Mode-1 Internal Tides Research Articles

Tomography and the global predictability of mode‐1 internal tides

Twenty years ago, temporally coherent, mode-1 internal tides were detected in the central North Pacific using acoustic tomography. The spatial sampling of tomography is a natural filter for these internal waves. The signals were conjectured to have originated from the Hawaiian Ridge 2000 km to the south, and shortly thereafter Ray and Michum found radiation of internal tides from that undersea ridge using satellite altimetry. The two data types are complementary: tomography demonstrates astonishing temporal coherence, altimetry demonstrates astonishing spatial coherence. In the Atlantic, diurnal internal tides, resonantly trapped between Puerto Rico and their 30N turning latitude, were observed by AMODE tomography, while the semidiurnal variability consisted of a complicated interference pattern. While several conventional in situ observations indicated incoherent components to mode-1 internal-tide variability, both tomography (directly) and altimetry (indirectly) show the incoherent component is minimal. Resolution of mode-1 is challenging, but, without basis, oceanographers have been reluctant to accept the tomography measurements. A combined frequency and wavenumber tidal analysis of altimetry data has recently demonstrated that the amplitude and phase of mode‐1 internal tides are predictable, except, perhaps, in more variable regions. Attenuation appears to be negligible, and waves coherent in time and space extend across ocean basins.

A Coupled Model for Laplace's Tidal Equations in a Fluid with One Horizontal Dimension and Variable Depth

AbstractTide–topography interactions dominate the transfer of tidal energy from large to small scales. At present, it is poorly understood how low-mode internal tides reflect and scatter along the continental margins. Here, the coupling equations for linear tides model (CELT) are derived to determine the independent modal solutions to Laplace's Tidal Equations (LTE) over stepwise topography in one horizontal dimension. CELT is (i) applicable to arbitrary one-dimensional topography and realistic stratification without requiring numerically expensive simulations and (ii) formulated to quantify scattering because it implicitly separates incident and reflected waves. Energy fluxes and horizontal velocities obtained using CELT are shown to converge to analytical solutions, indicating that “flat bottom” modes, which evolve according to LTE, are also relevant in describing tides over sloping topography. The theoretical framework presented can then be used to quantify simultaneous incident and reflected energy fluxes in numerical simulations and observations of tidal flows that vary in one horizontal dimension. Thus, CELT can be used to diagnose internal-tide scattering on continental slopes. Here, semidiurnal mode-1 scattering is simulated on the Australian northwest, Brazil, and Oregon continental slopes. Energy-flux divergence and directional energy fluxes computed using CELT are shown to agree with results from a finite-volume model that is significantly more numerically expensive. Last, CELT is used to examine the dynamics of two-way surface–internal-tide coupling. Semidiurnal mode-1 internal tides are found to transmit about 5% of their incident energy flux to the surface tide where they impact the continental slope. It is hypothesized that this feedback may decrease the coherence of sea surface displacement on continental shelves.

Patterns of K1 and M2 internal tides and their seasonal variations in the northern South China Sea

Seasonal variations of baroclinic tides for K1 and M2 constituents were separately studied using two-dimensional numerical simulations along the 21°N section of the northern South China Sea (SCS). Results show that the continental slope of the northern SCS and the west ridge of the Luzon Strait are supercritical to K1 internal tides, which may be trapped in the deep basin of the SCS and form standing or partial standing waves. Meanwhile, these areas are sub-critical to M2 internal tides, which can transmit onto the shelf and are seldom reflected back into the basin. The trapped K1 internal tides are dominated by mode-2 and mode-3 in summer and by mode-1 and mode-3 in winter. Moreover, high mode K1 internal tides account for nearly 20–40 % of the total energy density in winter and 15–20 % in summer. The pattern of K1 internal tides in the basin is mainly determined by the percentage of reflected energy from the continental slope. The phase difference between the incoming mode-1 and mode-2 K1 internal tides near the continental slope are nearly out of phase in winter, which means that the percentage of reflection of the K1 internal tide is larger than that in summer. Both the convergence and high mode K1 internal tides can enhance the vertical shear. The above results indicate that, in the deep basin of the SCS, water mixing potentially induced by internal tides in winter is stronger than in summer.

Observations of Internal Tides on the Oregon Continental Slope

Abstract A complex superposition of locally forced and shoaling remotely generated semidiurnal internal tides occurs on the Oregon continental slope. Presented here are observations from a zonal line of five profiling moorings deployed across the continental slope from 500 to 3000 m, a 24-h expendable current profiler (XCP) survey, and five 15–48-h lowered ADCP (LADCP)/CTD stations. The 40-day moored deployment spans three spring and two neap tides, during which the proportions of the locally and remotely forced internal tides vary. Baroclinic signals are strong throughout spring and neap tides, with 4–5-day-long bursts of strong cross-slope baroclinic semidiurnal velocity and vertical displacement . Energy fluxes exhibit complex spatial and temporal patterns throughout both tidal periods. During spring tides, local barotropic forcing is strongest and energy flux over the slope is predominantly offshore (westward). During neap tides, shoaling remotely generated internal tides dominate and energy flux is predominantly onshore (eastward). Shoaling internal tides do not exhibit a strong spring–neap cycle and are also observed during the first spring tide, indicating that they originate from multiple sources. The bulk of the remotely generated internal tide is hypothesized to be generated from south of the array (e.g., Mendocino Escarpment), because energy fluxes at the deep mooring 100 km offshore are always directed northward. However, fluxes on the slope suggest that the northbound internal tide is turned onshore, most likely by reflection from large-scale bathymetry. This is verified with a simple three-dimensional model of mode-1 internal tides propagating obliquely onto a near-critical slope, whose output conforms fairly well to observations, in spite of its simplicity.

On the predictability of mode-1 internal tides

A frequency–wavenumber tidal analysis for deriving internal-tide harmonic constants from TOPEX/Poseidon (T/P) measurements of sea-surface height (SSH) has been developed, taking advantage of the evident temporal and spatial coherence and the weak dissipation of internal tides. Previous analyses consisted of simple tidal analysis at individual points, which gave inconsistent harmonic constants at altimeter track crossover points. Such analyses have difficulty in distinguishing between the effects of interference, incoherence, and dissipation. The frequency–wavenumber analysis provides an objective way to interpolate the internal tides measured along altimetry tracks to any arbitrary point, while leveraging all available data for optimal tidal estimates. Tidal analysis of T/P data from 2000 to 2007 is used to predict in situ time series measured during the 2001–2002 Hawaiian Ocean mixing experiment (HOME), the 1987 reciprocal tomography experiment (RTE87), and the 1991 acoustic mid-ocean dynamics experiment (AMODE), demonstrating both the temporal coherence and the lack of incoherent elements to this wave propagation. It has been conjectured that significant energy would be lost from mode-1 internal tides as they cross the 28.9°N critical latitude of parametric subharmonic instability (PSI). No apparent change in amplitude at 28.9°N was detected by this analysis, however. Further, after correcting for changes in background stratification, the amplitude of the mode-1 internal tide was found to decrease by less than 20% over the 2000 km between the Hawaiian Ridge and 40°N. A significant fraction of the variability of internal waves, that component associated with mode-1 internal tides, appears to be predictable over most of the world's oceans, using harmonic constants derived from satellite altimetry.

Long-Range Propagation of the Semidiurnal Internal Tide from the Hawaiian Ridge

Abstract The northeastward progression of the semidiurnal internal tide from French Frigate Shoals (FFS), Hawaii, is studied with an array of six simultaneous profiling moorings spanning 25.5°–37.1°N (≈1400 km) and 13-yr-long Ocean Topography Experiment (TOPEX)/Poseidon (T/P) altimeter data processed by a new technique. The moorings have excellent temporal and vertical resolutions, while the altimeter offers broad spatial coverage of the surface manifestation of the internal tide’s coherent portion. Together these two approaches provide a unique view of the internal tide’s long-range propagation in a complex ocean environment. The moored observations reveal a rich, time-variable, and multimodal internal tide field, with higher-mode motions contributing significantly to velocity, displacement, and energy. In spite of these contributions, the coherent mode-1 internal tide dominates the northeastward energy flux, and is detectable in both moored and altimetric data over the entire array. Phase and group propagation measured independently from moorings and altimetry agree well with theoretical values. Sea surface height anomalies (SSHAs) measured from moorings and altimetry agree well in amplitude and phase until the northern end of the array, where phase differences arise presumably from refraction by mesoscale flows. Observed variations in SSHA, energy flux, and kinetic-to-potential energy ratio indicate an interference pattern resulting from superposed northeastward radiation from Hawaii and southeastward from the Aleutian Ridge. A simple model of two plane waves explains most of these features.

Mode-1 internal tides in the western North Atlantic Ocean

Mode-1 internal tides were observed the western North Atlantic using an ocean acoustic tomography array deployed in 1991–1992 centered on 25°N, 66°W. The pentagonal array, 700-km across, acted as an antenna for mode-1 internal-tides. Coherent internal-tide waves with O(1 m) displacements were observed traveling in several directions. Although the internal tides of the region were relatively quiescent, they were essentially phase locked over the 200–300 day data record lengths. Both semidiurnal and diurnal internal waves were detected, with wavenumbers consistent with those calculated from hydrographic data. The M 2 internal-tide energy flux was estimated to be about 70 W m −1, suggesting that mode-1 waves radiate 0.2 GW of energy, with large uncertainty, from the Caribbean island chain at this frequency. A global tidal model (TPXO 5) suggested that 1–2 GW is lost from the M 2 barotropic tide over this region, but the precise value was uncertain because the complicated topography makes the calculation problematic. In any case, significant conversion of barotropic to baroclinic tidal energy does not occur in the western North Atlantic basin. It is apparent, however, that mode-1 internal tides have very weak decay and retain their coherence over great distances, so that ocean basins may be filled up with such waves. Observed diurnal amplitudes were an order of magnitude larger than expected. The amplitude and phase variations of the K 1 and O 1 constituents observed over the tomography array were consistent with the theoretical solutions for standing internal waves near their turning latitude. The energy densities of the resonant diurnal internal waves were roughly twice those of the barotropic tide at those frequencies.