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Sea surface temperature (SST) bias in the climate models has been a focus in the past, but subsurface temperature biases have not received much attention yet. In this study, subsurface temperature biases in the tropical North Pacific (TNP) are investigated by analyzing the CMIP6, CMIP5 and OMIP products, and by performing ocean model simulations. It is found that almost all the CMIP and OMIP simulations have a pronounced subsurface warm bias (SWB) in the northeastern tropical Pacific (NETP), and the model developments over the past decade do not indicate obvious improvements in bias pattern and magnitude from CMIP5 to the latest version CMIP6. This SWB is primarily caused by the model deficiencies in the simulated surface wind stress curl (WSC) in the NETP, which is too weak to produce a sufficient Ekman upwelling, a bias that also exists in OMIP simulations. The uncertainties in the parameterizations of the oceanic vertical mixing processes also make a great contribution, and it is demonstrated that the estimated oceanic vertical diffusivities are overestimated both in the upper boundary layer and the interior in the CMIP and OMIP simulations. The relationships between the SWB and the misrepresented oceanic vertical mixing processes are investigated by conducting several ocean-only experiments, in which the upper boundary layer mixing is modified by reducing the wind stirring effect in the Kraus-Turner type bulk mixed-layer scheme, and the interior mixing is constrained by using the Argo-derived diffusivity. By applying these modifications to oceanic vertical mixing schemes, the SWB is greatly reduced in the NETP. The consequences of this SWB are further analyzed. Because the thermal structure in the NETP can influence the simulations of oceanic circulations and equatorial upper-ocean thermal structure, the large SWB in the CMIP6 models tends to produce a weak equatorward water transport in the subsurface TNP, a weak equatorial upwelling and a warm equatorial upper ocean.

The authors study small disturbances to the periodic, plane Couette flow in the 3D incompressible Navier-Stokes equations at high Reynolds number Re. They prove that for sufficiently regular initial data of size $\\epsilon \\leq c_0\\mathbf {Re}^-1$ for some universal $c_0 > 0$, the solution is global, remains within $O(c_0)$ of the Couette flow in $L^2$, and returns to the Couette flow as $t \\rightarrow \\infty $. For times $t \\gtrsim \\mathbf {Re}^1/3$, the streamwise dependence is damped by a mixing-enhanced dissipation effect and the solution is rapidly attracted to the class of \"2.5 dimensional\" streamwise-independent solutions referred to as streaks.

Vertical two‐dimensional numerical experiments incorporating Garrett‐Munk (GM) internal waves are conducted to investigate tide‐induced near‐field mixing over a finite‐amplitude sinusoidal seafloor, conventionally attributed to the breaking of high‐wavenumber internal tidal waves. Turbulent mixing is characterized by tidal excursion parameter (Te) and topographic steepness parameter (Sp) measuring tidal current strength and seafloor slope gradient, respectively. Under strong tidal currents (Te > 1), high‐wavenumber internal lee waves propagate upward from the seafloor. Even when Te and Sp are set to produce nearly the same upward energy flux, the vertical profile of mixing hotspots varies with Sp. For Sp ≳$\\mathit{\\gtrsim }$0.2, near‐inertial currents above the seafloor rapidly amplify by absorbing energy of internal lee waves from below, hindering their upward propagation and creating “short mixing hotspots.” For Sp < 0.2, these near‐inertial currents diminish, allowing internal lee waves to propagate upward and interact with the GM background internal waves, creating “tall mixing hotspots.” Plain Language Summary We perform numerical experiments to study how tidal currents cause mixing in the ocean near a rough seafloor. By considering the interaction between strong tidal currents and small‐scale rough seafloor features, we find that high‐frequency internal waves, different from those previously thought, propagate rapidly upward from the seafloor and interact with background waves, causing mixing above the seafloor. The pattern of this mixing changes with the steepness of the seafloor slope. If the seafloor slope is steep, the currents near the seafloor quickly absorb the energy of the upward‐propagating waves, creating a mixing region confined to the seafloor (short mixing hotspot). In contrast, if the seafloor slope is gentle, less energy is absorbed, allowing the upward‐propagating waves to travel higher and interact with background waves, creating a mixing region extending from the seafloor (tall mixing hotspot). These mixing processes have been overlooked due to limited knowledge of seafloor details. However, they are crucial because tall mixing hotspots can significantly affect global ocean circulation. Therefore, they deserve more attention in future studies. Key Points Strong tidal flows over rough seafloors induce internal lee waves that propagate upward while inducing mixing near the seafloor Over steep seafloors, inertial currents inhibit the upward propagation of internal lee waves, creating short mixing hotspots Over less steep seafloors, the lack of inertial currents allows internal lee waves to propagate upward, creating tall mixing hotspots

This review provides an overview of concepts and approaches for the quantification of passive, non-reactive solute mixing in steady uniform porous media flows across scales. Mixing in porous media is the result of the interaction of spatial velocity fluctuations and diffusion or local-scale dispersion, which may lead to the homogenization of an initially segregated system. Velocity fluctuations are induced by spatial medium heterogeneities at the pore, Darcy or regional scales. Thus, mixing in porous media is a multiscale process, which depends on the medium structure and flow conditions. In the first part of the review, we discuss the interrelated processes of stirring, dispersion and mixing, and review approaches to quantify them that apply across scales. This implies concepts of hydrodynamic dispersion, approaches to quantify mixing state and mixing dynamics in terms of concentration statistics, and approaches to quantify the mechanisms of mixing. We review the characterization of stirring in terms of fluid deformation and folding and its relation with hydrodynamic dispersion. The integration of these dynamics to quantify the mechanisms of mixing is discussed in terms of lamellar mixing models. In the second part of this review, we discuss these concepts and approaches for the characterization of mixing in Poiseuille flow, and in porous media flows at the pore, Darcy and regional scales. Due to the fundamental nature of the mechanisms and processes of mixing, the concepts and approaches discussed in this review underpin the quantitative analysis of mixing phenomena in porous media flow systems in general.

In this study, results from the Baltic Sea Tracer Release Experiment (BATRE) are described, in which deep water mixing rates and mixing processes in the central Baltic Sea were investigated. In September 2007, an inert tracer gas (CF3SF5) was injected at approximately 200 m depth in the Gotland Basin, and the subsequent spreading of the tracer was observed during six surveys until February 2009. These data describe the diapycnal and lateral mixing during a stagnation period without any significant deep water renewal due to inflow events. As one of the main results, vertical mixing rates were found to dramatically increase after the tracer had reached the lateral boundaries of the basin, suggesting boundary mixing as the key process for basin‐scale vertical mixing. Basin‐scale vertical diffusivities were of the order of 10−5 m2 s−1(about 1 order of magnitude larger than interior diffusivities) with evidence for a seasonal and vertical variability. In contrast to tracer experiments in the open ocean, the basin geometry (hypsography) was found to have a crucial impact on the vertical tracer spreading. The e‐folding time scale for deep water renewal due to mixing was slightly less than 2 years, the time scale for the lateral homogenization of the tracer patch was of the order of a few months. Key Points Mixing rates in the Gotland Basin are dominated by boundary mixing processes The time scale for Gotland Basin deep water renewal is approximately 2 years Mixing rates determined from the tracer CF3SF5

Diapycnal mixing plays a primary role in the thermodynamic balance of the ocean and, consequently, in oceanic heat and carbon uptake and storage. Though observed mixing rates are on average consistent with values required by inverse models, recent attention has focused on the dramatic spatial variability, spanning several orders of magnitude, of mixing rates in both the upper and deep ocean. Away from ocean boundaries, the spatiotemporal patterns of mixing are largely driven by the geography of generation, propagation, and dissipation of internal waves, which supply much of the power for turbulent mixing. Over the last 5 years and under the auspices of U.S. Climate Variability and Predictability Program (CLIVAR), a National Science Foundation (NSF)- and National Oceanic and Atmospheric Administration (NOAA)-supported Climate Process Team has been engaged in developing, implementing, and testing dynamics-based parameterizations for internal wave–driven turbulent mixing in global ocean models. The work has primarily focused on turbulence 1) near sites of internal tide generation, 2) in the upper ocean related to wind-generated near inertial motions, 3) due to internal lee waves generated by low-frequency mesoscale flows over topography, and 4) at ocean margins. Here, we review recent progress, describe the tools developed, and discuss future directions.

Observations of transiting gas giant exoplanets have revealed a pervasive depletion of methane 1 – 4 , which has only recently been identified atmospherically 5 , 6 . The depletion is thought to be maintained by disequilibrium processes such as photochemistry or mixing from a hotter interior 7 – 9 . However, the interiors are largely unconstrained along with the vertical mixing strength and only upper limits on the CH 4 depletion have been available. The warm Neptune WASP-107b stands out among exoplanets with an unusually low density, reported low core mass 10 , and temperatures amenable to CH 4 , though previous observations have yet to find the molecule 2 , 4 . Here we present a JWST-NIRSpec transmission spectrum of WASP-107b that shows features from both SO 2 and CH 4 along with H 2 O, CO 2 , and CO. We detect methane with 4.2 σ significance at an abundance of 1.0 ± 0.5 ppm, which is depleted by 3 orders of magnitude relative to equilibrium expectations. Our results are highly constraining for the atmosphere and interior, which indicate the envelope has a super-solar metallicity of 43 ± 8 × solar, a hot interior with an intrinsic temperature of T int  = 460 ± 40 K, and vigorous vertical mixing which depletes CH 4 with a diffusion coefficient of K zz  = 10 11.6±0.1  cm 2  s −1 . Photochemistry has a negligible effect on the CH 4 abundance but is needed to account for the SO 2 . We infer a core mass of 11.5 − 3.6 + 3.0 M ⊕ , which is much higher than previous upper limits 10 , releasing a tension with core-accretion models 11 . Observations of the warm Neptune WASP-107b show that the planet has a hot interior with an intrinsic temperature of about 460 K.

Simplified descriptions of the ocean are useful both for formulating explanatory theories and for conveying meaningful global attributes. Here, using a 26-yr average of a global state estimate from ECCO, the basis for Munk’s “abyssal recipes” is evaluated on a global scale between 1000- and 3000-m depth. The two specific hydrographic stations he used prove untypical, with potential temperature and salinity more generally displaying different vertical scale heights, and thus differing in one-dimensional (in the vertical) values of mixing coefficients and/or vertical velocities. The simplest explanation is that the circulation is fully three-dimensional with temperature and salinity fields not describable with a one-dimensional steady balance. In contrast, the potential density and buoyancy are quantitatively describable through a one-dimensional exponential balance, and which calls for an explanation in terms of turbulent mixing processes.

Vertical mixing is often regarded as the Achilles' heel of ocean models. In particular, few models include a comprehensive and energy‐constrained parameterization of mixing by internal ocean tides. Here, we present an energy‐conserving mixing scheme which accounts for the local breaking of high‐mode internal tides and the distant dissipation of low‐mode internal tides. The scheme relies on four static two‐dimensional maps of internal tide dissipation, constructed using mode‐by‐mode Lagrangian tracking of energy beams from sources to sinks. Each map is associated with a distinct dissipative process and a corresponding vertical structure. Applied to an observational climatology of stratification, the scheme produces a global three‐dimensional map of dissipation which compares well with available microstructure observations and with upper‐ocean finestructure mixing estimates. This relative agreement, both in magnitude and spatial structure across ocean basins, suggests that internal tides underpin most of observed dissipation in the ocean interior at the global scale. The proposed parameterization is therefore expected to improve understanding, mapping, and modeling of ocean mixing. Plain Language Summary When tidal ocean currents flow over bumpy seafloor, they generate internal tidal waves. Internal waves are the subsurface analog of surface waves that break on beaches. Like surface waves, internal tidal waves often become unstable and break into turbulence. This turbulence is a primary cause of mixing between stacked ocean layers—a key process regulating ocean currents and biology and a key ingredient of computer models of the global ocean. In this article, a three‐dimensional global map of mixing induced by internal tidal waves is presented. This map incorporates a large variety of energy pathways from the generation of tidal waves to turbulence, accounting for the conservation of energy. The map is compared to available observations of turbulence across the globe and found to reproduce with good fidelity the main patterns identified in observations. This relatively good agreement suggests that internal tidal waves are the main source of turbulence in the subsurface ocean and implies that the map may serve a range of applications. In particular, the three‐dimensional map provides an efficient and realistic means to represent mixing by internal tidal waves in global ocean models. Key Points A global three‐dimensional map of mixing induced by internal tides is presented The map can serve as a comprehensive and energy‐constrained tidal mixing parameterization in global ocean models The map compares well to available microstructure and upper‐ocean finestructure mixing estimates

This study presents both numerical and experimental analyses of enhanced mixing in a microflow system under the influence of a magnetic field. The research employed COMSOL Multiphysics for numerical simulations and Particle Image Velocimetry (PIV) for experimental validation. In the experimental microfluidic setup, permanent neodymium magnets were used to influence a laminar flow of water partially enriched with Ho(III) ions using the magnetic field. The findings confirmed that the strong interaction between Ho(III) ions and the magnetic field significantly affected the flow and may have resulted in vortex shedding downstream of the region with the highest magnetic field intensity. The numerical simulations demonstrated good agreement with the PIV experimental results. These findings suggest that it is possible to significantly enhance mixing in microflow systems without mechanical components, solely by exploiting the differences in the magnetic properties between the mixing substances. Traditionally, microreactors have been limited by mixing speeds governed by diffusion. These new results indicate the practical possibility of increasing mixing intensity in a cost-effective and safe manner.