Baroclinic Energy Flux Research Articles

Internal tide generation by seamounts

The generation of internal tidal wave fields by barotropic tidal flow past a representative seamount is computed by modelling the seamount as a pillbox, and linearising the equations for internal wave dynamics. This is justifiable for mid-ocean seamounts, which constitute steep topography for internal waves of tidal frequency. For linearly polarised barotropic tidal flow, the resulting flow field consists of conical beams radiating from the region above the seamount, with largest velocities aligned with the barotropic flow. These beams vary with azimuthal angle but resemble the corresponding beams from two-dimensional steep topography, particularly in the barotropic flow direction. They are primarily forced by the barotropic flow over the seamount, which is amplified by the topography and is independent of the stratification if the radius of the seamount is sufficiently large. In a barotropic tidal flow of 1 cm/s amplitude, energy fluxes from individual seamounts are of order 10 6 W. Summing this over all seamounts higher than 1 km gives baroclinic energy generation of order 5.10 9 W, a number that is less than estimates of baroclinic energy flux from the continental slopes and the Hawaiian ridge, but is comparable with them.

Baroclinic Energy Flux at the Hawaiian Ridge: Observations from the R/P FLIP

Abstract Estimates of baroclinic energy flux are made in the immediate “Nearfield” (September–October 2002) and 450 km offshore (“Farfield”; October–November 2001) of the Kaena Ridge, an active barotropic-to-baroclinic conversion site. The flux estimates are based on repeated profiles of velocity and density obtained from the Research Platform Floating Instrument Platform (FLIP) as an aspect of the Hawaii Ocean Mixing Experiment. Energetic beams associated with both semidiurnal and diurnal internal waves are observed in the Kauai Channel. Beam depths and orientations are consistent with generation along the upper flanks of the ridge. At the far-field site, the baroclinic energy flux is borne primarily by first-mode semidiurnal waves. The energy flux associated with the entire spectrum of internal waves is computed by cross-spectral analysis. Significant energy fluxes are found in the inertial, diurnal, semidiurnal, and twice-semidiurnal frequency bands. The semidiurnal energy flux strongly dominates the spectrum at both sites. The flux magnitude follows the spring–neap cycle of the semidiurnal barotropic tide. The averaged depth-integrated mode-1 semidiurnal energy flux (over the entire water column) in the Farfield is found to be 1.7 ± 0.3 kW m−1 away from the ridge, with peak values up to 4 kW m−1. Small fluxes toward the ridge are occasionally seen at neap tide. At both sites, energy fluxes in the diurnal frequency band represent 15%–20% of the semidiurnal energy flux. In the Farfield, the magnitude of the diurnal energy flux varies in accord with the fortnightly cycle of the barotropic semidiurnal tide, rather than with the diurnal forcing, suggesting that energy for those waves is supplied by a cross-frequency transfer from the low-vertical-mode M2 internal tide to higher-mode internal waves at frequencies ½M2. In the Nearfield, the diurnal flux varies with fluctuations in both diurnal and semidiurnal forcing.

Internal Tides and Turbulence along the 3000-m Isobath of the Hawaiian Ridge

Abstract Full-depth velocity and density profiles taken along the 3000-m isobath characterize the semidiurnal internal tide and bottom-intensified turbulence along the Hawaiian Ridge. Observations reveal baroclinic energy fluxes of 21 ± 5 kW m−1 radiating from French Frigate Shoals, 17 ± 2.5 kW m−1 from Kauai Channel west of Oahu, and 13 ± 3.5 kW m−1 from west of Nihoa Island. Weaker fluxes of 1–4 ± 2 kW m−1 radiate from the region near Necker Island and east of Nihoa Island. Observed off-ridge energy fluxes generally agree to within a factor of 2 with those produced by a tidally forced numerical model. Average turbulent diapycnal diffusivity K is (0.5–1) × 10−4 m2 s–1 above 2000 m, increasing exponentially to 20 × 10−4 m2 s–1 near the bottom. Microstructure values agree well with those inferred from a finescale internal wave-based parameterization. A linear relationship between the vertically integrated energy flux and vertically integrated turbulent dissipation rate implies that dissipative length scales for the radiating internal tide exceed 1000 km.

An examination of the radiative and dissipative properties of deep ocean internal tides

In this study, the energy flux and energy dissipation of deep ocean internal tides are examined. Properties of the internal tide from two distinct generation regions are contrasted: the Mid-Atlantic Ridge (MAR) and the Hawaiian Ridge. Considerable differences are noted for the baroclinic energy flux, hu 0 p 0 i; radiated from each site. Radiation from the MAR is relatively rich in high modes, with an energy flux spectral peak at mode 5 and modes 10 and greater accounting for 40% of the total flux. In contrast, Hawaiian Ridge radiation is dominantly composed of modes 1 and 2, with modes 10 and greater accounting for less than 5% of the total flux. Depth integrated energy flux levels are Oð1Þ kW m � 1 at the MAR site, and Oð10ÞkW m � 1 at the Hawaiian Ridge. Despite these differences, observed turbulent dissipation rates at these sites are similar in magnitude and depth dependence. Decay scales, estimated as L� ¼ð R 0 � H u 0 p 0 dzÞ=ð R 0 � H r0� dzÞ; range from Oð100Þkm to Oð1000Þ km: The mean decay scale based on the MAR data is 230 km, a factor of 3 smaller than at the Hawaiian Ridge site. We demonstrate that the dissipation level scales with the energy flux available in the high modes, which is comparable at both sites, rather than the total energy flux. r 2004 Elsevier Ltd. All rights reserved.

Structure and variability of semidiurnal internal tides in Mamala Bay, Hawaii

Moored current meter and temperature observations and results from a three‐dimensional primitive equation model are used to examine the energetic semidiurnal internal tides present in Mamala Bay on the south coast of Oahu, Hawaii. The steady, harmonic component of the internal tide is characterized by large vertical displacements in the central region of the bay (35 m amplitude for the M2 constituent), and enhanced alongshelf baroclinic currents at the headlands on either end of the bay (0.27 m s−1). Seasonal changes in amplitude and phase are observed. The model captures the qualitative spatial structure of the observations. Baroclinic energy flux estimates, from the mooring observations and the numerical simulations, suggest that internal tide energy propagates into the bay and does not originate within the bay. The model indicates that internal wave generation occurs over the flanks (500–1000 m depth) of the ridge, predominantly on the east side, with perhaps some additional contribution on the west from an energetic internal tide generated north of Oahu. Wave superposition is believed to account for the alongshelf spatial structure of currents and displacements. Incoherent modulations of the internal tide occur that are not related to local changes in stratification, at least on superannual timescales. Factors contributing to this signal may include stratification variations at the deep generation sites, mesoscale activity, and/or the shoaling of a random internal wave field into the bay from the open ocean.

Shear and Baroclinic Energy Flux on the Summer New England Shelf

Abstract Observations are presented of internal wave properties and energy fluxes through a site near the 70-m isobath on the New England shelf in late summer. Data collected from a shipboard ADCP and microstructure profiler over a three-week period and projected onto dynamic vertical modes reveals large variations in the magnitude and vertical structure of internal waves. Baroclinic energy and shear were primarily associated with low-mode near-inertial and semidiurnal waves and, at times, high-frequency solibores. The energies in each mode varied by factors from 2 to 10 over several days and were not significantly correlated with one another. The associated shear variance was concentrated in the thermocline. However, the strength and vertical range of shear varied significantly throughout the research period and depended sensitively on both the magnitude and evolving vertical mode content of the wave field. Shear during the quasi-two-layer solibores was strong enough to temporarily lower the 4-m Richards...

Internal Tide Radiation from Mendocino Escarpment

Abstract Strong semidiurnal internal tides are observed near Mendocino Escarpment in full-depth profile time series of velocity, temperature, and salinity. Velocity and density profiles are combined to estimate the internal tide energy flux. Divergence of this flux demonstrates that its source is the barotropic tide interacting with the escarpment. A baroclinic energy flux of 7 kW m−1 radiates from the escarpment, corresponding to 3% of the 220 kW m−1 fluxing poleward in the surface tide. Energy and energy flux are concentrated in packets that emanate from the flanks of the ridge surmounting the escarpment and one site ∼90 km north of the escarpment. Coherent beamlike structure along semidiurnal ray paths remains identifiable until the first surface reflection. Beyond the first surface reflection north of the escarpment, the energy flux drops by 2 kW m−1 and beams are no longer discernible. Turbulence, as inferred from finescale parameterizations, is elevated by over two orders of magnitude relative to th...

Model estimates of M2 internal tide energetics at the Hawaiian Ridge

A primitive equation model is used to examine the structure and energetics of M2 internal tides generated at the Hawaiian Ridge. Recent estimates based on altimeter data suggest that 20 GW of barotropic tidal dissipation occurs at the ridge, with conversion to internal tides believed to be the dominant dissipation mechanism. The model simulates an internal tide that accounts for 9.7 GW of radiated energy away from the ridge in the northeast and southwest directions. The strongest generation occurs at three sites where enhanced barotropic currents flow across elongated topographic features. The depth‐integrated baroclinic energy flux and energy densities at these sites are on the order of 104 W m−1 and 104 J m−2, respectively. A modal decomposition indicates that 62% of the outgoing energy flux is accounted for by the first internal mode, 15% is accounted for by the second mode, and less than 5% is accounted for by each subsequent higher mode. The tidal dissipation due to bottom friction along the ridge is estimated to be 0.1 GW. The level of turbulent dissipation near the ridge owing to tidal energy conversion remains to be determined to assess fully the barotropic‐baroclinic energy budget.

A regional model of the semidiurnal internal tide on the Australian North West Shelf

A fully three‐dimensional nonlinear primitive equation model is applied to a study of the semidiurnal internal tide on the Australian North West Shelf, a region of strong barotropic and baroclinic tide. The model shows a significant internal tide over most of the continental slope region, predominantly between 100‐ and 1000‐m depths. Energy flux is highly variable with regions of onshore flux and regions of offshore flux, corresponding to regions of subcritical and supercritical seabed slopes. A comparison between the model and detailed observations from one region shows reasonable agreement in vertical displacement, currents, and depth‐integrated energy flux. The comparison also highlights the difficulty in obtaining appropriate observations to provide a rigorous verification of internal tide models. The M2 and S2 internal tides show similar patterns of flow with energy in the S2 internal tide about 25% of that in the M2 constituent. Estimates of the total baroclinic M2 energy are about 2.2 GW for the North West Shelf, nearly an order of magnitude larger than suggested by earlier studies. This represents about 5% of the dissipation of the M2 barotropic tide in the model domain. The seasonal variability in the baroclinic energy flux is about 20% from the mean. The baroclinic energy extracted from the tide is expected to make a significant contribution to mixing in the region.

Numerical Modeling of Internal Tide Generation along the Hawaiian Ridge

Internal M2 tides near Hawaii are investigated with a two-dimensional, two-layer numerical model. It is seen that along the Hawaiian Ridge barotropic tidal energy is transformed into baroclinic internal tides that propagate in both northeast and southwest directions, as previously hypothesized. The internal tide for a certain beam is seen to propagate well over 1000 km. with an approximate decay scale of 1000 km. An asymmetric pattern in the baroclinic energy flux is observed to the north and south of the Hawaiian Ridge due to the spatially inhomogeneous baroclinic energy sources. The surface manifestation of the M2 internal tide in the model is compared with analysis results from TOPEX/ Poseidon satellite altimetry. The baroclinic short-wave variation of a few centimeters amplitude, superposed on the barotropic surface amplitude, agrees well with the altimeter analyses. This, together with snapshots of the interfacial disturbance, allows the authors to sketch the propagation pattern of internal waves emanating northward and southward from the Hawaiian Ridge. Tidal current ellipses in the upper layer are dominated by the baroclinic internal tide with large spatial variability in their magnitude compared to the barotropic tidal ellipses. The M2 baroclinic energy flux is over 10 kW m 21 for the strongest energy beam propagating toward the northeast. Along the western Hawaiian Ridge about 3.8 GW of tidal power is converted from barotropic to baroclinic motion. The average northward or southward flux density for the first baroclinic mode is about 1.35 kW m21 in the western Hawaiian Ridge. Also, if 2.7 kW m21 (1.35 kW m21 to each direction) is assumed for the whole 2000-km-long Hawaiian Ridge, a total of 5.4 GW is obtained. This value indicates that there is still a large uncertainty in the rate of barotropic to radiating baroclinic energy conversion along the Hawaiian Ridge.

Internal tide generation by seamounts, ridges, and islands

A numerical investigation is made into the generation of semidiurnal internal tides by tidal flow over steep topographic features in the deep ocean. A fully three‐dimensional, free surface, nonlinear, hydrostatic model (the Princeton Ocean Model) is used with real stratification, representative tidal forcing, and Gaussian‐shaped seamounts, ridges, and islands for the topography. The efficiencies of the different topographies in extracting energy from the barotropic tide and in generating an internal tide are considered. Each topography produces an internal tide characterized by signals propagating away from the feature as beams that follow internal wave characteristic paths. The strength of the signals, however, varies markedly for different topographies. This is largely attributed to the way in which the barotropic tide interacts with the three‐dimensional topography. Internal wave generation requires a significant vertical displacement of stratified water by the barotropic tide as it flows over topography. It is found that for symmetric seamounts and islands the barotropic flow tends to go around the feature, producing only a weak internal tide. When elongated into a ridge, barotropic flow is forced across isobaths, generating an energetic internal tide. Changing the horizontal aspect ratio of the topography from 1:1 (a seamount) to 3:1 (a ridge) increases the resulting baroclinic energy flux by nearly an order of magnitude. The slope of the topography relative to that of the internal wave characteristics is also shown to be important with strongest generation occurring at regions of critical or supercritical topographic slope.

Simulation of Barotropic and Baroclinic Tides off Northern British Columbia

Abstract The tidal response of northern British Columbia coastal waters is studied through simulations with a three-dimensional, prognostic, primitive equation model. The model is forced at the boundaries with the leading semidiurnal and diurnal constituents and experiments with stratified and homogeneous fluid are compared. The barotropic response shows good agreement with previously published studies of tides in the region. A comparison with tide gauge measurements indicates that average relative rms differences between observations and the model surface elevation field are less than 5% for the largest constituents. An internal tide is generated in cases where the model is initialized with a vertical stratification. Diagnostic calculations of the baroclinic energy flux are used to identify regions of generation and propagation of internal tidal energy. With a representative summer stratification, the integrated offshore flux is about 0.5 gigawatts, higher than previously estimated from theoretical model...

M2Baroclinic Tides in Johnstone Strait, British Columbia

Tide, current and water property data collected in the western basin of Johnstone Strait, British Columbia, are compared with analytical models for M2 semidiurnal motions in a stratified, rotating channel of uniform depth. We show that, for a rectangular basin in which there is a depth-independent mean flow, the tidal fluctuations are readily expressible in terms of a landward (eastward) propagating Kelvin wave and exponentially damped, seaward (westward) propagating baroclinic Kelvin waves. The internal M2 tide appears to be generated through interaction of the surface tide with the shallow sill at the eastern end of the basin and is dominated by a first-mode baroclinic wave whose amplitude undergoes attenuation over an e-folding distance of one wavelength (∼26 km). Near the sill the baroclinic current speed may exceed 50% of the barotropic flow speed. The along-channel energy flux (power) of the barotropic tide is comparatively uniform at ∼1.4×109 W throughout the western portion of the Strait but decreases by a factor of 2 across the sill. Less than 0.3% of this power loss is needed to account for the baroclinic energy flux of ∼2×106 W near the sill; dissipation due to bottom friction is the main sink for the barotropic tidal energy. Attenuation of the baroclinic waves appears to result from a combination of turbulent horizontal friction and bottom boundary layer friction. Based on the first mode amplitudes, we find a horizontal eddy viscosity of ∼4×106 cm2 s−1 and a vertical eddy viscosity of ∼103 cm2 s−1. Our analysis further indicates that higher modes may be subject to attenuation by critical-layer absorption in the presence of the mean estuarine circulation in the basin. The M2 tides and currents are shown to possess considerable variability over periods of weeks and to have seasonal trends that, qualitatively at least, are related to changes in the mean density structure.