Finescale Parameterization Research Articles

Employing generative adversarial neural networks as surrogate model for reactive transport modeling in the hyporheic zone

This study explores the application of advanced deep learning techniques, specifically conditional deep convolutional generative adversarial networks (cDC-GANs), to model and predict the complex dynamics of the hyporheic zone (HZ) driven by river stage fluctuations. The HZ is a critical transitional mixing zone between surface water and groundwater, where significant biogeochemical reactions occur. Traditional process-based reactive transport modeling methods are computationally intensive and require fine-scale parameterization. To overcome these challenges, we employ the cDC-GAN as a deep-learning-based surrogate model to predict zones of enhanced biogeochemical activity (i.e., hotspots) and reaction product concentrations in the HZ under varying bimodal sedimentary heterogeneity scenarios. The cDC-GAN model can efficiently capture nonlinear relationships between input data and output parameters without extensive parameterization, making it computationally less demanding. The model’s generative capabilities allow for the creation of new data instances, enabling the exploration of diverse scenarios and interpolation between observed data points. The model uses maps of liquid saturation and solute concentrations at different time steps to generate corresponding maps of reaction rates and reaction product concentrations. Results demonstrate the model’s qualitative and quantitative ability to capture complex relationships without relying on rigid assumptions about linearity or specific probability distribution functions. Notably, even amid variations in aquifer heterogeneity, the model consistently exhibits robust performance, validating its ability to adapt to dynamic geological settings. Our use of a simplified reaction scheme serves as a proof of concept for the cDC-GAN model’s ability to simulate solute transport in the HZ, opening avenues for future applications including more complex reaction networks within HZ system such as nutrient cycling, organic matter degradation, redox reactions, and beyond.

Parameterization of Shear‐To‐Strain Ratio Used in Finescale Parameterization

AbstractThe Gregg‐Henyey‐Polzin (GHP) finescale parameterization is widely employed to infer turbulent mixing when microstructure measurements are unavailable. However, the strain‐only GHP scaling is the only option when shear information is lacking, in which case the shear‐to‐strain ratio (Rω) is commonly treated as a constant. Since Rω has been reported to vary spatiotemporally, using a fixed value of Rω might result in a significant bias in inferring turbulent mixing. In this study, we present a global map of Rω, based on the microstructure database contributed by the Climate Process Team on internal wave‐driven ocean mixing, which covers the Indian, Pacific, and Atlantic oceans across both high and low latitudes. Then, we propose a parameterization of Rω by considering buoyancy frequency, Coriolis frequency, and topographic features. Compared to the GHP scaling with constant Rω, the turbulent dissipation rate values inferred from the GHP scaling with parameterized Rω are more accurate. In this manner, this study provides a reference for choosing optimal Rω when using the strain‐only GHP scaling to explore turbulent mixing in the open ocean.

Response of Internal Wave‐Induced Turbulent Dissipation to ENSO in the Western Pacific Warm Pool

AbstractThis paper utilizes a finescale parameterization scheme based on strain spectra and characterizes the temporal and spatial distributions of diapycnal turbulent mixing in the West Pacific Warm Pool. We use Array for Real‐Time Geostrophic Oceanography (Argo) profiles from 2011 to 2022 to generate the turbulent dissipation rate (ε) as a representative of internal‐wave‐induced mixing. We then discuss the influence of El Niño‐Southern Oscillation (ENSO) on turbulent mixing by considering seafloor topography, thermocline depth, and ENSO phases. Results indicate that ENSO can influence the vertical stratification in the ocean by changing the depth of the thermocline, causing the change of interaction between internal tides and seafloor topography, thereby affecting the intensity and vertical distribution of diapycnal turbulent mixing. During La Niña years, the value of ε is larger compared to that of El Niño years. Compared to rough regions, the thermocline variations induced by ENSO have a more pronounced impact in the smooth regions. The variability in turbulent mixing influenced by ENSO is crucial for heat and substance exchange in the equatorial Pacific.

Turbulence Across the Antarctic Circumpolar Current in the Indian Southern Ocean: Micro‐Temperature Measurements and Finescale Parameterizations

AbstractTurbulence structures across the Antarctic circumpolar current (ACC) in the Indian Ocean at around 50°E were revealed using microstructure measurements. Depth‐averaged turbulent energy dissipation rates (ε) in 320 m segments estimated using a conductivity‐temperature‐depth (CTD)‐attached micro‐temperature fast‐response thermistor (FP07) were well reproduced using existing finescale parameterizations excluding near‐surface and near‐bottom 160 m. The spatial variations of ε are explained by density stratification N2, bottom topographic roughness, and depth‐averaged current speed U. Diapycnal diffusivity Kρ(=0.2εN−2) is found proportional to the squared internal wave energy () and increases toward the bottom, especially over rough bottom topography. The decay scale height is >1000m and the turbulence remains large even in the upper pycnocline. Existing shear‐based finescale parameterizations were generally consistent with the FP07 measurements but tended to overestimate in the areas with large shear‐strain ratio Rω and low ε in the Continental Zone (CZ) south of the ACC fronts (58–65°S). This overestimation is improved by using the strain‐based finescale parameterization with a constant Rω = 3.

Enhanced Turbulent Diapycnal Mixing in the Northern Sargasso Sea Inferred From a Finescale Parameterization

AbstractThe Sargasso Sea, accommodating marine species and mode water, is highly productive relative to other oligotrophic subtropical regions with intense air‐sea carbon and heat exchanges. Turbulent diapycnal mixing regulates these processes and is generally thought to be weakened in a more stratified ocean under anthropogenic forcing. However, by applying a finescale parameterization to long‐term hydrographic profiles collected during the Bermuda Atlantic Time‐Series Study (BATS), we show that its intensity has become stronger from 1994 to 2019 in the permanent thermocline. The enhanced turbulent diapycnal mixing is mainly attributed to the increase of wind power on internal waves along the Gulf Stream extension. Numerical simulations suggest that stronger internal waves excited along the Gulf Stream extension radiate downward and equatorward, causing enhanced turbulent diapycnal mixing in the northern Sargasso Sea including the BATS station. The findings have important implications for understanding responses of mode water and ecosystem in the Sargasso Sea to anthropogenic forcing.

Energy cascade in the Garrett–Munk spectrum of internal gravity waves

We study the spectral energy transfer due to wave–triad interactions in the Garrett–Munk spectrum of internal gravity waves based on a numerical evaluation of the collision integral in the wave kinetic equation. Our numerical evaluation builds on the reduction of the collision integral on the resonant manifold for a horizontally isotropic spectrum. We evaluate directly the downscale energy flux available for ocean mixing, whose value is in close agreement with the finescale parameterization. We further decompose the energy transfer into contributions from different mechanisms, including local interactions and three types of non-local interactions, namely parametric subharmonic instability, elastic scattering (ES) and induced diffusion (ID). Through analysis on the role of each mechanism, we resolve two long-standing paradoxes regarding the mechanism for forward cascade in frequency and zero ID flux for the GM76 spectrum. In addition, our analysis estimates the contribution of each mechanism to the energy transfer in each spectral direction, and reveals new understanding of the importance of local interactions and ES in the energy transfer.

Enhanced Mixing Induced by Near-Inertial Waves Inferred by Glider Observation in the Northern South China Sea

Enhanced turbulence triggered by near-inertial wave (NIW) trapping by a mesoscale anticyclone and typhoon “Kompasu” was observed in the northern South China Sea. The observations provide evidence for the trapping of NIW packets of amplitude ~0.2 m/s near the base of an anticyclonic eddy, and of ~0.3 m/s after the passage of typhoon “Kompasu”. The wave energy was amplified in a layer located near the base of the anticyclonic eddy, between 150 and 300 m, while stronger NIWs triggered by the typhoon extended to depths > 500 m. Diffusivity was calculated by a fine-scale parameterization. A diffusivity elevated by one order of magnitude, the occurrence of high near-inertial velocity shears, and the low (≤1) Richardson numbers were consistent with turbulence production and mixing from the base of the anticyclonic eddy and following the passage of the typhoon, and were associated with the trapped NIWs. This study showed that, by serving as a bridge between mesoscale eddies and small-scale motion, NIWs are an important pathway for ocean energy transmission. Mesoscale-NIW interactions represent a significant source of NIWs as well as a sink of mesoscale energy.

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.

M2 Internal Tide Energetics and Behaviors in the Subpolar North Pacific

Abstract Energetic internal tides in the Pacific Ocean generated from multiple sources are the subject of many studies, although the subpolar North Pacific (SNP) is known as a high-latitude hotspot that remains less explored. The present study is the first detailed investigation on M2 internal tide energetics and dynamics in the SNP by high-resolution numerical simulations. The M2 internal tides in the SNP mainly originate from the Aleutian Ridge (area-integrated 5.51 GW and averaged ∼10−3 W m−2 of barotropic-to-baroclinic conversion rate), wherein the Amukta Pass is the most significant source. The Amukta Pass radiates northward 0.55 GW (averaged 2.3 kW m−1) to the Bering Sea and southward 1.40 GW (averaged 3.7 kW m−1) to the North Pacific. The subsequent south–north asymmetric radiation pattern is consistent with satellite altimeter detection. In the Bering basin, multiwave superposition in the near field between the Amukta Pass and adjacent sources generates two standing wave patterns. After approaching the Bering Sea slope, remote internal tides from Aleutian Ridge enhance local generation and dissipation. The dissipation field is relatively similar to the generation map, which is explained by the higher local dissipation efficiency q (>1/2) and the faster energy attenuation than in the midlatitudes. The simulated dissipation rates compare favorably with the estimate from fine-scale parameterization, indicating the dominance of internal tidal mixing. The averaged dissipation rate in SNP is O(10−10) W kg−1, and the depth-integrated dissipation rates reach O(10−1) W m−2 near the Amukta Pass. It is important to understand the unique physics and dissipative process of high-latitude internal tides to fully characterize the redistribution of global tidal energy and associated mixing.

Diapycnal and isopycnal mixing along the continental rise in the Australian–Antarctic Basin

Shipboard measurements of temperature, salinity and horizontal current velocity were used to estimate diapycnal and isopycnal diffusivities in the Australian sector of the Southern Ocean between 120∘E and 150∘E near 64∘S, along the climatological positions of the Southern Antarctic Circumpolar Current Front and the Southern Boundary. The diapycnal diffusivities estimated by the finescale parameterization on the neutral density surfaces of 1028.05, 1028.2, and 1028.3 kg m−3 are (9.5±6.8)×10−5, (10.7±2.6)×10−5, and (13.8±3.7)×10−5 m2s−1, respectively (mean ± one standard deviation). At these densities, salinity and temperature decreased with depth but salt fingering was unlikely. Using the water mass transformation framework and a box inverse model, the isopycnal diffusivities were estimated from the diapycnal diffusivities. Climatological estimates of the isopycnal diffusivities in the density ranges of Upper Circumpolar Deep Water, Lower Circumpolar Deep Water, and Antarctic Bottom Water were −30±116, 16±319, and −30±83 m2s−1, respectively. These diffusivities were likely underestimates by 10 to 20 m2s−1 because eddy transport could not be considered in the climatological data. The weak isopycnal diffusivities were not inconsistent with diffusivity suppressed by the frontal jets. The large uncertainties were caused by the uncertainty in the box inverse model and the fact that the size of the box was comparable to the advection speed times the diffusion time scale.

Energetics of semidiurnal internal tides near Madagascar in the Southwest Indian Ocean

The semi-diurnal internal tidal energetics near Madagascar Island in the Southwest Indian Ocean were analyzed based on a numerical simulation. The baroclinic energy budget revealed that internal tides radiating from the north of Madagascar Island (NMI) and the south of Madagascar Island (SMI), especially those from the continental slope, were the dominant energy sources of the baroclinic energy dissipation in the deep ocean of surrounding areas. In NMI and SMI, the most intense baroclinic energy dissipation and internal tide-induced diapycnal mixing occurred near ridges and seamounts, with depth-integrated energy dissipation of O(10-1-100) W·m−2, dissipation rates of O(10-7-10-6) W·kg−1 and diapycnal diffusivity of O(10-3-10-2) m2·s−1, about one order of magnitude larger than those in most areas of the Mozambique Channel near the 200-m isobath. These estimates based on the numerical simulation were comparable with previous results based on microstructure measurements or fine-scale parameterizations, and suggested that the remotely generated internal tides played an important role in the baroclinic energy dissipation in the deep ocean.

Diapycnal mixing variations induced by subthermocline eddies observed in the north Pacific western boundary region

Recent observations prove that subthermocline eddies (SEs) are energetic in the north Pacific western boundary region, where interhemispheric waters meet. Our previous study showed that the SEs play an important role in isopycnal mixing of interhemispheric intermediate waters. Whether the SEs can induce diapycnal mixing in the western boundary region is unknown although it has been found true in the interior region. In this study, based on in-situ observations and fine-scale parameterization method, we show spatial structure and variability of diapycnal mixing induced by the SEs in the north Pacific western boundary region. The SEs are located between 200 and 750 m with a maximum swirl speed reaching 0.5 m s-1 and exhibit significant intra-seasonal variability with the period ranging between 50 and 100 days. Compared with shears induced by tides and near-inertial oscillation, sub-inertial shears induced by the SEs are dominant in the subthermocline layer. Consequently, diapycnal diffusivity is elevated up to O(10-4) m2 s-1 about one order higher than the background value when the SEs were passing by. The integrated diapycnal diffusivity between 200 and 750 m is increased by 210%. Modulated by the SEs, diapycnal mixing in the subthermocline has significant intra-seasonal variations. With more and more SEs being observed around the global oceans, we suggest that SE-induced mixing may not be trivial in closing the global ocean energy budget.

Two-Dimensional Wavenumber Spectra on the Horizontal Submesoscale and Vertical Finescale

Abstract Horizontal and vertical wavenumbers (kx, kz) immediately below the Ozmidov wavenumber (N3/ε)1/2 are spectrally distinct from both isotropic turbulence (kx, kz > 1 cpm) and internal waves as described by the Garrett–Munk (GM) model spectrum (kz < 0.1 cpm). A towed CTD chain, augmented with concurrent Electromagnetic Autonomous Profiling Explorer (EM-APEX) profiling float microstructure measurements and shipboard ADCP surveys, are used to characterize 2D wavenumber (kx, kz) spectra of isopycnal slope, vertical strain, and isopycnal salinity gradient on horizontal wavelengths from 50 m to 250 km and vertical wavelengths of 2–48 m. For kz < 0.1 cpm, 2D spectra of isopycnal slope and vertical strain resemble GM. Integrated over the other wavenumber, the isopycnal slope 1D kx spectrum exhibits a roughly +1/3 slope for kx > 3 × 10−3 cpm, and the vertical strain 1D kz spectrum a −1 slope for kz > 0.1 cpm, consistent with previous 1D measurements, numerical simulations, and anisotropic stratified turbulence theory. Isopycnal salinity gradient 1D kx spectra have a +1 slope for kx > 2 × 10−3 cpm, consistent with nonlocal stirring. Turbulent diapycnal diffusivities inferred in the (i) internal wave subrange using a vertical strain-based finescale parameterization are consistent with those inferred from finescale horizonal wavenumber spectra of (ii) isopycnal slope and (iii) isopycnal salinity gradients using Batchelor model spectra. This suggests that horizontal submesoscale and vertical finescale subranges participate in bridging the forward cascade between weakly nonlinear internal waves and isotropic turbulence, as hypothesized by anisotropic turbulence theory.

Turbulent Mixing Variability in an Energetic Standing Meander of the Southern Ocean

Abstract This study presents novel observational estimates of turbulent dissipation and mixing in a standing meander between the Southeast Indian Ridge and the Macquarie Ridge in the Southern Ocean. By applying a finescale parameterization on the temperature, salinity, and velocity profiles collected from Electromagnetic Autonomous Profiling Explorer (EM-APEX) floats in the upper 1600 m, we estimated the intensity and spatial distribution of dissipation rate and diapycnal mixing along the float tracks and investigated the sources. The indirect estimates indicate strong spatial and temporal variability of turbulent mixing varying from O(10−6) to O(10−3) m2 s−1 in the upper 1600 m. Elevated turbulent mixing is mostly associated with the Subantarctic Front (SAF) and mesoscale eddies. In the upper 500 m, enhanced mixing is associated with downward-propagating wind-generated near-inertial waves as well as the interaction between cyclonic eddies and upward-propagating internal waves. In the study region, the local topography does not play a role in turbulent mixing in the upper part of the water column, which has similar values in profiles over rough and smooth topography. However, both remotely generated internal tides and lee waves could contribute to the upward-propagating energy. Our results point strongly to the generation of turbulent mixing through the interaction of internal waves and the intense mesoscale eddy field.

Turbulent Heat Fluxes in a Mediterranean Eddy Quantified Using Seismic and Hydrographic Observations

Mediterranean eddies (meddies) play an essential role in transferring heat, salinity and momentum into the Atlantic Ocean. The rate of heat (and salt) flux from the meddy and its ultimate lifetime are key proxies to understanding how meddies impact the redistribution of heat and salt in the ocean system. A Mediterranean eddy was observed in the Gulf of Caidz in 2007 using seismic and hydrographic data. The spatial distribution of turbulent dissipation rates around the meddy is estimated from the seismically derived internal wave spectra subrange using fine-scale parameterization. Turbulent dissipated rates are lowest (10−11 W/kg) within the core of the meddy but rise by nearly two orders of magnitude at the upper and lower boundaries, where signs of double diffusive convection are observed. Along the left flank of the meddy, thermohaline intrusions and interleaving of water masses are found in inverted temperature and salinity profiles, transporting heat laterally from the warm core to the Atlantic water with a flux of around 470 Wm−2. The meddy presented in this study is shown to decay in 2 years, primarily due to the heat loss associated with thermohaline intrusions. For the first time, heat fluxes around the meddy and its lifetime are quantified using seismic oceanography data, and the methods proposed here can be applied to more seismic datasets in the global oceans.

Enhanced turbulent mixing in mesoscale eddies near the critical latitude of the M2 internal tides

Mesoscale eddies can elevate turbulent mixing, but the mechanisms have not been fully understood. Based on a field experiment in two mesoscale eddies near the critical latitude of the M2 internal tides in the northwestern Pacific Ocean, enhanced turbulent mixing was found both in and below the mixed layer. Microstructure observations indicate that enhanced turbulent mixing mainly appeared outside the eddy center in the mixed layer (approximately 117 m), which was speculated to be related to geostrophic current shear. By analyzing the CTD and Argo measurements through a fine-scale parameterization method, enhanced turbulent mixing was found to be concentrated at the southern flank of the anticyclonic eddy below 300 m, which showed little correlation with topographic roughness and local winds. Based on a ray-tracing model, the wind-generated near-inertial waves at higher latitudes were also excluded as the cause of the enhanced turbulent mixing. The enhanced turbulent mixing below 300 m was generally consistent with the features of subthermocline eddies and eddy-modulated parametric subharmonic instability (PSI) of the M2 internal tides. However, due to the limitation of observations, the eddy-modulated PSI mechanism was not fully validated.

Turbulent Mixing and Lee‐Wave Radiation in Drake Passage: Sensitivity to Topography

AbstractRadiation and breaking of internal lee waves are thought to play a significant role in the energy and heat budget of the Southern Ocean. Open questions remain, however, regarding the amount of energy converted from the deep flows of the Antarctic Circumpolar Current (ACC) into lee waves and how much of this energy dissipates locally. This study estimated the linear lee‐wave energy radiation using a unique 4‐year time series of stratification and near‐bottom currents from an array of Current and Pressure measuring Inverted Echo Sounders (CPIES) spanning Drake Passage. Lee‐wave energy was calculated from two 2D anisotropic and one 1D isotropic abyssal hill topographies. Lee‐wave energy radiation from all three topographies was largest in the Polar Front Zone associated with strong deep meandering of the ACC fronts. Both baroclinic and barotropic instabilities appeared to modulate the conversion to lee waves in the Polar Front Zone. Fine structure temperature, salinity, and velocity profiles at the CPIES locations were used to estimate turbulent dissipation due to breaking internal waves by employing a finescale parameterization. High dissipation near the bottom was consistent with upward‐propagating, high‐frequency lee waves as found by earlier studies. In contrast to idealized numerical predictions of 50% local dissipation of lee‐wave energy, this study found less than 10% dissipated locally similar to some other studies. Improving the representation of the abyssal hills by accounting for anisotropy did not reduce the discrepancy between radiated lee‐wave energy and local dissipation. Instead, alternative fates must be considered for the excess radiated lee‐wave energy.

Decadal Observations of Internal Wave Energy, Shear, and Mixing in the Western Arctic Ocean

AbstractAs Arctic sea ice declines, wind energy has increasing access to the upper ocean, with potential consequences for ocean mixing, stratification, and turbulent heat fluxes. Here, we investigate the relationships between internal wave energy, turbulent dissipation, and ice concentration and draft using mooring data collected in the Beaufort Sea during 2003–2018. We focus on the 50–300 m depth range, using velocity and CTD records to estimate near‐inertial shear and energy, a finescale parameterization to infer turbulent dissipation rates, and ice draft observations to characterize the ice cover. All quantities varied widely on monthly and interannual timescales. Seasonally, near‐inertial energy increased when ice concentration and ice draft were low, but shear and dissipation did not. We show that this apparent contradiction occurred due to the vertical scales of internal wave energy, with open water associated with larger vertical scales. These larger vertical scale motions are associated with less shear, and tend to result in less dissipation. This relationship led to a seasonality in the correlation between shear and energy. This correlation was largest in the spring beneath full ice cover and smallest in the summer and fall when the ice had deteriorated. When considering interannually averaged properties, the year‐to‐year variability and the short ice‐free season currently obscure any potential trend. Implications for the future seasonal and interannual evolution of the Arctic Ocean and sea ice cover are discussed.

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.

Spatial distribution of turbulent diapycnal mixing along the Mindanao current inferred from rapid-sampling Argo floats

The Mindanao Current (MC) bridges the North Pacific low-latitude western boundary current system region and the Indonesian Seas by supplying the North Pacific waters to the Indonesian Throughflow. Although the previous study speculated that the diapycnal mixing along the MC might be strong on the basis of the water mass analysis of the gridded climatologic dataset, the real spatial distribution of diapycnal mixing along the MC has remained to be clarified. We tackle this question here by applying a finescale parameterization to temperature and salinity profiles obtained using two rapid-sampling profiling Argo floats that drifted along the MC. The western boundary (WB) region close to the Mindanao Islands and the Sangihe Strait are the two mixing hotspots along the MC, with energy dissipation rate ε and diapycnal diffusivity Kρ enhanced up to ~ 10–6 W kg−1 and ~ 10–3 m2 s−1, respectively. Except for the above two mixing hotspots, the turbulent mixing along the MC is mostly weak, with ε and Kρ to be 10–11–10–9 W kg−1 and 10–6–10–5 m2 s−1, respectively. Strong mixing in the Sangihe Strait can be basically attributed to the existence of internal tides, whereas strong mixing in the WB region suggests the existence of internal lee waves. We also find that water mass transformation along the MC mainly occurs in the Sangihe Strait where the water masses are subjected to strong turbulent mixing during a long residence time.