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1. Introduction Wave-following buoys are commonly used as devices to measure free surface elevation in the oceans. This is, in part, owing to their relative ease of installation; unlike the majority of Eulerian measurement devices, buoys do not require a supporting structure. Measurements made with both buoys and Eulerian devices are used in operational oceanography and ocean engineering in various forms. Summary statistics such as significant wave height H s and peak period T p are
1. Introduction Wave-following buoys are commonly used as devices to measure free surface elevation in the oceans. This is, in part, owing to their relative ease of installation; unlike the majority of Eulerian measurement devices, buoys do not require a supporting structure. Measurements made with both buoys and Eulerian devices are used in operational oceanography and ocean engineering in various forms. Summary statistics such as significant wave height H s and peak period T p are
1. Introduction Wave-following measurement buoys are widely deployed across the oceans, as they provide a cost effective, easy-to-install alternative to their Eulerian counterparts. As a result of this, they represent an abundant source of data and metocean statistics, outnumbering Eulerian observations by an order of magnitude ( Christou and Ewans 2014 ). However, within the oceanographic community, it is generally perceived that the measurements these devices produce are less accurate
1. Introduction Wave-following measurement buoys are widely deployed across the oceans, as they provide a cost effective, easy-to-install alternative to their Eulerian counterparts. As a result of this, they represent an abundant source of data and metocean statistics, outnumbering Eulerian observations by an order of magnitude ( Christou and Ewans 2014 ). However, within the oceanographic community, it is generally perceived that the measurements these devices produce are less accurate
1. Introduction a. On phase-averaged models Spectral wave modeling has been performed for the last 50 years, using the wave energy balance equation ( Gelci et al. 1957 ). This approach is based on a spectral decomposition of the surface elevation variance across wavenumbers k and directions θ . The spectra density F evolves in five dimensions that are the two spectral dimensions k and θ , the two physical dimensions of the ocean surface (usually longitude and latitude), and time t
1. Introduction a. On phase-averaged models Spectral wave modeling has been performed for the last 50 years, using the wave energy balance equation ( Gelci et al. 1957 ). This approach is based on a spectral decomposition of the surface elevation variance across wavenumbers k and directions θ . The spectra density F evolves in five dimensions that are the two spectral dimensions k and θ , the two physical dimensions of the ocean surface (usually longitude and latitude), and time t
1. Introduction It is well known that the stable background density stratification of the ocean interior allows for the vertical propagation of internal waves (e.g., Gill 1982 ). Furthermore, this process has been studied experimentally in the laboratory (e.g., Stevens and Imberger 1994 ). Moreover, it is also well known that a monochromatic internal wave is an exact solution of the fully nonlinear Euler equations for an unbounded stratified fluid (in the Boussinesq approximation) with a
1. Introduction It is well known that the stable background density stratification of the ocean interior allows for the vertical propagation of internal waves (e.g., Gill 1982 ). Furthermore, this process has been studied experimentally in the laboratory (e.g., Stevens and Imberger 1994 ). Moreover, it is also well known that a monochromatic internal wave is an exact solution of the fully nonlinear Euler equations for an unbounded stratified fluid (in the Boussinesq approximation) with a
1. Introduction Wave–wave interactions in continuously stratified fluids have been a subject of intensive research in the last few decades. Of particular importance is the observation of a nearly universal internal-wave energy spectrum in the ocean, first described by Garrett and Munk ( Garrett and Munk 1972 , 1975 ; Cairns and Williams 1976 ; Garrett and Munk 1979 ). However, it appears that ocean is too complex to be described by one universal model. Accumulating evidence suggests that
1. Introduction Wave–wave interactions in continuously stratified fluids have been a subject of intensive research in the last few decades. Of particular importance is the observation of a nearly universal internal-wave energy spectrum in the ocean, first described by Garrett and Munk ( Garrett and Munk 1972 , 1975 ; Cairns and Williams 1976 ; Garrett and Munk 1979 ). However, it appears that ocean is too complex to be described by one universal model. Accumulating evidence suggests that
1. Introduction When random or directional ocean waves propagate through a current field that varies spatially, their statistical properties, such as significant wave height or mean wave direction, can be modulated. In general, changes in wave characteristics are attributed to physical processes of wave refraction and/or straining ( Holthuijsen and Tolman 1991 ) caused by the horizontal shear current. Recent studies using spaceborne altimeter data have indicated that strong ocean currents, such
1. Introduction When random or directional ocean waves propagate through a current field that varies spatially, their statistical properties, such as significant wave height or mean wave direction, can be modulated. In general, changes in wave characteristics are attributed to physical processes of wave refraction and/or straining ( Holthuijsen and Tolman 1991 ) caused by the horizontal shear current. Recent studies using spaceborne altimeter data have indicated that strong ocean currents, such
1. Introduction Tropical cyclones (TCs) are intense cyclonic atmospheric vortices originated in warm tropical oceans. They are strongly coupled to ocean mixed layer and surface waves through momentum, heat, and moisture exchanges at the air–sea interface. In a TC system, the atmospheric forcing drives sea surface waves and underlying ocean currents, while the energy for a TC to maintain or strengthen its intensity comes mainly from the ocean through air–sea heat and moisture
1. Introduction Tropical cyclones (TCs) are intense cyclonic atmospheric vortices originated in warm tropical oceans. They are strongly coupled to ocean mixed layer and surface waves through momentum, heat, and moisture exchanges at the air–sea interface. In a TC system, the atmospheric forcing drives sea surface waves and underlying ocean currents, while the energy for a TC to maintain or strengthen its intensity comes mainly from the ocean through air–sea heat and moisture
1. Introduction a. Background Oceanic Kelvin waves are a dominant mode of variability in the equatorial Pacific ( Knox and Halpern 1982 ; Johnson and McPhaden 1993 ; Cravatte et al. 2003 ). The apparent relationships between the Madden–Julian oscillation (MJO; Madden and Julian 1994 ; Zhang 2001 ), oceanic Kelvin waves, and the El Niño–Southern Oscillation (ENSO) have been the subjects of much recent debate (e.g., Zhang and Gottschalck 2002 ). Each of these processes are characterized by
1. Introduction a. Background Oceanic Kelvin waves are a dominant mode of variability in the equatorial Pacific ( Knox and Halpern 1982 ; Johnson and McPhaden 1993 ; Cravatte et al. 2003 ). The apparent relationships between the Madden–Julian oscillation (MJO; Madden and Julian 1994 ; Zhang 2001 ), oceanic Kelvin waves, and the El Niño–Southern Oscillation (ENSO) have been the subjects of much recent debate (e.g., Zhang and Gottschalck 2002 ). Each of these processes are characterized by
1. Introduction Ocean waves are an important component of upper ocean dynamics. The synthetic aperture radar (SAR) has been widely used to measure ocean surface wave spectra from space since the Seasat satellite was launched in 1978. Many papers have been published dealing with the wave imaging mechanism and slope retrieval method; for example, Alpers et al. (1981) reviewed the detectability of ocean waves by real and synthetic aperture radar, and Hasselmann et al. (1985) summarized the
1. Introduction Ocean waves are an important component of upper ocean dynamics. The synthetic aperture radar (SAR) has been widely used to measure ocean surface wave spectra from space since the Seasat satellite was launched in 1978. Many papers have been published dealing with the wave imaging mechanism and slope retrieval method; for example, Alpers et al. (1981) reviewed the detectability of ocean waves by real and synthetic aperture radar, and Hasselmann et al. (1985) summarized the
1. Spectral conversions Ocean wave height variance spectra can be functions of either wavenumber or frequency. We refer to the first as the wavenumber spectrum and the second as the frequency spectrum. In a recent paper, I briefly mentioned that the peak of the frequency spectrum ( f p ) cannot in general be related to the peak of the wavenumber spectrum ( k p ) by the ocean wave dispersion relationship ( Plant et al. 2005 ). Unfortunately, this fact does not seem to be widely recognized
1. Spectral conversions Ocean wave height variance spectra can be functions of either wavenumber or frequency. We refer to the first as the wavenumber spectrum and the second as the frequency spectrum. In a recent paper, I briefly mentioned that the peak of the frequency spectrum ( f p ) cannot in general be related to the peak of the wavenumber spectrum ( k p ) by the ocean wave dispersion relationship ( Plant et al. 2005 ). Unfortunately, this fact does not seem to be widely recognized
