Buoyancy Frequency Research Articles

High‐Frequency Gravity Waves and Kelvin‐Helmholtz Billows in the Tropical UTLS, as Seen From Radar Observations of Vertical Wind

AbstractThe present study analyzes novel observations of vertical wind in the tropical upper troposphere‐lower stratosphere obtained from a radar wind profiler in Cochin, India. Between December 2022 and April 2023, 63 consecutive 4 hr curtains of were measured with a vertical spacing of 180 m and a sampling time step of 44 s, thus resolving almost the whole spectrum of vertical motions. Spectra of strongly vary with altitude. They are generally flat up to the local Brunt‐Väisälä frequency (BVF), but sometimes exhibit a peak of variance closer to BVF, a feature which may be attributed to trapped gravity waves. At other times and locations, the profiles reveal Kelvin‐Helmholtz billows. Finally, the variability of variance over the 4 month campaign period is investigated. Using brightness temperature from geostationary satellites as a convective proxy, it is found that variance is highly correlated with fluctuations in convective activity.

Synergistic Impact of Diurnal Warm Layers and Inertial Wave Mixing on Sea Surface Temperature Warming and Upper Ocean Stratification

AbstractWe study two sea surface temperature (SST) warming events and upper ocean stratification changes in the northern South China Sea in 2022 using data from an EM‐APEX float and satellite observations. The diurnal warm layers (DWLs) and the increasing buoyancy frequency N2 above the top of the thermocline can restrict the penetration depth of nighttime convection and wind‐driven mixing, which prevents cooler water from mixing upward, allowing solar heating to increase the SST by more than 1°C in a few days. The stratification budget approach is used to reproduce observations below 40 m despite some uncertainties in estimating variables such as horizontal gradient. After the first SST warming event, the stratification changes in the subsurface layers constituted by an increase in N2 above 70 m and a decrease below this depth can be attributed to the combined effects of turbulent diffusion and vertical advection rather than to horizontal advection or penetrative solar radiation. This ocean interior mixing is likely caused by the shear of near‐inertial waves at ∼50 m, when the nighttime convection could not penetrate through the DWL's base around 20 m. The stratification budget approach fails to simulate the changes above 40 m after the second SST warming event partly due to the presence of a near‐surface freshwater layer. Our observations offer insights into the effect of inertial wave‐induced mixing in the ocean interior when near‐surface stratified layers are present, which can lead to changes in upper ocean stratification and SST.

Diagnosing tracer transport in convective penetration of a stably stratified layer

We use large-eddy simulations to study the penetration of a buoyant plume carrying a passive tracer into a stably stratified layer with constant buoyancy frequency. Using a buoyancy-tracer volume distribution, we develop a method for objectively partitioning plume fluid in buoyancy-tracer space into three regions, each of which corresponds to a coherent region in physical space. Specifically, we identify a source region where undiluted plume fluid enters the stratified layer, a transport region where much of the transition from undiluted to mixed fluid occurs in the plume cap and an accumulation region corresponding to a radially spreading intrusion. This method enables quantification of different measures of turbulence and mixing within each of the three regions, including potential energy and turbulent kinetic energy dissipation rates, an activity parameter and the instantaneous mixing efficiency. We find that the most intense buoyancy gradients lie in a thin layer at the cap of the penetrating plume. This provides the primary stage of mixing between plume and environment and exhibits a mixing efficiency around 50 %. Newly generated mixtures of environmental and plume fluid join the intrusion and experience relatively weak turbulence and buoyancy gradients. As the intrusion spreads radially, environmental fluid surrounding the intrusion is mixed into the intrusion with moderate mixing efficiency. This dominates the volume of environmental fluid entrained into the region containing plume fluid. However, the ‘strongest’ entrainment, as measured by the specific entrainment rate, is largest in the plume cap, where the most buoyant environmental fluid is entrained.

A Statistical Study of Polar Mesospheric Cloud Fronts in the Northern Hemisphere

AbstractComplex spatial structures in polar mesospheric cloud (PMC) images provide visual clues to the dynamics that occur in the summer mesosphere. In this study, we document one such structure, a PMC front, by analyzing PMC images in the northern hemisphere from the Cloud Imaging and Particle Size (CIPS) instrument onboard the aeronomy of ice in the mesosphere (AIM) satellite. A PMC front is defined as a sharp boundary that separates cloudy and mostly clear regions, and where the clouds at the front boundary are brighter than the clouds in the cloudy region. We explore the environment that supports the formation of PMC fronts using near‐coincident temperature and water vapor observations from the Sounding of the Atmosphere using Broadband Emission Radiometry (SABER) satellite instrument. A comparison of PMC front locations to near‐coincident temperature profiles reveals the presence of inversion layers at PMC altitudes. The adiabatic and superadiabatic topside lapse rates of these temperature inversions indicate that some of the identified inversion layers may have been formed by gravity wave (GW) dissipation. The structure of the squared buoyancy frequency profiles indicates a stable layer or thermal duct that can be associated with large‐amplitude mesospheric inversion layers (MILs) that extend large distances. These inversion layers may be conducive to horizontal wave propagation. We hypothesize that ducted GWs may be a formation mechanism of PMC fronts.

Oceanic response to tropical cyclone in the northern South China Sea observed by underwater gliders during 2018 and 2020

In this study, we mainly used in-situ observations from underwater gliders to analyze the ocean response in the northern South China Sea affected by Son-tinh (2018), Mandal et al. (2018) Mangkhut (2018)and Noul (2020). The results showed that these TCs caused 0.6 °C, 1.1 °C and 1.7 °C maximum sea surface temperature cooling respectively, which were weaker than general conditions because of long distance, weak intensity and fast movement speed. Net solar radiation, precipitation, 10-m wind and sea surface heat flux also made contribution in changes of SST. The mixed layer depth (MLD) became shallower after Son-Tinh and Noul passed through, while during Mangkhut it did not change significantly. After TCs passed through, the stratification around MLD became more obvious, with a banded distribution and stronger high-value areas of buoyancy frequency. Within 1 week after the shortest distance, the temperature and salinity responses in the upper ocean were stronger than those at the sea surface, and the gradients of temperature and salinity and their anomalies were more evident in the subsurface layer. The results of this study show that underwater glider observations are important for understanding oceanic responses to tropical cyclones and are useful for studying tropical cyclone activities.

Full-scale experimental and numerical study of smoke spread and temperature distribution in a room-corridor structure building

This paper aims to study the smoke spread and temperature distribution inside a full-scale room-corridor structure building. A series of experiments and simulations with different fuel properties and fuel configurations (crib and pool fires) were carried out. There was a barrier at the top of the left end of the corridor, and the end wall was on the right side. The fire source was located in the room. The evolution of the smoke spread process, pressure distribution, and temperature distribution in rooms and corridors were obtained and analyzed. The results indicate that the barrier and the end wall hinder the smoke spread and make it to accumulate below the corridor ceiling. This causes the smoke layer height of the corridor to be lower than the top of the door, which changes the pressure distribution inside and outside the room and also affects the temperature distribution. Based on the changes of pressure distribution, some correction formulas for the gas flow rate and mass flux at the opening are proposed. Under the effect of the barrier and the end wall, the smoke temperature in the room and the corridor increases. A smoke temperature decaying model along the corridor direction is proposed. Some methods are used and compared to calculate the smoke layer height based on the vertical temperature distribution. The smoke layer height determined by the buoyancy frequency method is most consistent with the experimental observation values.

Internal Waves Force Elevated Turbulent Mixing at Barkley Canyon

AbstractSubmarine canyons are hot spots for topography‐internal wave interactions, with elevated mixing contributing to regional water mass transport and productivity. Two velocity time series compare and contrast internal waves deep inside Barkley Canyon to a nearby site on the shelf‐break slope of the Vancouver Island Continental Shelf. Elevation of internal wave energy occurs near topography, up to a factor of 10 above the slope and 100 in the canyon. All frequency bands display strong seasonal variability but weak interannual variability. Diurnal (K1) energy is sub‐inertial, trapped along topography, and forced locally through barotropic motions. Both sites have high near‐inertial (NI) energy linked to wind events, though fewer events are observed deep inside the canyon. At the slope site, near‐inertial energy is attenuated with depth, while in the canyon it is amplified near the bottom. Freely propagating semidiurnal (M2) energy appears focused near critical shelf‐break and canyon floor topography, due to local and remote baroclinic forcing. The high‐frequency internal wave continuum has enhanced near‐bottom energy at both sites (up to 7 × the Garrett‐Munk spectrum), and inferred dissipation rates, ɛ, reaching 10−7 W kg−1 near topography. Dissipation is most strongly correlated with semidiurnal energy variability at both sites, with secondary contributors that are site dependent. Forcing power law fits are on the slope, and NI0.2 in the canyon. There is also a build‐up of “shoulder” energy (PSh) near the buoyancy frequency, with a power law fit to dissipation of PSh ∼ ɛ0.3 at both sites.

Effect of two-dam coexistence on thermal regime: A special withdrawal measure in Fengman reservoir, China

The Fengman Reservoir in China employs a distinctive approach termed two-dam coexistence to mitigate the risks associated with aging and hazardous dams. This method involves the partial demolition of the old dam and construction of a new dam downstream, which allows the remaining part of the old dam to act as a retaining wall for selective water withdrawal. Through a comprehensive study, long-term water temperature data were analyzed, along with the characteristics of the two-dam coexistence system, to comprehend its effects on thermal stratification in the main basin near the dams and the withdrawal water temperature (WWT) regime. The results revealed that the metalimnion shifted upwards, strengthening stratification, and the temperature gradient expanded from 0–0.9 °C/m to 0–10.5 °C/m compared to that under the one-dam condition. Vertical mixing was reduced, causing the temperature difference between surface and bottom waters to range from 6.8 to 26.8 °C. This enhanced the stratification stability by 1.8 times compared with the one-dam condition, with some annual variability. Thus, the buoyancy frequency decreased accordingly. Furthermore, two-dam coexistence influenced the WWT, resulting in higher WWT during the warming period (averaging 4.3 °C from May to June) and lower WWT during the freeze-up period (averaging 0.1 °C from January to February) than that of the one-dam condition. The most significant temperature difference between the main basin near the old dam and the one near the new dam occurred at the bottom of the reservoir (ranging from 3.5 to 12.0 °C), confirming that the old dam functioned as a retaining wall, allowing the thermal regime to change. Owing to the two-dam coexistence, the withdrawal layer shifted by 20.0 m from near the intake to close to the demolition elevation. These changes in stable stratification and variations in WWT play crucial roles in reservoir management. This study offers practical insights for treating similar aging and hazardous reservoirs and serves as a reference for optimizing water quality management strategies.

Dynamical reconstruction of the upper-ocean state in the central Arctic during the winter period of the MOSAiC expedition

Abstract. This paper presents a methodological tool for dynamic reconstruction of the state of the ocean, based, as an example, on observations from the Multidisciplinary drifting Observatory for the Study of Arctic Climate (MOSAiC) experiment. The data used in this study were collected in the Amundsen Basin between October 2019 and January 2020. Analysing observational data to assess tracer field and upper-ocean dynamics is highly challenging when measurement platforms drift with the ice pack due to continuous drift speed and direction changes. We have equipped the new version of the coastal branch of the global Finite-volumE sea ice–Ocean Model (FESOM-C) with a nudging method. Model nudging was carried out assuming a quasi-steady state. Overall, the model can reproduce the lateral and vertical structure of the temperature, salinity, and density fields, which allows for projecting dynamically consistent features of these fields onto a regular grid. We identify two separate depth ranges of enhanced eddy kinetic energy located around two maxima in buoyancy frequency: the depth of the upper halocline and the depth of the warm (modified) Atlantic Water. Simulations reveal a notable decrease in surface layer salinity and density in the Amundsen Basin towards the north but no significant gradient from east to west. However, we find a mixed-layer deepening from east to west, with a 0.084 m km−1 gradient at 0.6 m km−1 standard deviation, compared to a weak deepening from south to north. The model resolves several stationary eddies in the warm Atlantic Water and provides insights into the associated dynamics. The model output can be used to further analyse the thermohaline structure and related dynamics associated with mesoscale and submesoscale processes in the central Arctic, such as estimates of heat fluxes or mass transport. The developed nudging method can be utilized to incorporate observational data from a diverse set of instruments and for further analysis of data from the MOSAiC expedition.

Recommendations on setup in simulating atmospheric gravity waves under conventionally neutral boundary layer conditions

Wind farm-induced atmospheric gravity waves have been the subject of recent research as they can impact wind farm performance. Pressure variations associated with gravity waves can contribute to the global blockage effect and wind farm wake recovery. Therefore, accurate numerical simulation of flow fields, where wind-farm-induced gravity waves may be produced, is important. Three main considerations in such simulations are the overall domain size, the use of Rayleigh damping near domain boundaries to dampen gravity waves, and advection damping at the inlet to prevent spurious oscillations. Often these considerations are treated ad hoc rather than systematically. This work aims to test and extend the systematic modelling of internal gravity waves proposed in a preliminary investigation to modelling of both internal and trapped gravity waves. The preliminary study identifies the length scales to set the domain and damping layer sizes and the time scale to configure the Rayleigh damping coefficient but under linearly stratified conditions. Large eddy simulations of flow through a wind farm canopy are performed under conventionally neutral boundary layer (CNBL) conditions to test the validity of proposed setups for CNBL conditions. Background atmospheric parameters, such as Froude number (Fr), inversion height (Hi ), and inversion layer Froude number (Fri ) control most of the atmospheric gravity wave characteristics. We validated for CBNL conditions that the effective wavelengths of the internal gravity waves are the correct length scale to configure the domain size and damping layer thickness. Likewise, the optimum damping coefficient to dampen the internal gravity waves relates to the free atmosphere’s buoyancy frequency or buoyant perturbations’ time scale. We infer that the damping coefficient in the inversion layer may relate to the inversion buoyancy frequency to effectively dampen the trapped gravity waves. Moreover, the advection damping length is linked to the horizontal wavelength of the trapped gravity waves in the inversion layer to prevent spurious waves at the inlet by retaining wave energy accumulation.

Added mass of oscillating bodies in stratified fluids

The concept of added mass is generalized to stratified fluids, accounting for the presence of internal waves. Once the added mass of a moving body is known, so is the hydrodynamic force exerted on it by the fluid, and the energy imparted by it to the fluid. As a function of frequency, added mass is complex. Its real part is associated with inertia and its imaginary part, only present in the frequency range of propagating waves, with wave damping. Owing to causality, these two parts satisfy Kramers–Kronig relations. The added masses of an elliptic cylinder of horizontal axis, typical of two-dimensional bodies, and a spheroid of vertical axis, typical of three-dimensional bodies, are deduced from their dipole strengths, themselves deduced from their representations as single layers. The wave power is shown to be a maximum, for fixed oscillation amplitude, at approximately $0.8$ times the buoyancy frequency. In the temporal domain, added mass appears as a new memory force taking the form of a convolution integral. The kernel of this integral combines algebraically decaying oscillations at the buoyancy frequency on the one hand; and an exponentially damped oscillation for the horizontal motion of the spheroid, implying short-term memory, an aperiodic algebraic decay for its vertical motion, implying long-term memory, and a constant for the motion of the cylinder, implying everlasting memory, on the other hand. A limitation of the study is its restriction to translational motion.

A 3-D minimum-enstrophy vortex in stratified quasi-geostrophic flows

Applying a variational analysis, a minimum-enstrophy vortex in three-dimensional (3-D) fluids with continuous stratification is found, under the quasi-geostrophic hypothesis. The buoyancy frequency is held constant. This vortex is an ideal limiting state in a flow with an enstrophy decay while energy and generalized angular momentum remain fixed. The variational method used to obtain two-dimensional (2-D) minimum-enstrophy vortices is applied here to 3-D integral quantities. The solution from the first-order variation is expanded on a basis of orthogonal spherical Bessel functions. By computing second-order variations, the solution is found to be a true minimum in enstrophy. This solution is weakly unstable when inserted in a numerical code of the quasi-geostrophic equations. After a stage of linear instability, nonlinear wave interaction leads to the reorganization of this vortex into a tripolar vortex. Further work will relate our solution with maximal entropy 3-D vortices.

Near‐Inertial Wave Propagation in the Deep Canadian Basin: Turning Depths and the Homogeneous Deep Layer

AbstractThe internal wave climate in the deep Arctic Ocean, away from the shelves, is quiet because the ice cover shields the ocean from wind energy input, and tidal amplitudes are small. Hence, mixing due to internal wave breaking is small. The shrinking Arctic sea ice cover, however, exposes more open ocean areas to energy transfer by wind. Consequently, more energetic near‐inertial internal waves (NIWs) may carry energy to the bottom, potentially enhancing deep mixing. In the deep Canadian Basin, weakly stratified layers with local buoyancy frequencies smaller than the wave frequency may prevent NIW propagation to the seafloor. We estimate the distribution of these near‐inertial turning depths from temperature and salinity data of the years 2005–2014. Near‐inertial turning depths are ubiquitous in the deep Canadian Basin at ∼2,750 m depth, between 100 and 1,200 m above the bottom. A deep homogeneous layer below 3,300 m is characterized by small squared buoyancy frequencies N2 ∼ 0 with locally unstable layers (N2 < 0). The turning depths reflect NIWs and hence limit their contribution to deep mixing, but the waves create an evanescent perturbation with exponentially decreasing amplitude that can interact with the bathymetry, especially above slopes and ridges where the height of the turning depths above the seafloor is small. After reflection, the main part of the wave energy is trapped between turning depths and the surface, so that a potential increase of wave energy input mainly affects mixing of mid‐depth water masses like the Atlantic Water.

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.

A comprehensive Earth system model (AWI-ESM2.1) with interactive icebergs: effects on surface and deep-ocean characteristics

Abstract. The explicit representation of cryospheric components in Earth system models has become more and more important over the last years. However, there are few advanced coupled Earth system models that employ interactive icebergs, and most iceberg model studies focus on iceberg trajectories or ocean surface conditions. Here, we present multi-centennial simulations with a fully coupled Earth system model including interactive icebergs to assess the effects of heat and freshwater fluxes by iceberg melting on deep-ocean characteristics. The icebergs are modeled as Lagrangian point particles and exchange heat and freshwater fluxes with the ocean. They are seeded in the Southern Ocean, following a realistic present-day size distribution. Total calving fluxes and the locations of discharge are derived from an ice sheet model output which allows for implementation in coupled climate–ice sheet models. The simulations show a cooling of up to 0.2 K of deep-ocean water masses in all ocean basins that propagates from the southern high latitudes northward. We also find enhanced deep-water formation in the continental shelf area of the Ross Sea, a process commonly underestimated by current climate models. The vertical stratification is weakened by enhanced sea ice formation and duration due to the cooling effect of iceberg melting, leading to a 10 % reduction of the buoyancy frequency in the Ross Sea. The deep-water formation in this region is increased by up to 10 %. By assessing the effects of heat and freshwater fluxes individually, we find latent heat flux to be the main driver of these water mass changes. The altered freshwater distribution by freshwater fluxes and synergetic effects play only a minor role. Our results emphasize the importance of realistically representing both heat and freshwater fluxes in the high southern latitudes.

Influence of Fluvial Discharges and Tides on the Salt Wedge Position of a Microtidal Estuary: Magdalena River

The linkage between the salt wedge, tidal patterns, and the Magdalena River discharge is established by assessing the ensuing parameters: stratification (ϵ), buoyancy frequency (β), potential energy anomaly (φ), Richardson number by layers (RL), and bottom turbulent energy production (P). The salinity, temperature, density, and water velocity data utilized were derived from MOHID 3D, a previously tailored and validated model for the Magdalena River estuary. To grasp the dynamics of the river, a flow regime analysis was conducted during both the wet and dry climatic seasons of the Colombian Caribbean. The utilization of this model aimed to delineate the estuary’s spatial reach, considering flow rates spanning from 2000 to 6500 m3/s across two tidal cycles. This approach facilitates the prediction of the position, stability, and stratification degree of the salt front. Among the conclusions drawn, it is highlighted that: 1. The river flow serves as the principal conditioning agent for the system, inducing a strong estuary response to weather stations; 2. The extent of wedge intrusion and the river discharge exhibit a non-linear, inversely correlation; 3. Tidal waves cause differences of up to 1000 m in the horizontal extent of the wedge; 4. Widespread channel erosion occurs during the rainy season when the salt intrusion does not exceed 2 km; 5. Flocculation processes intensify during the transition between the dry and wet seasons; 6. The stability of the salt layering and the consolidation of the FSI–TMZ are contingent upon the geometric attributes of the channel.

Laboratory experiments of melting ice in warm salt-stratified environments

Melting icebergs provide nearly half of the total freshwater flux from ice shelves to the ocean, but the availability of accurate, data-constrained melting rate parametrisations limits the correct representation of this process in ocean models. Here, we investigate the melting of a vertical ice face in a warm, salt-stratified environment in a laboratory setting. Observations of the depth-dependent melting rates ${m}$ and boundary layer flow speed $U$ are reported for a range of initially uniform far-field ambient temperatures $T_a$ above ${10}\,^{\circ }{\rm C}$ . Ice scallops are characteristic features observed in all experiments, with the width of the scallops consistent with the theory of double-diffusive layers. The morphology of the scallops changes from symmetric about the scallop centre in the colder experiments to asymmetric in the warmer experiments. Observed melting rates are consistent with a melting rate scaling of the form ${m}\propto U\,\Delta T_a$ proposed by previous work in less extreme parameter regimes, where $\Delta T_a$ is the magnitude of thermal driving between the ambient and ice–fluid interface. Our results indicate that ice scalloping is closely linked to the naturally convecting flow of the ambient fluid. Depth-averaged melting rates depend on the buoyancy frequency in the ambient fluid, and double-diffusive convection promotes a turbulent-flux regime distinct from that explained previously in an unstratified regime. These findings have implications for parametrising melting rates of icebergs and glaciers in numerical models or potential freshwater harvesting operations, and provide insights into the interplay between stratification and ice melting.

Note on volume and distribution of fresh water in the Amazon River plume under low discharge conditions

In this research communication, we report the results of a field survey conducted in a part of the plume of the Amazon River between 0° and 5°N and offshore of the 28 m isobaths in November of 2022, during the low river discharge season. By comparing the observed vertical salinity profiles ‘disturbed’ by continental discharges within the plume with the virtually ‘undisturbed’ ones outside the plume, we estimated the total content of fresh water in the area covered by the measurements as 203 ± 22 km3, which equals to less than 3% of the average annual Amazon River discharge. Furthermore, we argue that the river-borne continental water was not confined to the upper mixed layer and show that about 37%, or 76 km3, of its volume was entrained into the plume-underlying layer between the mixed layer and the salinity maximum. This point is additionally supported by analysis of chromophoric dissolved organic matter (CDOM) fluorescence in water samples, demonstrating significant concentrations of terrigenous CDOM to depths up to 140 m. We also observed that there was a significant direct correlation between the volume of freshwater accumulated in the affected layer and background stratification (expressed as buoyancy frequency) in the unaffected layer below it.

Quantitative asymptotic stability of the quasi-linearly stratified densities in the IPM equation with the sharp decay rates

We analyze the asymptotic stability of the quasi-linearly stratified densities in the 2D inviscid incompressible porous medium equation on R2 with respect to the buoyancy frequency N. Our target density of stratification is the sum of the large background linear profile with its slope N and the small perturbation that could be both non-linear and non-monotone. Quantification in N will be performed not only on how large the initial density disturbance is allowed to be but also on how much the target densities can deviate from the purely linear density stratification without losing their stability.For the purely linear density stratification, our method robustly applies to the three fundamental domains R2, T2, and T×[−1,1], improving both the previous result by Elgindi (2017) [18] on R2 and T2, and the study by Castro et al. (2019) [12] on T×[−1,1]. The obtained temporal decay rates to the stratified density on R2 and to the newly found asymptotic density profiles on T2 and T×[−1,1] are all sharp, fully realizing the level of the linearized system. We require the initial disturbance to be small in Hm for any integer m≥4, which we even relax to any positive number m>3 via a suitable anisotropic commutator estimate.

Prandtl number effects on extreme mixing events in forced stratified turbulence

Relatively strongly stratified turbulent flows tend to self-organise into a ‘layered anisotropic stratified turbulence’ (LAST) regime, characterised by relatively deep and well-mixed density ‘layers’ separated by relatively thin ‘interfaces’ of enhanced density gradient. Understanding the associated mixing dynamics is a central problem in geophysical fluid dynamics. It is challenging to study LAST mixing, as it is associated with Reynolds numbers $Re := UL/\nu \gg 1$ and Froude numbers $Fr :=(2{\rm \pi} U)/(L N) \ll 1$ ( $U$ and $L$ being characteristic velocity and length scales, $\nu$ the kinematic viscosity and $N$ the buoyancy frequency). Since a sufficiently large dynamic range (largely) unaffected by stratification and viscosity is required, it is also necessary for the buoyancy Reynolds number $Re_{b} := \epsilon /(\nu N^{2}) \gg 1$ , where $\epsilon$ is the (appropriately volume-averaged) turbulent kinetic energy dissipation rate. This requirement is exacerbated for oceanically relevant flows, as the Prandtl number $Pr := \nu /\kappa = {O}(10)$ in thermally stratified water (where $\kappa$ is the thermal diffusivity), thus leading (potentially) to even finer density field structures. We report here on four forced fully resolved direct numerical simulations of stratified turbulence at various Froude ( $Fr=0.5, 2$ ) and Prandtl ( $Pr=1, 7$ ) numbers forced so that $Re_{b}=50$ , with resolutions up to $30\,240 \times 30\,240 \times 3780$ . We find that, as $Pr$ increases, emergent ‘interfaces’ become finer and their contribution to bulk mixing characteristics decreases at the expense of the small-scale density structures populating the well-mixed ‘layers’. However, extreme mixing events (as quantified by significantly elevated local destruction rates of buoyancy variance $\chi _0$ ) are always preferentially found in the (statically stable) interfaces, irrespective of the value of $Pr$ .