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summertime stratification. The model is biased somewhat fresh in the upper ocean ( Almansi et al. 2017 ; Saberi et al. 2020 ), and is therefore more stratified than observations (cf. the contours in Figs. 2a and 2b ). As will be shown in section 4d , differences in stratification have only a minor impact on the wave properties. Fig . 3. Vertical density stratification quantified with the buoyancy frequency N . Solid lines are summer profiles (June–September); dashed lines are winter profiles (October
summertime stratification. The model is biased somewhat fresh in the upper ocean ( Almansi et al. 2017 ; Saberi et al. 2020 ), and is therefore more stratified than observations (cf. the contours in Figs. 2a and 2b ). As will be shown in section 4d , differences in stratification have only a minor impact on the wave properties. Fig . 3. Vertical density stratification quantified with the buoyancy frequency N . Solid lines are summer profiles (June–September); dashed lines are winter profiles (October
1. Introduction Internal waves are the dominant sources of finescale velocity variance in the frequency range from f (local inertial) to N (Brunt–Väisälä) and are important contributors to mixing the abyssal ocean ( Munk and Wunsch 1998 ; Egbert and Ray 2000 ). They act as intermediaries between narrowband forcing mechanisms (e.g., tides and storms) and eventual dissipation into heat. By breaking, these waves produce mixing that brings deep dense cold water formed at high latitudes to the
1. Introduction Internal waves are the dominant sources of finescale velocity variance in the frequency range from f (local inertial) to N (Brunt–Väisälä) and are important contributors to mixing the abyssal ocean ( Munk and Wunsch 1998 ; Egbert and Ray 2000 ). They act as intermediaries between narrowband forcing mechanisms (e.g., tides and storms) and eventual dissipation into heat. By breaking, these waves produce mixing that brings deep dense cold water formed at high latitudes to the
1. Introduction The acoustic Doppler current profiler (ADCP) is the most widely used instrument for observing ocean currents. Many studies have demonstrated the unique capabilities of this technique (based on sampling the range-gated Doppler return of acoustic beams); it can map the detailed space–time evolution of internal waves (e.g., Pinkel 1979 , 1983 ) and small-scale nearshore circulation features ( Smith 1993 ; Smith and Largier 1995 ), and it can resolve the directional properties of
1. Introduction The acoustic Doppler current profiler (ADCP) is the most widely used instrument for observing ocean currents. Many studies have demonstrated the unique capabilities of this technique (based on sampling the range-gated Doppler return of acoustic beams); it can map the detailed space–time evolution of internal waves (e.g., Pinkel 1979 , 1983 ) and small-scale nearshore circulation features ( Smith 1993 ; Smith and Largier 1995 ), and it can resolve the directional properties of
comprehensive reviews]. In the literature, time-mean properties of the dominant waves in each regime of the QBO cycle are examined via statistical methods, such as composite and spectral analysis ( Tindall et al. 2006a , b ; Yang et al. 2011 ) or windowed spectral analysis ( Alexander et al. 2008 ; Ern et al. 2008 ). To the authors’ knowledge, the continuous mutual evolution of equatorial waves and the QBO has not been examined from instantaneous fields, although the continuous evolution of the wave drag
comprehensive reviews]. In the literature, time-mean properties of the dominant waves in each regime of the QBO cycle are examined via statistical methods, such as composite and spectral analysis ( Tindall et al. 2006a , b ; Yang et al. 2011 ) or windowed spectral analysis ( Alexander et al. 2008 ; Ern et al. 2008 ). To the authors’ knowledge, the continuous mutual evolution of equatorial waves and the QBO has not been examined from instantaneous fields, although the continuous evolution of the wave drag
; Dunkerton 1997 ), and they are a dominant source for turbulence due to gravity wave breaking and dissipation [cf. Fritts and Alexander (2003) for a review of middle atmospheric gravity waves]. As gravity waves influence the mesoscale flow (e.g., Zhang 2004 ), their accurate simulation is of great interest. One of the problems associated with the simulation of gravity waves is their dispersive property. The physical dispersion is mainly influenced by the static stability of the air. However, in
; Dunkerton 1997 ), and they are a dominant source for turbulence due to gravity wave breaking and dissipation [cf. Fritts and Alexander (2003) for a review of middle atmospheric gravity waves]. As gravity waves influence the mesoscale flow (e.g., Zhang 2004 ), their accurate simulation is of great interest. One of the problems associated with the simulation of gravity waves is their dispersive property. The physical dispersion is mainly influenced by the static stability of the air. However, in
of the surface mooring for more than 2 h. ISW properties, energetics, and instabilities are studied using the combined shipboard and mooring measurements. 3. Energetics of internal solitary waves The theoretical framework of the energetics of two-dimensional nonhydrostatic ISWs is described by Moum et al. (2007a , b ) and Lamb and Nguyen (2009) . ISW KE is defined as where ρ 0 = 1000 kg m −3 is a constant Boussinesq density, and u and w are the along-wave velocity and vertical velocity
of the surface mooring for more than 2 h. ISW properties, energetics, and instabilities are studied using the combined shipboard and mooring measurements. 3. Energetics of internal solitary waves The theoretical framework of the energetics of two-dimensional nonhydrostatic ISWs is described by Moum et al. (2007a , b ) and Lamb and Nguyen (2009) . ISW KE is defined as where ρ 0 = 1000 kg m −3 is a constant Boussinesq density, and u and w are the along-wave velocity and vertical velocity
still active in directional wave fields with typical angular spreads and typical mean steepness. The steepness is a recognized key property for this instability that is routinely identified by the modulational index (i.e., Benjamin and Feir 1967 ; Onorato et al. 2002 ; Janssen 2003 ; among others), where k 0 and f 0 are characteristic wavenumber and frequency in a wave train or wave field and Δ f is the bandwidth that defined the wave groups in this field. As an approximate rule, for the
still active in directional wave fields with typical angular spreads and typical mean steepness. The steepness is a recognized key property for this instability that is routinely identified by the modulational index (i.e., Benjamin and Feir 1967 ; Onorato et al. 2002 ; Janssen 2003 ; among others), where k 0 and f 0 are characteristic wavenumber and frequency in a wave train or wave field and Δ f is the bandwidth that defined the wave groups in this field. As an approximate rule, for the
-Jelloul (1997) in that they do not assume a mean flow with low Ro g and high Ri g and are, thus, appropriate for currents with strong baroclinicity and O (1) Ro g and Ri g . In sections 3 and 4 , we discuss the mechanics, energetics, and propagation of waves under this governing system. Several of the unusual properties of these waves are elucidated using parcel arguments to understand the fundamental physics. In section 5 , we present a numerical solution to the wave propagation problem in an
-Jelloul (1997) in that they do not assume a mean flow with low Ro g and high Ri g and are, thus, appropriate for currents with strong baroclinicity and O (1) Ro g and Ri g . In sections 3 and 4 , we discuss the mechanics, energetics, and propagation of waves under this governing system. Several of the unusual properties of these waves are elucidated using parcel arguments to understand the fundamental physics. In section 5 , we present a numerical solution to the wave propagation problem in an
) , while Jones’ equation is itself a generalization of an equation used earlier ( Eady 1949 ). A solution method for the equation is outlined. An important character of modes in shear is that the wave speed and modal shapes at a given location can be functions of wave direction, for example, the modal properties are anisotropic. It is convenient but incomplete to refer to the modes as having anisotropic wavenumbers, as there is also spatial dependence, that is, modal properties are heterogeneous. The
) , while Jones’ equation is itself a generalization of an equation used earlier ( Eady 1949 ). A solution method for the equation is outlined. An important character of modes in shear is that the wave speed and modal shapes at a given location can be functions of wave direction, for example, the modal properties are anisotropic. It is convenient but incomplete to refer to the modes as having anisotropic wavenumbers, as there is also spatial dependence, that is, modal properties are heterogeneous. The
experiments or observations to validate their results. In practice, engineers rely on probability distributions of wave heights for design and safety procedures. In particular, the likelihood of encountering very large waves is needed. Previous studies have attempted to predict the statistical properties of surface gravity waves employing both first- and second-order theories. In the linear theory, under the narrowband spectrum condition, free surface elevation is described by a Gaussian distribution and
experiments or observations to validate their results. In practice, engineers rely on probability distributions of wave heights for design and safety procedures. In particular, the likelihood of encountering very large waves is needed. Previous studies have attempted to predict the statistical properties of surface gravity waves employing both first- and second-order theories. In the linear theory, under the narrowband spectrum condition, free surface elevation is described by a Gaussian distribution and
