Observations of the Vertical Structure of Internal Waves (original) (raw)
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Ocean Science, 2012
Hydrographic data from full-depth moorings maintained by the Rapid/MOCHA project and spanning the Atlantic at 26 • N are decomposed into vertical modes in order to give a dynamical framework for interpreting the observed fluctuations. Vertical modes at each mooring are fit to pressure perturbations using a Gauss-Markov inversion. Away from boundaries, the vertical structure is almost entirely described by the first baroclinic mode, as confirmed by high correlation between the original signal and reconstructions using only the first baroclinic mode. These first baroclinic motions are also highly coherent with altimetric sea surface height (SSH). Within a Rossby radius (45 km) of the western and eastern boundaries, however, the decomposition contains significant variance at higher modes, and there is a corresponding decrease in the agreement between SSH and either the original signal or the first baroclinic mode reconstruction. Compared to the full transport signal, transport fluctuations described by the first baroclinic mode represent < 25 km of the variance within 10 km of the western boundary, in contrast to 60 km at other locations. This decrease occurs within a Rossby radius of the western boundary. At the eastern boundary, a linear combination of many baroclinic modes is required to explain the observed vertical density profile of the seasonal cycle, a result that is consistent with an oceanic response to wind-forcing being trapped to the eastern boundary.
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Global patterns of internal wave variability from observations of full-depth rotary shear spectra
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Journal of Geophysical Research, 1993
Statistics of high-frequency (0.2-0.5 cph) fluctuations are derived from moored upper ocean measurements of currents and temperatures at four latitudes spanning the equator along 140øW. Some of the more unusual statistics include (1) nonunity ratios of kinetic energy to potential energy; (2) nonunity ratios of zonal to meridional kinetic energy; (3) nonzero current-temperature coherence amplitudes, with depth-dependent phases; and (4) high vertical coherence amplitudes, With approximately 180 ø phases, between current measurements spanning the thermocline. A simple model of •hear-modified internal waves is employed to gain insight into the causes of the latitudinal variability of the statistics. Much of this variability can be attributed to the vertical advection of significantly different mean vertical shears by a spectrum of internal waves. The statistics also suggest that the spectrum of high-frequency internal waves in the upper equatorial Pacific differs in important ways from canonical spectral models. The statistics are consistent with a model based on vertical modes which neglect advection by the mean flow, provided the energy in the first mode is much less than (about 0.3 funes) that in the spectrum described by and Munk (1981) and two to four times as much energy propagates eastward as westward. Some of the statistics are inconsistent with the simple internal wave model examined, possibly indicating contamination by mooring motion. 0.5 cph) with canonical models of linear internal waves in an ocean with no mean currents. As a first step toward rationalizing the spectral statistics, an interpretation in terms o f stable, shear-modified internal waves is attempted under the extreme, simplifying assumption that the waves are neithei' advected by the mean flow nor refracted in the vertical by the mean shear but only vertically advect the mean flow. Predictions from this model in various shear flows are compared with observations in order to identify the unique features of the data which cannot be explained by an isotropic spectrum of no-mean-flow modes (per Garrett and Munk [1972, 1975, 1979] and Munk [1981], hereinafter collectively referred to as GM) and to gain insight into which features can be explained by kinematic modifications of the wave field and which features require modification of the energy spectrum. The empirically based GM spectral model of the deepocean internal wave field depends on the following assUmptions: (1) the no-mean-flow linear internal wave dispersion relation is valid; (2) the internal Wave field is vertically symmetric and horizontally isotropic with respect to energy propagation; (3) the distinction between a mode and the sum of upward and downward propagating waves Of equal energy is not important; and (4) the internal wave energy spectrum is separable into a function of frequency times a function of wavenumber, where the function of frequency is indepen-18,089 18,090 BOYD ET AL.: HIGH-FREQUENCY INTERNAL WAVES IN THE EQUATORIAL PACIFIC dent of wavenumber and the function of wavenumber is independent of frequency except for a bandwidth scale factor. Statistics of the internal wave field derived from the GM model spectrum fit numerous observed statistics in the deep ocean quite well, while not matching others (e.g., vertical coherence of velocity components). Some of the model-data inconsistencies have been postulated to be due to fine structure and noise contamination [e.g., Miiller et al., 1978], while others appear to be related to the presence of sources and sinks of energy, especially near boundaries (for example, see the review by Olbers [1983]). Despite these known inadequacies of the GM spectrum, it nevertheless remains a well-known and useful benchmark against which observed internal wave characteristics can be compared in searching for unusual behavior. Several of the GM model assumptions are expected to be violated in the strong vertically sheared near-surface zonal mean flows at the equator along 140øW, including the following: (1) the linear dispersion relation will be modified by the vertical curvature of the mean flow and by Doppler shifting in the intrinsic frequency (Doppler shifting of downstream waves to intrinsic frequencies, i.e., in mean-flow coordinates, that are lower than fixed coordinate frequencies results in a failure of linearization near the critical layer depths where the intrinsic frequency approaches zero); (2) the mean zonal currents may impose directional asymmetry on the energy spectrum through critical layers involving east-west propagating waves; and (3) in the neighborhood of the ocean surface, a fixed phase relationship between upward and downward propagating components is expected. Adding to these contradictions of the GM assumptions, the fact that linear internal waves advect the mean flow readily leads to the expectation that many of the observed statistics of fluctuations at internal wave frequencies in the upper equatorial Pacific will differ significantly from predictions derived from the GM spectrum. Following brief descriptions of the data and mean-flow conditions at the equator (sections 2 and 3, respectively), we introduce our internal wave model in section 4. We present statistics derived from the observations in section 5 and the analysis of those statistics in section 6. This analysis proceeds on the hypotheses (1) that the recorded fluctuations of temperature and velocity are due to internal wave motions only and (2) that a single internal wave energy spectrum can explain observations from all of the moorings between 3øS and 1.5øN. Our model makes a simplifying approximation to the internal wave modes which retains the kinematic effects of internal waves in mean shear flows while ignoring the dynamical modifications to the wave vertical structure. These modes are combined using a GM-like separable spectrum to which modifications (suggested by comparison with the observed statistics) are made to the mode number and azimuthal dependences of the spectrum; the frequency dependence is not addressed here, since we average over a small part of the internal wave frequency band in this paper. The shear-modified modes that we have avoided here have been calculated by Boyd [1989], who shows that the low vertical modes are not strongly affected by the shallow, energetic equatorial mean flows. Boyd's [1989] spectral model using the shear-modified modes validates the basic conclusions reached with the simpler model presented here. Specifically, the empirical statistics suggest that the internal wave energy spectrum must have much less mode 1 energy than in the GM spectrum and that the spectrum must be east-west asymmetric. Section 7 contains a discussion of the comparison between model and data statistics, and section 8 summarizes the conclusions about the wave field based on those statistics. Some of the statistics do not appear to be in agreement with the simple wave model presented, possibly indicating contamination by mooring motion. 2. DATA The Tropic Heat experiment (see Eriksen [1985a] for an overview) included a period of intensive measurements from approximately November 1984 to June 1985, during which time four tautly moored surface floats supported current meters and temperature/pressure gauges at fixed depths in the upper 300 m of the equatorial ocean along 140øW at nominal latitudes of were deployed by R. Knox and D. Luther, and the mooring at the equator was deployed by D. Halpern under the auspices of both Tropic Heat and the National Oceanic and Atmospheric Administration's EP-OCS program. The 1.5øN, 1.5øS, and 3øS moorings were instrumented with vector-averaging current meters (VACMs) and vector-measuring current meters (VMCMs) that stored data every 8 or 15 min. The Draper Laboratory temperature/pressure recorders on these moorings sampled at 16-rain intervals. On the equatorial mooring, temperature recorders and VACMs recorded at 15-min intervals. The available measurements are listed in Table 1. For details of the data-editing procedures, see work by Halpern et al. [1988] and R. A. Knox et al. (manuscript in preparation, 1993, hereinafter referred to as Knox et al., 1993). The focus of this study is on the "high-frequency" fluctuations, where 0.2 cph -< w -< 0.5 cph. The lower limit was chosen in order to avoid potentially deterministic tidal energy, and the upper limit was chosen because the VACM response appears to be different from the VMCM response for •o > 0.5 cph at 1.5øN and 1.5øS. Furthermore, currents and temperatures observed in the 0.2-to 0.5-cph band at midlatitudes in the deep ocean have been shown [Miiller et al., 1978] to be dominated by a spectrum of internal waves that is more horizontally isotropic, vertically symmetric, and free from contaminating fine structure than any other frequency band where free internal waves exist. For the record durations shown in Table 1, the 0.2-to 0.5-cph band has substantial degrees of freedom, containing between 416 and 1579 Fourier transform harmonics; for most records the band contains more than 1000 harmonics. Conductivity-temperature-depth (CTD) profiles were obtained by D. Halpern near the equatorial mooring site when moorings were deployed and recovered. For the Tropic Heat period from October 1983 to October 1985, seven CTD profiles are available from the 0øN, 140øW site. 3. MEAN CONDITIONS The mean upper ocean currents in the central equatorial Pacific during non-El Nifio years are well known [e.g., Firing et al., 1981]. Figure la shows the average zonal velocity profiles for the Tropic Heat data listed in Table 1. The 3øS mooring is in a region of relatively low vertical shear (0.25 cm s-• m -x , maximum) typical of the southern hemisphere BOYD ET AL.' HIGH-FREQUENCY INTERNAL WAVES IN THE EQUATORIAL PACIFIC 18,091
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Estimating vertical velocity in the oceanic upper layers is a key issue for understanding ocean dynamics and the transport of biogeochemical elements. This paper aims to identify the physical sources of vertical velocity associated with sub-mesoscale dynamics (fronts, eddies) and mixed-layer depth (MLD) structures, using (a) an ocean adaptation of the generalized Q-vector form of the ωequation deduced from a primitive equation system which takes into account the turbulent buoyancy and momentum fluxes and (b) an application of this diagnostic method for an ocean simulation of the Programme Océan Multidisciplinaire Méso Echelle (POMME) field experiment in the North-Eastern Atlantic. The approach indicates that wsources can play a significant role in the ocean dynamics and strongly depend on the dynamical structure (anticyclonic eddy, front, MLD, etc.). Our results stress the important contribution of the ageostrophic forcing, even under quasigeostrophic conditions. The turbulent w-forcing was split into two components associated with the spatial variability of (a) the buoyancy and momentum (Ekman pumping) surface fluxes and (b) the MLD. Process (b) represents the trapping of the buoyancy and momentum surface energy into the MLD structure and is identified as an atmosphere/ oceanic mixed-layer coupling. The momentum-trapping process is 10 to 100 times stronger than the Ekman pumping and is at least 1,000 times stronger than the buoyancy w-sources. When this decomposition is applied to a filamentary mixed-layer structure simulated during the POMME experiment, we find that the associated vertical velocity is created by trapping the surface wind-stress energy into this structure and not by Ekman pumping.
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