Variability Of Internal Waves Research Articles

Using long-range transmissions in the Beaufort Gyre to test the sound-speed equation at high pressure and low temperature.

An ocean acoustic tomography array with a radius of 150 km was deployed in the central Beaufort Gyre during 2016-2017 for the Canada Basin Acoustic Propagation Experiment. Five 250-Hz transceivers were deployed in a pentagon, with a sixth transceiver at the center. A long vertical receiving array was located northwest of the central mooring. Travel-time anomalies for refracted-surface-reflected acoustic ray paths were calculated relative to travel times computed for a range-dependent sound-speed field from in situ temperature and salinity observations. Travel-time inversions for the three-dimensional sound-speed field consistent with the uncertainties in travel time [∼2 ms root mean square (rms)], receiver and source positions (∼ 3 m rms), and sound speed calculated from conductivity-temperature-depth casts could not be obtained without introducing a deep sound-speed bias (below 1000 m). Because of the precise nature of the travel-time observations with low mesoscale and internal wave variability, the conclusion is that the internationally accepted sound-speed equation (TEOS-10) gives values at high pressure (greater than 1000 m) and low temperature (less than 0 °C) that are too high by 0.14-0.16 m s-1.

Projected climate variability of internal waves in the Andaman Sea

The Andaman Sea, in the northeast Indian Ocean, is renowned for large-amplitude internal waves. Here, we use a global climate model (CanESM5) to investigate the long-term variability of internal waves in the Andaman Sea under a range of shared socioeconomic pathway (SSP) scenarios. SSPs are future societal development pathways related to emissions and land use scenarios. We project that mean values of depth-averaged stratification will increase by approximately 6% (SSP1-2.6), 7% (SSP2-4.5), and 12% (SSP5-8.5) between 1871-1900 and 2081-2100. Simulating changes in internal tides between the present (2015-2024) and the end-century (2091-2100), we find that the increase in stratification will enhance internal tide generation by approximately 4 to 8%. We project that the propagation of internal tides into the Andaman Sea and the Bay of Bengal will increase by 8 to 18% and 4 to 19%, respectively, under different SSP scenarios. Such changes in internal tides under global warming will have implications for primary production and ecosystem health not only in the Andaman Sea but also in the Bay of Bengal.

Observations of enhanced internal waves in an area of strong mesoscale variability in the southwestern East Sea (Japan Sea)

Oceanic internal waves near the local inertial frequency or near-inertial internal waves and internal waves of tidal origin or internal tides are two types of low-frequency internal waves. Their interactions, interaction with background field, and resulting internal waves at higher frequencies beyond the near-inertial and tidal frequencies have rarely been reported despite its importance on ocean mixing and circulation of energy and materials. Here, we present five episodic enhancements of the high-frequency or continuum frequency waves (CFWs) observed in the southwestern East Sea (Japan Sea) and discuss causes for the enhanced CFWs in relation to near-inertial waves (NIWs), semidiurnal internal tides (SDITs), mesoscale flow fields, and their interactions. The NIWs were amplified due to local surface wind forcing, significantly interacting with mesoscale strain via wave capture. The SDITs were generated in a remote place and propagated into the observational site, largely depending on the mesoscale fields. The observational results suggest that the five episodes of CFWs are results of enhanced NIWs or SDITs, or their wave-wave interaction, rather than locally generated lee-waves. Our study suggests the significant impact of mesoscale circulation on the variability of internal waves from near-inertial to buoyancy frequencies through multiple pathways.

Inter-seasonal variability of internal tides in the western Bay of Bengal

MITgcm is configured in a realistic situation to study the inter-seasonal variability of internal waves (IWs) in the western Bay of Bengal. Monthly climatology of the density fields from WOA09, modified ETOPO2 topography and barotropic tidal forcing are feed to the model for simulating IWs. The preliminary objective of the study is to identify IWs through the stratification and topographic configuration that support IWs. In this context numerical experiments are performed for January, April, July and October representing the winter, pre-monsoon, summer monsoon and post-monsoon, respectively, and analyses are made extensively over the western Bay of Bengal. Mixing caused by density overturning and shear instability is studied at the Gopalpur cross section for all seasons. The density time series are subjected to spectral analysis to find the energy associated with IWs of semi-diurnal frequency. Analysis depicts that the spectral estimates are high in the concave coastline pockets in the southern part and over a broader region on the shelf slope in the northern part. October shows higher estimates in response to highly stratified waters. Several cross sections are analyzed to obtain the spectral energy extent over the shelf slope. It is noticed in October that the peak estimate is within the shelf for shelf angles greater than 0.12° and it falls outside the shelf for shelf angles less than 0.12°.

Multiscale ocean prediction and uncertainty estimation for acoustic studies

We discuss the prediction and estimation of multiscale ocean fields and their probability density distribution for acoustic studies. In high-fidelity multi-resolution simulations, the probability density function of the full ocean state is predicted and estimated, combining the governing equations with observations. Dynamically balanced stochastic forcing are included, so as to represent effects of sub-grid-scales not resolved by the deterministic model equations. The results are stochastic partial differential equations that allow to capture both deterministic effects (advection, Coriolis, etc.) and statistical effects (smaller-scale turbulence, internal wave variability, etc.) on the environment. With this modeling and data assimilation, accurate estimates of the probability density functions (pdf) of oceanographic variability are possible. They become inputs to end-to-end oceanographic-seabed-acoustic-sonar dynamical systems. This end-to-end uncertainty quantification approach is described, evaluated, and illustrated in several simulations and ocean regions.

Neap—spring variability of internal waves over the shelf-slope along western Bay of Bengal associated with local stratification

Interaction of barotropic tide with the continental shelf break region is studied in the presence of local stratification. To achieve this, MITgcm is developed for the western part of Bay of Bengal to simulate the internal tide that manifests itself as internal wave (IW) of predominant M2 tidal frequency. The QuikSCAT daily winds and real-time tides along with monthly climatology of density are used as initial forcing fields to drive the model. From the energy spectra analysis, variability of dominant semi-diurnal IWs is addressed on both spatial and temporal scales. Computed spectral estimates of temperature and density fields off Visakhapatnam using the time series data are in good agreement with observations during 23–25 February 2007 and 18–20 October 2006. Isopycnal displacement of about 15 m is computed which compared well with observations for February 2007, confirming the presence of internal tides. Spectral energy peak is higher for spring than for neap as the associated astronomical forcing is maximum. The IW peak is simulated at 75 m depth which falls within the pycnocline depth. Two vertical cross sections bearing different stratifications along the Bay of Bengal coast are studied to delineate IW energy propagation over the shelf-slope region. The spatial model results show that the location of peak energy shifted a few kilometres onto the shelf towards the coast during October. Our simulation results during February and October demonstrate that IW energy varies across the shelf break with energy peaks at the shelf break, and their dissipation range is affected by the degree of stratification.

Spatial variability of internal waves in an open bay with a narrow steep shelf in the Pacific off NW Mexico

Small scale spatial patterns (<10km) in nearshore internal wave fields are rarely reported on, yet can have a large impact on nearshore mixing and productivity. In this study, the spatial pattern of internal wave characteristics were explored in Todos Santos Bay, Baja California (Mexico), using time series of temperature and currents from moored and towed thermistor chains and acoustic profiling current meters, as well as cross-shore transects with a towed undulating CTD system. Spectra of temperature and currents showed significant spatial variability within the bay, with the northern sector dominated by the internal tidally-forced semidiurnal signal, and the southern sector dominated by wind-forced, subinertial, baroclinic, diurnal fluctuations, which decreased with distance from shore. Semidiurnal internal tidal waves were generated by the barotropic tide at various sites on the continental slope to the west of the bay. They traveled toward the NE and reached the observation site in the northern part of the bay, after bouncing once or twice off the surface and the bottom. Despite the narrowness of the shelf, the semidiurnal internal tides at this site presented a first-mode structure, although not completely formed at times. On average, the semidiurnal internal waves had a ~9km wavelength, traveled in the form of an arc, and propagated with a phase velocity of ~20cm/s. When they reached shallow waters near the coast, they disintegrated rapidly into groups of short, nonlinear internal waves, with 15–20m amplitudes, 5–20min periods, and 50–200m wavelengths. The spatial patterns found in this study are most likely due to variability in distance from generation sites, complex bottom topography, and small scale (<10km) spatial variability in meteorological conditions such as winds.

The ocean's internal motion: A short overview of NIOZ thermistor string observations

Detailed observations of the variability in space and time of motions that dominate redistribution of material and heat are rare. However, these motions are vital for life in seas and ocean. Modern electronics have allowed the manufacturing of 1-Hz high-sampling rate, <1-mK precision, 6000-m depth-rated temperature sensors with the potential of 1-year uninterrupted stand-alone operation. These sensors have been specifically developed for use in a vertical array of many O(100), to study dynamic processes like fronts and internal waves in shallow seas and deep ocean. Under conditions of sufficient spatial vertical resolution, O(0.1–1m), and temperature acting as a proper tracer for density variations, the sensors are excellent in estimating turbulence parameters generated by such processes. In the ocean interior, they reveal continuous internal wave variability and step-like vertical layering in temperature, but very little turbulence. Above sloping topography, small- and large-scale overturnings yield turbulence parameter values which vary by up to four orders of magnitude as a function of time. Largest values are observed in bursts lasting typically 500–1000s and associated with nonlinear internal wave passages. These bursts occur irregularly in a tidal phase. When extrapolated to the ocean at large, sufficient mixing is observed above sloping boundaries to maintain the overall vertical density stratification.

Large internal waves advection in very weakly stratified deep Mediterranean waters

[1] The Eastern Mediterranean Sea contains relatively small trenches O(1–10 km) horizontal width that go deeper than 4000 m. At a first glance, these deep waters are homogeneous, with weak currents <0.1 m s−1. This viewpoint is modified after evaluation of new detailed yearlong temperature observations using 103 high-precision sensors that reveal intense variability of internal waves. Even though temperature variations are within the range of a few mK only, requiring precise correction for the adiabatic lapse rate during post-processing, the images are permanently dynamic. The weak density stratification of buoyancy close to the inertial frequency supports large turbulent overturns indirectly governed or advected by large internal waves. In strongly stratified (near-surface) waters low-frequency inertial internal motions are horizontal, but here they attain a vertical current amplitude sometimes comparable to horizontal currents. This results in occasionally very large internal wave amplitudes (250 m peak-trough), which are generated via geostrophic adjustment presumably from local collapse of fronts.

Effects of random bottom bathymetry on temporal and spatial coherence in shallow water propagation

Fixed system measurements for three experimental shallow water sites reveal systematic dependence of temporal and spatial coherence of individual mode arrivals on frequency and mode number that cannot be fully explained with internal wave variability. Here random fluctuations in bottom bathymetry are introduced to propagation models. Mode structures are randomized and coherence times and lengths decrease with increasing amplitude of bathymetry fluctuations for the same internal wave variations. Distinct mode features blur as frequency of pulse signals increased. Mode coupling and eventually a smearing of continuous modes are observed with increasing frequency and magnitude of bathymetry variations. For low frequencies and bathymetry variations constrained a small fraction of a wavelength, the bottom appears flat and nearly perfect discrete modes are formed. Modes are reinforced by specular reflections all along the path of propagation. Coherence depends entirely on internal wave fluctuations. All mode arrivals have nearly the same coherence times. But modes break up as height of bathymetry fluctuations become comparable to acoustic wavelength. Then sensitivity to sound speed fluctuation increases and coherence is reduced. Two dimensional bathymetry fluctuations account for observation out to 10–20 km and three-dimensional effects become important at longer ranges.

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.

High‐resolution open‐ocean temperature spectra

Accurate (&lt;1 mK) temperature sensors have been stiffly moored at ∼1450 m in the open Canary Basin for 1.5 years while sampling at 1 Hz. The sensors were in an area where regular density steps occur. In this article, we investigate the variability of internal waves in such “steppy” environment. The waves vertically move layers of persistent temperature gradients for particular temperatures. The frequency (σ) spectra of temperature, and more clearly those of inferred vertical currents w, show an internal wave band IWB that extends from 0.97f &lt; σ &lt; Nt, where f denotes the inertial frequency or vertical Coriolis parameter. Transition frequency Nt is higher than buoyancy frequency N, computed over large vertical scales Δz = O(100) m. The extension of IWB beyond the traditional bounds [f,N] is probably due to small‐vertical–scale layering (Δz ≈ 1 m). The associated weak stratification between such thin layers provides small‐scale Ns ≈ 4fh, where fh denotes the horizontal Coriolis parameter. This minimum stable stratification Ns is associated with tilting of vorticity away from gravity, which causes the subinertial spectral extent to 0.97f. Isothermal smoothing reveals details of coherent vertical internal wave and incoherent motions. The present w spectrum continuum of coherent IWB motions is not flat, as in previous near‐surface observations, but linearly increases from σ = f to a peak at σ ∼ 0.8N. The coherence spectrum shows a weak, significant peak at approximately twice the local buoyancy frequency for 2.5 ≤ Δz ≤ 100 m. Instead of dominant mode 1, zero phase difference, observed in IWB across the 130 m of observations, these super‐buoyancy motions show mode 2 dominance, π phase difference.

Influence of a cold water bottom dome on internal wave trapping

A numerical model of a cross section through a cold water bottom dome is used to examine the influence of wind forcing frequency, dome length, and density field upon the variability of internal waves in the region. Forcing at super‐inertial frequencies produces internal waves in the frontal regions that propagate into the centre of the dome producing a standing wave. The wavelength of the internal wave depends upon water depth forcing frequency and stratification. At the edges of the dome internal waves are trapped by the bottom fronts. At sub‐inertial forcing waves are trapped close to the dome's boundary giving different mixing to that found with super‐inertial forcing. These calculations suggest significant differences in internal wave spectra in domes compared with open sea observations. These spectral differences would be a critical test of the model's dynamics.

Internal wave variability in the Beaufort Sea during the winter of 1993/1994

Acoustic Doppler current profiler observations were obtained at the Sea Ice Mechanics Initiative Ice Camp as it drifted through the Beaufort Sea over the winter of 1993–1994. In this paper, the variability of the internal wave field is examined. Initially (December 1993–January 1994), the camp drifted westward through the central Canada Basin (75°N, 139°–153°W). Numerous anticyclonic baroclinic eddies were encountered. Internal wave energy levels averaged 1/25 of the Garrett‐Munk (GM) standard. Shear variance averaged 1/17 GM. During February–March 1994, the camp drifted meridionally along 156°W (near the Northwind Ridge), reversing direction several times. Large baroclinic vortices were not detected. Internal wave energy levels were significantly greater during this period, peaking at 1/6 GM. Shear variance peaked at 1/3 GM. The waves were predominantly near inertial, resulting from three distinct surface generation events. Downward vertical energy fluxes ranged from typical values of 0.02 mW/m2 to a peak value of 0.15 mW/m2. Two thirds of the downward flux was associated with waves of vertical scale greater than 55 m; the remainder with smaller‐scale waves. Upward energy fluxes ranged from 0.02 mW/m2 (typical) to 0.10 mW/m2 (peak), supported almost entirely by the larger‐scale waves. High ice‐water relative velocities (atmospheric storms), accompanied by ice deformation, appear to be necessary, but not sufficient, to assure a downward propagating wave generation event. The highly variable mesoscale has a significant effect on the near‐inertial wave field propagation. The data suggest that the vertical propagation of near‐inertial waves is strongly affected by the depth variation of the vertical component of mesoscale vorticity. The large Beaufort Sea vortices appear to have a dual effect on the wave field. Enhanced vertical propagation speed (and decreased energy density) is found in the negative vorticity cores. Propagation into the positive vorticity regions surrounding the cores is inhibited. The increase in wave energy experienced as the ice camp left the central Beaufort Sea is jointly associated with the passage of storms and the absence of large baroclinic vortices over the Northwind Ridge.

A Fast and Accurate Thermistor String1

A ‘‘fast thermistor string’’ has been built to accommodate the scientific need to accurately monitor internal wave activity in shelf seas and above sloping bottoms in the ocean. The performance of the thermistors and their custom-designed electronics allow temperature variations to be registered at an estimated relative accuracy better than 0.5 mK with a response time faster than 0.25 s. Quantization noise is less than about 40 mK and dominates instrumental noise. Currently, the string holds 32 sensors, which are sampled within 4 s. When sampling every 30 s, the batteries and the memory capacity of the recorder allow deployments up to 3 months. In all respects, this performance is about an order of magnitude superior to thermistor strings currently available commercially. Moored in combination with an acoustic Doppler current profiler the thermistor string provides data to estimate directly quasi-turbulent (high-frequency internal wave band) vertical temperature fluxes and flux gradients. Examples of field observations are given, which show enhanced levels of temperature variance extending above the canonical internal wave spectral levels near the buoyancy frequency, and detailed variations of high-frequency internal wave variability.

Accuracy of current profile measurements: Effect of tropical and midlatitude internal waves

The effect of midlatitude and tropical internal wave variability on current profile measurements is investigated and quantified to yield practical error estimates. First, a data set of Pegasus current profiles from the tropical Atlantic (6°S to 6°N) is analyzed for their rms down/up differences, which are compared with predictions from Garrett‐Munk type internal wave theory and with statistics derived from current meter moorings in the same region. The agreement in terms of amplitudes and vertical distribution proves that most of those differences are due to internal waves and not instrumental errors. Nonetheless, this is the noise of the measurements, if low‐frequency motions are sought, and the errors can thus be quantified using the same internal wave theories. At midlatitudes the error variance is the usual 44(N/3 cph) cm2/s2 with some latitude dependence, and the effect of averaging in the vertical or summing several profiles (e.g., up and down) is estimated. The same is done for equatorial situations, where construction of a crude equatorial frequency spectrum for internal waves yields 77(N/3 cph)cm2/s2 for the error variance. Again, error reduction due to averaging is estimated.

Diurnal Cycle of Internal Wave Variability in the Equatorial Pacific Ocean: Results from Moored Observations

Abstract A diurnal cycle in temperature and vertical displacement variance has been observed in the stratified region below the surface mixed layer using moored time-series data at 0°, 140°W for there periods: November 1984, April 1987, and May–June 1987. The November 1984 and April 1987 periods coincided with the TROPIC HEAT and TROPIC HEAT-2 experiments, during which direct measurements of turbulent dissipation rates were made near the mooring site. In May–June 1987, a special set of moored time series were collected between 30-m and 61-m depth with 1-minute temporal resolution in addition to standard measurements at 15-minute resolution. The high-resolution data indicated the existence of a diurnal cycle in variance that was most pronounced at frequencies of 10–30 cph and that was coherent over the 31-m extent of the vertical array. It is likely that this diurnal cycle in variance was due in part to internal waves remotely generated at the base of the nighttime mixed layer and that the appearance of in...

Fine‐scale temperature variability: The influence of near‐inertial waves

Measurements made with a towed thermistor chain and acoustic doppler current profiler in the seasonal thermocline of the Sargasso Sea are examined for relationships among small‐scale temperature “activity,” shear, and internal wave variability. Patches of intense activity measuring 5–10 m high and several kilometers in length are found to persist within a near‐inertial wave packet. The packet was tagged with a drogue and followed for about 16 hours as it was advected along an edge of a cold‐core ring. The patches occur along surfaces of high vertical shear, where the Richardson number (7‐m vertical resolution) falls to values less than one. Within the patches are groups of small‐scale internal waves and fluid overturns. The overturns are 1–3 m high and are associated with wave‐breaking events. Away from the wave packet, activity levels are less, and the active fraction of the water column appears to be linked to variability in the internal wave field. It is conjectured that the near‐inertial wave patches are the same species as persistent mixing patches observed by Gregg et al. (1986), which were also associated with a near‐inertial wave.

On the internal wave variability during the internal wave experiment (IWEX)

The relation between internal wave variability and larger and smaller scales of motion is investigated, using the IWEX data set. To investigate the role of internal waves in the vertical diffusion of large scale momentum, the time variability of the vertical flux of horizontal internal wave momentum (estimated from temperature and current data) is compared to that of the mean vertical shear. It is found that internal waves cannot cause a vertical viscosity as large as proposed by Müller (1976), but that the data are too noisy to detect a possible wave‐induced viscosity in absolute value of the order of 10−2 m2 s−1 or less. Similarities in the time behavior of the total internal wave energy and that of the square mean vertical shear suggest that some kind of dynamical coupling exists between internal waves and larger scale flows. There is some evidence that the level of temperature finestructure activity also varies in a related way. An analysis of CTD station data taken during Mode demonstrates the mappability of the finestructure activity, and again suggests a relation with the geostrophic eddy flow.