illustrates the parametric dependence of force coefficient estimates on the Dean eccentricity parameter and their sensitivity to phase/amplitude measurements of the ambient wave. The algorithm is based on linear regression analysis of error in the computed force assuming that the Morison equation and linear wave theory represent the 'true' force and wave kinematics exactly. Ocean Engng Prog., Dept. of Civ. Engng, Oregon State Univ., Corvallis, OR 97331, USA. (emm) 88:3260 Janssen, P.A.E.M., 1987. The initial evolution of gravity--capillary waves. J. Fluid Mech., 184: 581 597. Discussed here is the initial evolution of windgenerated, gravity-capillary waves by means of a dynamical model that includes the effects of wind input, viscous dissipation and three-wave interactions. Studies of the generation of the initial wavelets by wind reveal that under certain conditions a sudden migration of the peak wavenumber is found, related to the phenomenon of second-harmonic resonance. During the generation of the initial wavelets by wind, nonlinear three-wave interactions may be important. Therefore, the experimental determination of the growth rate of the waves by wind by just analysing the time series of the surface elevation might be in error. ECMWF, Shinfield Park, Reading, UK. 88:3261 Kirby, J.T. (comment), 1988. Discussion of 'Refraction--diffraction model for linear water waves,' by B,A. Ebersole. J. WatWay Port coast. Ocean Engng, Am. Soc. civ. Engrs, l l4(1):101-103. 88:3262 McCalpin, J.D., 1987. A note on the reflection of low-frequency equatorial Rosshy waves from realistic western boundaries. J. phys. Oceanogr., 17(11): 1944-1949. The analytic theory of Cane and Gent on the reflection of low frequency equatorial waves from arbitrary boundaries is applied to the reflection of long Rossby waves from realistic approximations to the western boundaries of the Atlantic, Pacific, and Indian oceans. Results show that low-frequency, first meridional mode, first baroclinic mode reflection is close to that of a straight north-south boundary in all three basins. Increasing the frequency, meridional mode number, a n d / o r vertical mode number causes drastic changes in the energy flux reflection coefficients. Corresponding to the general slope and complexity of the coastline, effects are greatest for the Pacific Ocean and least for the Indian Ocean.