Oceanic Internal Wave Field Research Articles

Validating Finescale Parameterizations for the Eastern Arctic Ocean Internal Wave Field

AbstractIn the Arctic Ocean, vertical transport of heat by turbulent mixing is ultimately coupled to the sea‐ice cover, with immediate and far‐reaching impacts on the climate and ecosystem. Unfortunately, direct observations of mixing are difficult, expensive and sparse. Finescale Parameterization (FS) of turbulent energy dissipation rate (ɛ) allows for the quantification of turbulence from breaking internal waves using standard measurements, such as profiles of hydrography and velocity. While FS proved to be reliable in mid‐latitudes, the Arctic Ocean internal wave field is distinct in terms of composition and energy level, rendering the applicability of FS uncertain. To test FS in a wide range of eastern Arctic conditions, we compiled data from eight cruises. All profiles used to calculate FS were collocated with in‐situ measurements of ɛ obtained from microstructure profilers. FS was applied between 50 and 450 m below the surface. Results show a satisfactory performance of FS, with 84% of FS‐derived ɛ being within a factor of 5 to observations. This improved to 90% when using lower‐noise velocity profiles of lowered current meters instead of ship‐mounted current meters. In our data, FS performance is independent of the shear‐strain ratio (Rω) and internal wave field bandwidth (N/f), but there is evidence that highly stratified environments with large potential energy, low turbulence and substantially non‐white shear spectra are less suitable for FS. A widely used formulation of FS using only hydrography and a prescribed Rω = 7 results in 73% of FS estimates being within a factor of 5 to observations.

The structure of energy fluxes in wave turbulence

We calculate the net energy per unit time exchanged between two sets of modes in a generic system governed by a three-wave kinetic equation. Our calculation is based on the property of detailed energy conservation of the triadic resonant interactions. In a first application to isotropic systems, we re-derive the previously used formula for the energy flux as a particular case for adjacent sets. We then exploit the new formalism to quantify the level of locality of the energy transfers in the example of surface capillary waves. A second application to anisotropic wave systems expands the currently available set of tools to investigate magnitude and direction of the energy fluxes in these systems. We illustrate the use of the formalism by characterizing the energy pathways in the oceanic internal wavefield. Our proposed approach, unlike traditional approaches, is not limited to stationarity, scale invariance and strict locality. In addition, we define a number $w$ that quantifies the scale separation necessary for two sets of modes to having negligible mutual energy exchange, with potential consequences in the interpretation of wave turbulence experiments. The methodology presented here provides a general, simple and systematic approach to energy fluxes in wave turbulence.

On the Origins of the Oceanic Ultraviolet Catastrophe

Abstract We provide a first-principles analysis of the energy fluxes in the oceanic internal wave field. The resulting formula is remarkably similar to the renowned phenomenological formula for the turbulent dissipation rate in the ocean, which is known as the finescale parameterization. The prediction is based on the wave turbulence theory of internal gravity waves and on a new methodology devised for the computation of the associated energy fluxes. In the standard spectral representation of the wave energy density, in the two-dimensional vertical wavenumber–frequency (m–ω) domain, the energy fluxes associated with the steady state are found to be directed downscale in both coordinates, closely matching the finescale parameterization formula in functional form and in magnitude. These energy transfers are composed of a “local” and a “scale-separated” contributions; while the former is quantified numerically, the latter is dominated by the induced diffusion process and is amenable to analytical treatment. Contrary to previous results indicating an inverse energy cascade from high frequency to low, at odds with observations, our analysis of all nonzero coefficients of the diffusion tensor predicts a direct energy cascade. Moreover, by the same analysis fundamental spectra that had been deemed “no-flux” solutions are reinstated to the status of “constant-downscale-flux” solutions. This is consequential for an understanding of energy fluxes, sources, and sinks that fits in the observational paradigm of the finescale parameterization, solving at once two long-standing paradoxes that had earned the name of “oceanic ultraviolet catastrophe.” Significance Statement The global circulation models cannot resolve the scales of the oceanic internal waves. The finescale parameterization of turbulent dissipation, a formula grounded in observations, is the standard tool by which the energy transfers due to internal waves are incorporated in the global models. Here, we provide an interpretation of this parameterization formula building on the first-principles statistical theory describing energy transfers between waves at different scales. Our result is in agreement with the finescale parameterization and points out a large contribution to the energy fluxes due to a type of wave interactions (local) usually disregarded. Moreover, the theory on which the traditional understanding of the parameterization is mainly built, a “diffusion approximation,” is known to be partly in contradiction with observations. We put forward a solution to this problem, visualized by means of “streamlines” that improve the intuition of the direction of the energy cascade.

Experimental evidence of internal wave attractor signatures hidden in large-amplitude multi-frequency wave fields

Abstract

Decay Rates of Internal Tides Estimated by an Improved Wave–Wave Interaction Analysis

AbstractRecent numerical and observational studies have reported that resonant wave–wave interaction may be a crucial process for the energy loss of internal tides and the associated vertical water mixing in the midlatitude deep ocean. Special attention has been directed to the remarkable latitudinal dependence of the resonant interaction intensity; semidiurnal internal tides promptly lose their energy to near-inertial motions through parametric subharmonic instability equatorward of the critical latitudes 29°N/S, where half the tidal frequency coincides with the local inertial frequency. This feature contradicts the classical theoretical prediction that resonant wave–wave interaction does not play a major role in the tidal energy loss in the open ocean. By reformulating the kinetic equation for long internal waves and developing its calculation method, we estimate the energy decay rates of the low-vertical-mode semidiurnal internal tides interacting with the “ubiquitous” oceanic internal wave field. The result shows rapid energy decay of the internal tides, typically within O(10) days for the lowest-mode component, near their critical latitudes. This decay time is severalfold shorter than those in the classical studies and, additionally, varies by a factor of 2 depending on the local depth and density structure. We suggest from this study that the numerical integration of the kinetic equation is a more effective approach than recognized to determine the decay parameter of wave energy, which is indispensable for the global ocean models.

An Oceanic Ultra-Violet Catastrophe, Wave-Particle Duality and a Strongly Nonlinear Concept for Geophysical Turbulence

There is no theoretical underpinning that successfully explains how turbulent mixing is fed by wave breaking associated with nonlinear wave-wave interactions in the background oceanic internal wavefield. We address this conundrum using one-dimensional ray tracing simulations to investigate interactions between high frequency internal waves and inertial oscillations in the extreme scale separated limit known as “Induced Diffusion”. Here, estimates of phase locking are used to define a resonant process (a resonant well) and a non-resonant process that results in stochastic jumps. The small amplitude limit consists of jumps that are small compared to the scale of the resonant well. The ray tracing simulations are used to estimate the first and second moments of a wave packet’s vertical wavenumber as it evolves from an initial condition. These moments are compared with predictions obtained from the diffusive approximation to a self-consistent kinetic equation derived in the ‘Direct Interaction Approximation’. Results indicate that the first and second moments of the two systems evolve in a nearly identical manner when the inertial field has amplitudes an order of magnitude smaller than oceanic values. At realistic (oceanic) amplitudes, though, the second moment estimated from the ray tracing simulations is inhibited. The transition is explained by the stochastic jumps obtaining the characteristic size of the resonant well. We interpret this transition as an adiabatic ‘saturation’ process which changes the nominal background wavefield from supporting no mixing to the point where that background wavefield defines the normalization for oceanic mixing models.

TOWARD REGIONAL CHARACTERIZATIONS OF THE OCEANIC INTERNAL WAVEFIELD

Many major oceanographic internal wave observational programs of the last 4 decades are reanalyzed in order to characterize variability of the deep ocean internal wavefield. The observations are discussed in the context of the universal spectral model proposed by C. J. R. Garrett and W. H. Munk. The Garrett and Munk model is a good description of wintertime conditions at Site D on the continental rise north of the Gulf Stream. Elsewhere and at other times, significant deviations in terms of amplitude, separability of the 2‐D vertical wavenumber‐frequency spectrum, and departure from the model's functional form are reported. Specifically, the Garrett and Munk model overestimates annual average frequency domain spectral levels both at Site D and in general. The bias at Site D is associated with the Garrett and Munk model being a fit to wintertime data from Site D and the presence of an annual cycle in high‐frequency energy in the western subtropical North Atlantic having a maximum in winter. The wave spectrum is generally nonseparable, with near‐inertial waves typically having greater bandwidth (occupying smaller vertical scales) than continuum frequency waves. Separability is a better approximation for more energetic states, such as wintertime conditions at Site D. Subtle geographic differences from the high‐frequency and high vertical wavenumber power laws of the Garrett and Munk spectrum are apparent. Such deviations tend to covary: whiter frequency spectra are partnered with redder vertical wavenumber spectra. We review a general theoretical framework of statistical radiative balance equations and interpret the observed variability in terms of the interplay between generation, propagation, and nonlinearity. First, nonlinearity is a fundamental organizing principle in this work. The observed power laws lie close to the induced diffusion stationary states of the resonant kinetic equation describing the lowest‐order nonlinear transfers. Second, eddy variability and by implication wave mean interactions are also an organizing principle. Observations from regions of low eddy variability tend to be outliers in terms of their parametric spectral representation; other data tend to cluster in two regions of parameter space. More tentatively, the seasonal cycle of high‐frequency energy is in phase with the near‐inertial seasonal cycle in regions of significant eddy variability. In regions of low eddy variability, the seasonal cycle in high‐frequency energy lags that of near‐inertial energy. The induced diffusion stationary states are approximate analytic solutions to the resonant kinetic equation, and the Garrett and Munk spectrum represents one such analytic solution. We present numerical solutions of the resonant kinetic equation, however, that are inconsistent with the Garrett and Munk model representing a stationary state, either alone or in combination with other physical mechanisms. We believe this to be the case for other regional characterizations as well. We argue that nonstationarity of the numerical solutions is related to local transfers in horizontal wavenumber, whereas the analytic induced diffusion stationary states consider only nonlocal transfers in vertical wavenumber. Consequences for understanding the pathways by which energy is transferred from sources to sinks are considered. Further progress likely requires self‐consistent solutions to a broadened kinetic equation.

Response of internal waves to 2005 Typhoon Damrey over the northwestern shelf of the South China Sea

Continuous observation of sea water temperature and current was made at Wenchang Station (19°35′N, 112°E) in 2005. The data collected indicate vigorous internal waves of both short periods and tidal and near-inertial periods. The temperature and current time series during 18–30 September were examined to describe the upper ocean internal wave field response to Typhoon Damrey (0518). The strong wind associated with the typhoon, which passed over the sea area about 45 km south of Wenchang Station on 25 September, deepened the mixed layer depth remarkably. It decreased the mixed layer temperature while increasing the deep layer temperature, and intensified the near-inertial and high-frequency fluctuations of temperature and current. Power spectra of temperature and current time series indicate significant deviations from those obtained by using the deep ocean internal wave models characterized by a power law. The frequency spectra were dominated by three energetic bands: around the inertial frequency (7.75×10−6 Hz), tidal frequencies (1.0×10−5 to 2.4×10−5 Hz), and between 1.4×10−4 and 8.3×10−4 Hz. Dividing the field data into three phases (before, during and after the typhoon), we found that the typhoon enhanced the kinetic energy in nearly all the frequency bands, especially in the surface water. The passage of Damrey made a major contribution to the horizontal kinetic energy of the total surface current variances. The vertical energy density distribution, with its peak value at the surface, was an indication that the energy injected by the strong wind into the surface current could penetrate downward to the thermocline.

Correction to “Latitudinal dependence of diapycnal diffusivity in the thermocline observed using a microstructure profiler”

[1] In the paper “Latitudinal dependence of diapycnal diffusivity in the thermocline observed using a microstructure profiler” by T. Hibiya et al. (Geophysical Research Letters, 34, L24602, doi:10.1029/2007GL032323) there were textual errors inadvertently overlooked during the production proofing process. [2] The second sentence in Paragraph 5 should read as follows. In the present study, we deployed the velocity microstructure profiler TurboMAP-D to a depth below the main thermocline at 53 locations in the interior Pacific Ocean between 53°N and 10°S (Figure 1). [3] Paragraph 9 should read as follows. Figure 3 shows the average diapycnal diffusivities over the depth range of ∼1000 m to ∼1600 m inferred from microstructure observations (hereinafter referred to as KρMSP) and those inferred by incorporating XCP data into Gregg's fine-scale parameterization [Gregg, 1989] (hereinafter referred to as KρPRM). [4] The third sentence of paragraph 10 should read as follows. The latitudinal distribution of KρMSP thus obtained from microstructure observations is in qualitative agreement with predictions based on parameterized estimates KρPRM at mid- and high-latitudes (poleward of 20°N) [Nagasawa et al., 2002; Hibiya and Nagasawa, 2004; Hibiya et al., 2006] and previous microstructure observations at low latitudes (equatorward of 20°N) [Gregg et al., 2003], although fine-scale parameterizations overestimate diapycnal diffusivities by a factor of 2–3. [5] The first sentence of paragraph 12 should read as follows. By deploying the un-tethered free-fall microstructure profiler called “TurboMAP-D” at 53 locations in the interior Pacific Ocean between 53°N and 10°S, we have examined the efficacy of the latitudinal dependence of diapycnal diffusivity in the main thermocline predicted based on parameterized estimates at mid- and high-latitudes [Nagasawa et al., 2002; Hibiya and Nagasawa, 2004; Hibiya et al., 2006] and previous microstructure observations at low-latitudes [Gregg et al., 2003]. [6] The second sentence of paragraph 13 should read as follows. One of the strong candidates that might make up for the deficiency of diapycnal mixing in the main thermocline is thought to be intense diapycnal mixing above abyssal rough bottom topography [Polzin et al., 1997; Ledwell et al., 2000]. [7] The pagination for Furuichi et al. [2005] was incorrect. The reference should read as follows.Furuichi, N., T. Hibiya, and Y. Niwa (2005), Bispectral analysis of energy transfer within the two-dimensional oceanic internal wave field, J. Phys. Oceanogr., 35(11), 2104–2109. [8] Ledwell et al. [1993] reference should be replaced with the following reference.Ledwell, J. R., E. T. Montgomery, K. L. Polzin, L. C. St. Laurent, R. W. Schmitt, and J. M. Toole (2000), Evidence for enhanced mixing over rough topography in the abyssal ocean, Nature, 403, 179–182. [9] The journal in Munk [1966] reference was incorrect. The reference should read as follows.Munk, W. (1966), Abyssal recipes, Deep Sea Res., 13(4), 707–730.

Intense mixing of lower thermocline water on the crest of the Mid-Atlantic Ridge

Buoyancy exchange between the deep and the upper ocean, which is essential for maintaining global ocean circulation, mainly occurs through turbulent mixing. This mixing is thought to result primarily from instability of the oceanic internal wave field, but internal waves tend to radiate energy away from the regions in which they are generated rather than dissipate it locally as turbulence and the resulting distribution of turbulent mixing remains unknown. Another, more direct, mixing mechanism involves the generation of turbulence as strong flows pass through narrow passages in topography, but the amount of turbulence generated at such locations remains poorly quantified owing to a lack of direct measurements. Here we present observations from the crest of the Mid-Atlantic Ridge in the subtropical North Atlantic Ocean that suggest that passages in rift valleys and ridge-flank canyons provide the most energetic sites for oceanic turbulence. Our measurements show that diffusivities as large as 0.03 m2 s(-1) characterize the mixing downstream of a sill in a well-stratified boundary layer, with mixing levels remaining of the order of 10(-4) m2 s(-1) at the base of the main thermocline. These mixing rates are significantly higher than the diffusivities of the order of 10(-5) m2 s(-1) that characterize much of the global thermocline and the abyssal ocean. Our estimates suggest that overflows associated with narrow passages on the Mid-Atlantic Ridge in the North Atlantic Ocean produce as much buoyancy flux as has previously been estimated for the entire Romanche fracture zone, a large strait in the Mid-Atlantic Ridge that connects the North and South Atlantic basins. This flux is equivalent to the interior mixing that occurs in the entire North Atlantic basin at the depth of the passages, suggesting that turbulence generated in narrow passages on mid-ocean ridges may be important for buoyancy flux at the global scale.

Consideration of Fine-Scale Coastal Oceanography and 3-D Acoustics Effects for the ESME Sound Exposure Model

Results and recommendations for evaluating the effects of fine-scale oceanographic scattering and three-dimensional (3-D) acoustic propagation variability on the Effects of Sound on the Marine Environment (ESME) acoustic exposure model are presented. Pertinent acoustic scattering theory is briefly reviewed and ocean sound-speed fluctuation models are discussed. Particular attention is given to the nonlinear and linear components of the ocean internal wave field as a source of sound-speed inhomogeneities. Sound scattering through the mainly isotropic linear internal wave field is presented and new results relating to acoustic scattering by the nonlinear internal wave field in both along and across internal wave wavefront orientations are examined. In many cases, there are noteworthy fine-scale induced intensity biases and fluctuations of order 5-20 dB

Bispectral Analysis of Energy Transfer within the Two-Dimensional Oceanic Internal Wave Field

Abstract Bispectral analysis of the numerically reproduced spectral responses of the two-dimensional oceanic internal wave field to the incidence of the low-mode semidiurnal internal tide is performed. At latitudes just equatorward of 30°, the low-mode semidiurnal internal tide dominantly interacts with two high-vertical-wavenumber diurnal (near inertial) internal waves, forming resonant triads of parametric subharmonic instability (PSI) type. As the high-vertical-wavenumber near-inertial energy level is raised by this interaction, the energy cascade to small horizontal and vertical scales is enhanced. Bispectral analysis thus indicates that energy in the low-mode semidiurnal internal tide is not directly transferred to small scales but via the development of high-vertical-wavenumber near-inertial current shear. In contrast, no noticeable energy cascade to high vertical wavenumbers is recognized in the bispectra poleward of ∼30° as well as equatorward of ∼25°. A new finding is that, although PSI is possible equatorward of ∼30°, the efficiency drops sharply as the latitude falls below ∼25°. At all latitudes, another resonant interaction suggestive of induced diffusion is found to occur between the low-mode semidiurnal internal tide and two high-frequency internal waves, although bispectral analysis shows that this interaction plays only a minor role in cascading the low-mode semidiurnal internal tide energy.

Estimates of Energy Dissipation Rates in the Three-Dimensional Deep Ocean Internal Wave Field

Using the “Eikonal Approach” (Henyey et al., 1986), we estimate energy dissipation rates in the three-dimensional Garrett-Munk internal wave field. The total energy dissipation rate within the undisturbed GM internal wave field is found to be 4.34 × 10−9 W kg−1. This corresponds to a diapycnal diffusivity of about 0.3 × 10−4 m2s−1, which is less than the value 10−4 m2s−1 required to sustain the global ocean overturning circulation. Only when the high vertical wavenumber, near-inertial current shear is enhanced can diapycnal diffusivity reach ∼10−4 m2s−1. It follows that the energy supplied at low vertical wavenumbers and low frequencies is efficiently transferred to high vertical wavenumbers and near-inertial frequencies in the mixing hotspots in the real ocean.

A Modification of the Garrett–Munk Internal Wave Spectrum

The Garrett–Munk (GM) spectrum continues to be a useful description of the oceanic internal wave field. However, there are several inconsistencies and ambiguities that make it difficult to use in comparing internal wave fields at different latitudes, stratifications, and water depths. A modified spectral formulation is presented that treats three problems with the Garrett–Munk formulation: the normalization of the energy spectrum as a function of frequency bandwidth, the energy distribution at frequencies below the semidiurnal tide, and the treatment of vertical boundaries and turning points. Addressing these problems leads to a substitution of the GM parameters E (nondimensional energy), b (vertical length scale), and N0 (buoyancy frequency scale) with two new dimensional scales: Eref, the energy per unit mass, and D(ω), the Wentzel–Kramers–Brillouin (WKB)-scaled thickness of the vertical waveguide. The advantages of the modified spectrum are illustrated by comparing with observations from the equator and the continental shelf.

Correction to “Response of the deep ocean internal wave field to traveling midlatitude storms as observed in long‐term current measurements” by Yoshihiro Niwa and Toshiyuki Hibiya

Correction to “Response of the deep ocean internal wave field to traveling midlatitude storms as observed in long‐term current measurements” by Yoshihiro Niwa and Toshiyuki Hibiya

Response of the deep ocean internal wave field to traveling midlatitude storms as observed in long‐term current measurements

It has been demonstrated in a recent numerical experiment that double‐inertial frequency internal waves may play a crucial role in diapycnal mixing processes in the deep ocean, with the energy effectively transferred across the internal wave spectrum down to small dissipation scales by nonlinear wave‐wave interactions [Hibiya et al., 1998]. To examine whether or not such double‐inertial frequency waves are actually generated in the real deep ocean, current meter data from long‐term moorings in the northwest Pacific basin are analyzed together with global sea surface wind data. By incorporating the wind data into a simple damped slab model, predominant inertial currents are shown to be excited in the mixed layer in the northwest Pacific basin by traveling midlatitude storms during fall and winter. The multiple filter analysis demonstrates that double‐inertial frequency waves as well as near‐inertial frequency waves are significantly amplified in the deep ocean internal wave field during the periods strong inertial currents are excited in the mixed layer. This suggests that in addition to near‐inertial frequency waves, double‐inertial frequency waves are actually excited by strong atmospheric disturbances through nonlinear effects as demonstrated in the numerical experiment by Niwa and Hibiya [1997]. Double‐inertial frequency waves thus excited seem to propagate over horizontal distances of the order of 1000 km from their source region while feeding their energy to the local internal wave field, consistent with the theoretical prediction based on the magnitudes of group velocity and nonlinear interaction time [Olbers, 1983].

Measurements of multi-megameter travel-time bias and coherence

The quality of ocean acoustic travel-time measurements depends on the coherence as well as the bandwidth of the signal. Ocean internal-wave fields are thought to be responsible for the loss of coherence in low-frequency acoustic signals. If the coherence bandwidth is less than the signal bandwidth, it is possible to consider sub-bands of the signal as separate measurements. The separate measurements can then be combined incoherently to improve the quality of the travel-time measurement. Theoretical work and computer simulations also predict that the travel-time of acoustic signals is biased by the ocean internal wave field. The path-integral theory for scattering predicts that the size of the travel-time bias depends on the logarithm of the center frequency of the acoustic signal, thus separate sub-bands would have different travel times and incoherent recombination would not be an optimal procedure. A recent experiment, in which two acoustic signals with different center frequencies were transmitted simultaneously, makes it possible to measure the bias experimentally and to determine the efficiency of sub-band averaging. Preliminary results suggest that the bias is about 50 ms at 3500-km range, which is roughly as large as expected.

Measurements of the travel-time bias caused by internal waves

Theoretical work and computer simulations predict that the travel-time of acoustic signals is biased by the ocean internal wave field. The path integral theory for scattering predicts that the size of the travel time bias depends on the logarithm of the center frequency of the acoustic signal. A recent experiment, in which two acoustic signals with different center frequencies were transmitted simultaneously, makes it possible to measure the bias experimentally. Preliminary results suggest that the bias is about 50 ms at 3500-km range, which is roughly as large as expected. a)The AST group is T. G. Birdsall (U. Michigan), B. M. Howe (U. Washington), J. A. Mercer (U. Washington), K. Metzger (U. Michigan), R. C. Spindel (U. Washington), and P. F. Worcester (SIO).

Nonlinear processes of energy transfer from traveling hurricanes to the deep ocean internal wave field

Generation of large‐scale internal waves by a hurricane traveling over the ocean with a uniform velocity is investigated by using a three‐dimensional, multilevel numerical model. It is found that two distinctive kinds of internal waves are excited in the wake of the hurricane, namely, near‐inertial waves, which can be explained based on the linear theory, and superinertial waves with frequencies 2ƒ0 and 3ƒ0(ƒ0 is the inertial frequency at the latitude of the hurricane track), which are generated through nonlinear effects. Our special attention is directed to the superinertial waves with frequencies 2ƒ0 and 3ƒ0 because these internal waves are considered to be efficient energy sources for small‐scale mixing in the deep ocean. These superinertial waves predominantly have low‐vertical‐mode structures and satisfy the dispersion relation for lee waves. In areas away from the hurricane track, in particular, the double‐inertial frequency waves become larger than the near‐inertial waves. The nonlinear resonant triads causing the generation of such superinertial waves are examined by calculating the bispectrum, which clearly shows that the lowest‐vertical‐mode double‐inertial frequency wave is generated efficiently through the nonlinear interaction between the high‐vertical‐mode near‐inertial waves.

Chaotic properties of internal wave triad interactions

We discuss the stochasticities of two-triad interactions that occur in two-degree-of-freedom autonomous Hamiltonian systems. The system we study is a two-triad test-wave system consisting of a single internal wave mode (test-wave) interacting with a spectrum of ambient internal wave modes; the ambient modes, however, do not interact among themselves except through a three-wave interaction which includes the test-wave. The present study concerns the effect of nonlinearities on the ocean internal wave field. Our numerical results using the physical parameters appropriate for the deep ocean confirm that the test-wave system is non-integrable. Moreover, there exists a certain separatrix net that fills the phase space and is covered by a thin stochastic layer for a two-triad pure resonant interaction. The stochastic web implies the existence of diffusion of the Arnold type for the minimal dimension of a non-integrable autonomous system. For the non-resonant case, the stochastic layer is formed where the separatrix from KAM theory is disrupted. However, the stochasticity does not increase monotonically with increasing energy.