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The Reflection of Equatorial Waves from Oceanic Boundaries

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  • 1 Department of Oceanography and Geophysical Fluid Dynamics Institute, Florida State University, Tallahassee, FL 32306
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Abstract

Theory is developed to discuss the reflection of long equatorial waves from ocean boundaries. The main results are as follows:

1) Energy flux reflection coefficients for the reflection of equatorial waves from meridional eastern and western ocean boundaries have been plotted as a function of frequency. The coefficients enable one to determine, for example, how much energy of an incoming equatorial wave of frequency ω is transmitted along an eastern oceanic boundary as poleward propagating Kelvin waves. The coefficients are useful for, both modal and vertically propagating descriptions of equatorial waves. As an example, the reflection of the Yanai wave observed in the equatorial Pacific is discussed in connection with poleward propagating sea levels along the South American coast.

2) Moore (1968) showed that the reflection of an incoming equatorial wave to an eastern meridional boundary consists, in part, of poleward propagating Kelvin waves. Here the same result is generalized to non-meridional small curvature boundaries. The analytic formula associated with this result is useful for determining whether energy of equatorial origin will have Kelvin-like characteristics along a strongly non-meridional boundary.

3) Low-frequency reflection near a non-meridional small curvature eastern boundary can be described analytically. If there is effectively no wind forcing new the boundary, linear solutions near the boundary shores that no matter how complicated the interior motion, near the boundary the motion can be described in terms of long westward propagating Rossby waves (low enough frequency) or poleward propagating Kelvin waves (high enough latitude). The Rossby waves are unaffected by coastline curvature at first order. When the Rossby wave solution is valid, there is no phase propagation along the coast and this result is discussed with reference to the poleward propagating low-frequency “El Niño" sea level signals recently reported in the literature. It seems that in the El Niño frequency band (2π/2 to 2π/5 year−1) the coastal sea level is partly described by Rossby waves and partly by poleward propagating Kelvin waves. There is also some discussion of eastern boundaries with severe bending (the Atlantic eastern boundary) and the seasonal propagation of an upwelling signal along that boundary. Observations indicate that the signal is in the form of a poleward, vertically propagating Kelvin wave and this is consistent with the theory. In both Atlantic and Pacific low-frequency coastal poleward propagating phenomena, dissipation does not appear to play a fundamental role.

Abstract

Theory is developed to discuss the reflection of long equatorial waves from ocean boundaries. The main results are as follows:

1) Energy flux reflection coefficients for the reflection of equatorial waves from meridional eastern and western ocean boundaries have been plotted as a function of frequency. The coefficients enable one to determine, for example, how much energy of an incoming equatorial wave of frequency ω is transmitted along an eastern oceanic boundary as poleward propagating Kelvin waves. The coefficients are useful for, both modal and vertically propagating descriptions of equatorial waves. As an example, the reflection of the Yanai wave observed in the equatorial Pacific is discussed in connection with poleward propagating sea levels along the South American coast.

2) Moore (1968) showed that the reflection of an incoming equatorial wave to an eastern meridional boundary consists, in part, of poleward propagating Kelvin waves. Here the same result is generalized to non-meridional small curvature boundaries. The analytic formula associated with this result is useful for determining whether energy of equatorial origin will have Kelvin-like characteristics along a strongly non-meridional boundary.

3) Low-frequency reflection near a non-meridional small curvature eastern boundary can be described analytically. If there is effectively no wind forcing new the boundary, linear solutions near the boundary shores that no matter how complicated the interior motion, near the boundary the motion can be described in terms of long westward propagating Rossby waves (low enough frequency) or poleward propagating Kelvin waves (high enough latitude). The Rossby waves are unaffected by coastline curvature at first order. When the Rossby wave solution is valid, there is no phase propagation along the coast and this result is discussed with reference to the poleward propagating low-frequency “El Niño" sea level signals recently reported in the literature. It seems that in the El Niño frequency band (2π/2 to 2π/5 year−1) the coastal sea level is partly described by Rossby waves and partly by poleward propagating Kelvin waves. There is also some discussion of eastern boundaries with severe bending (the Atlantic eastern boundary) and the seasonal propagation of an upwelling signal along that boundary. Observations indicate that the signal is in the form of a poleward, vertically propagating Kelvin wave and this is consistent with the theory. In both Atlantic and Pacific low-frequency coastal poleward propagating phenomena, dissipation does not appear to play a fundamental role.

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