Development Of Turbulence Research Articles

Assessment of a multiphase formulation of one-dimensional turbulence using direct numerical simulation of a decaying turbulent interfacial flow

The interaction between turbulence and surface tension is studied numerically using the one-dimensional-turbulence (ODT) model. ODT is a stochastic model simulating turbulent flow evolution along a notional one-dimensional line of sight by applying instantaneous maps that represent the effects of individual turbulent eddies on property fields. It provides affordable high resolution of interface creation and property gradients within each phase, which are key for capturing the local behavior as well as overall trends, and has been shown to reproduce the main features of an experimentally determined regime diagram for primary jet breakup. Here ODT is used to investigate the interaction of turbulence with an initially planar interface. The notional flat interface is inserted into a periodic box of decaying homogeneous isotropic turbulence, simulated for a variety of turbulent Reynolds and Weber numbers. Unity density and viscosity ratios serve to focus solely on the interaction between fluid inertia and the surface-tension force. Statistical measures of interface surface density and spatial structure along the direction normal to the initial surface are compared to corresponding direct-numerical-simulation (DNS) data. Allowing the origin of the lateral coordinate system to follow the location of the median interface element improves the agreement between ODT and DNS, reflecting the absence of lateral nonvortical displacements in ODT. Beyond the DNS-accessible regime, ODT is shown to obey the predicted parameter dependencies of the Kolmogorov critical scale in both the inertial and dissipative turbulent-cascade subranges. Notably, the probability density function of local fluctuations of the critical scale is found to collapse to a universal curve across both subranges. Published by the American Physical Society 2024

Modeling magnetic field amplification in supernova remnants driven by laser

Abstract The origin of magnetic fields and their amplification have always been hot topics in fields such as astrophysics and high-energy-density physics. Among them, the turbulent dynamo effect is an important candidate mechanism, and the interaction between supernova remnants (SNRs) is an important carrier for studying the amplification effect of turbulent magnetic fields. In this paper, we use the radiation magnetohydrodynamic simulation program to carry out a scaling simulation study on the amplification effect of turbulent magnetic fields in the interaction of SNRs driven by powerful lasers. We investigate and compare the evolution of turbulence under different laser driving methods, different directions, and different intensities of initial external environmental magnetic fields. Here, we carefully identify the contributions of Biermann self-generated magnetic fields and environmental magnetic fields in the process of magnetic field amplification, present magnetic energy spectra, and magnetic field amplification factors, and analyze the influence of radiative cooling effect on turbulence and magnetic field evolution. The results show that the collision direction component of the environmental magnetic field dominates the process of magnetic field amplification, and the frequency spectrum of turbulence is consistent with Kolmogorov’s law. The research results are necessary for sorting out and elucidating the physical mechanism of magnetic field amplification in SNRs, and have reference significance for regulating turbulence in strong magnetic fields in the future.

Brightening and Fading in the Youngest Galactic Supernova Remnant G1.9+0.3: 13 Years of Monitoring with the Chandra X-Ray Observatory

We report 13 years of Chandra monitoring of the youngest Galactic supernova remnant G1.9+0.3, the only remnant known to be increasing in brightness. We confirm the spatially integrated rate of flux increase of (1.2 ± 0.2)% yr−1 (1–7 keV), but find large spatial variations, from −3% yr−1 to +7% yr−1, over length scales as small as 10″ or smaller. We observe relatively little change in spectral slope, though one region shows significant hardening as it brightens by 1% yr−1. Such rates of change can be accommodated by any of several explanations, including steady blast-wave evolution, expansion or compression of discrete plasma blobs, magnetic turbulence, or variations in magnetic-field aspect angle. Our results do not constrain the mean magnetic-field strength, but a self-consistent picture can be produced in which the maximum particle energies are limited by the remnant age (applying both to electrons and to ions) to about 20 TeV, and the remnant-averaged magnetic-field strength is about 30 μG. The deceleration parameter m (average shock radius varying as t m ) is about 0.7, consistent with estimates from overall expansion dynamics and confirming an explosion date of about 1900 CE. Shock-efficiency factors ϵ e and ϵ B (fractions of shock energy in relativistic electrons and magnetic field) are 0.003 and 0.0002 in this picture. However, the large range of rates of brightness change indicates that such a global model is oversimplified. Temporal variations of photon index, expected to be small but measurable with longer time baselines, can discriminate among possible models.

Metis Observation of the Onset of Fully Developed Turbulence in the Solar Corona

This Letter reports the first observation of the onset of fully developed turbulence in the solar corona. Long time series of white-light coronal images, acquired by Metis aboard Solar Orbiter at 2 minutes cadence and spanning about 10 hr, were studied to gain insight into the statistical properties of fluctuations in the density of the coronal plasma in the time domain. From pixel-by-pixel spectral frequency analysis in the whole Metis field of view, the scaling exponents of plasma fluctuations were derived. The results show that, over timescales ranging from 1 to 10 hr and corresponding to the photospheric mesogranulation-driven dynamics, the density spectra become shallower moving away from the Sun, resembling a Kolmogorov-like spectrum at 3 R ⊙. According to the latest observation and interpretive work, the observed 5/3 scaling law for density fluctuations is indicative of the onset of fully developed turbulence in the corona. Metis observation-based evidence for a Kolmogorov turbulent form of the fluctuating density spectrum casts light on the evolution of 2D turbulence in the early stages of its upward transport from the low corona.

A reduced ideal MHD system for nonlinear magnetic field turbulence in plasmas with approximate flux surfaces

This paper studies the nonlinear evolution of magnetic field turbulence in proximity of steady ideal Magnetohydrodynamics (MHD) configurations characterized by a small electric current, a small plasma flow, and approximate flux surfaces, a physical setting that is relevant for plasma confinement in stellarators. The aim is to gather insight on magnetic field dynamics, to elucidate accessibility and stability of three-dimensional MHD equilibria, as well as to formulate practical methods to compute them. Starting from the ideal MHD equations, a reduced dynamical system of two coupled nonlinear partial differential equations for the flux function and the angle variable associated with the Clebsch representation of the magnetic field is obtained. It is shown that under suitable boundary and gauge conditions such reduced system preserves magnetic energy, magnetic helicity, and total magnetic flux. The noncanonical Hamiltonian structure of the reduced system is identified, and used to show the nonlinear stability of steady solutions against perturbations involving only one Clebsch potential. The Hamiltonian structure is also applied to construct a dissipative dynamical system through the method of double brackets. This dissipative system enables the computation of MHD equilibria by minimizing energy until a critical point of the Hamiltonian is reached. Finally, an iterative scheme based on the alternate solution of the two steady equations in the reduced system is proposed as a further method to compute MHD equilibria. A theorem is proven which states that the iterative scheme converges to a nontrivial MHD equilbrium as long as solutions exist at each step of the iteration.

The MAGPI Survey: The evolution and drivers of gas turbulence in intermediate-redshift galaxies

Abstract We measure the ionised gas velocity dispersions of star-forming galaxies in the MAGPI survey (z ∼ 0.3) and compare them with galaxies in the SAMI (z ∼ 0.05) and KROSS (z ∼ 1) surveys to investigate how the ionised gas velocity dispersion evolves. For the first time, we use a consistent method that forward models galaxy kinematics from z = 0 to z = 1. This method accounts for spatial substructure in emission line flux and beam smearing. We investigate the correlation between gas velocity dispersion and galaxy properties to understand the mechanisms that drive gas turbulence. We find that in both MAGPI and SAMI galaxies, the gas velocity dispersion more strongly correlates with the star-formation rate surface density (ΣSFR) than with a variety of other physical properties, and the average gas velocity dispersion is similar, at the same ΣSFR, for SAMI, MAGPI and KROSS galaxies. The results indicate that mechanisms related to ΣSFR could be the dominant driver of gas turbulence from z ∼ 1 to z ∼ 0, for example, stellar feedback and/or gravitational instability. The gas velocity dispersion of MAGPI galaxies is also correlated with the non-rotational motion of the gas, illustrating that in addition to star-formation feedback, gas transportation and accretion may also contribute to the gas velocity dispersion for galaxies at z ∼ 0.3. KROSS galaxies only have a moderate correlation between gas velocity dispersion and ΣSFR and a higher scatter of gas velocity dispersion with respect to ΣSFR, in agreement with the suggestion that other mechanisms, such as gas transportation and accretion, are relatively more important at higher redshift galaxies.

The Relative Prevalence of Wave Packets and Coherent Structures in the Inertial and Kinetic Ranges of Turbulence as Seen by Solar Orbiter

The Solar Orbiter (SO) mission provides the opportunity to study the evolution of solar wind turbulence. We use SO observations of nine extended intervals of homogeneous turbulence to determine when turbulent magnetic field fluctuations may be characterized as: (i) wave packets and (ii) coherent structures (CSs). We perform the first systematic scale-by-scale decomposition of the magnetic field using two wavelets known to resolve wave packets and discontinuities, the Daubechies 10 (Db10) and Haar, respectively. The probability distribution functions (PDFs) of turbulent fluctuations on small scales exhibit stretched tails, becoming Gaussian at the outer scale of the cascade. Using quantile–quantile plots, we directly compare the wavelet fluctuations PDFs, revealing three distinct regimes of behavior. Deep within the inertial range (IR) both decompositions give essentially the same fluctuation PDFs. Deep within the kinetic range (KR) the PDFs are distinct as the Haar decompositions have larger variance and more extended tails. On intermediate scales, spanning the IR–KR break, the PDF is composed of two populations: a core of common functional form containing ∼97% of fluctuations, and tails that are more extended for the Haar decompositions than the Db10 decompositions. This establishes a crossover between wave-packet (core) and CS (tail) phenomenology in the IR and KR, respectively. The range of scales where the PDFs are two-component is narrow at 0.9 au (4–16 s) and broader (0.5–8 s) at 0.4 au. As CS and wave–wave interactions are both candidates to mediate the turbulent cascade, these results offer new insights into the distinct physics of the IR and KR.

The ALMA-ALPAKA survey. II. Evolution of turbulence in galaxy disks across cosmic time: Difference between cold and warm gas

The gas in the interstellar medium (ISM) of galaxies is supersonically turbulent. Measurements of turbulence typically rely on cold gas emission lines for low-$z$ galaxies and warm ionized gas observations for $z > 0$ galaxies. Studies of warm gas kinematics at $z > 0$ conclude that the turbulence strongly evolves as a function of redshift, due to the increasing impact of gas accretion and mergers in the early Universe. However, recent findings suggest potential biases in turbulence measurements derived from ionized gas at high-$z$, impacting our understanding of turbulence origin, ISM physics and disk formation. We investigate the evolution of turbulence using velocity dispersion (sigma ) measurements from cold gas tracers (i.e., CO CI CII ). The initial dataset comprises 17 galaxy disks with high data quality from the ALPAKA sample, supplemented with galaxies from the literature, resulting in a sample of 57 galaxy disks spanning the redshift range $z = 0 - 5$. This extended sample consists of main-sequence and starburst galaxies with stellar masses $ M_ odot $. The comparison with current Halpha kinematic observations and existing models demonstrates that the velocity dispersion inferred from cold gas tracers differ by a factor of $ 3$ from those obtained using emission lines tracing the warm, ionized gas. We show that stellar feedback is the main driver of turbulence measured from cold gas tracers and the physics of turbulence driving does not appear to evolve with time. This is fundamentally different from the conclusions of studies based on warm gas, which had to consider additional turbulence drivers to explain the high values of sigma . We present a model predicting the redshift evolution of turbulence in galaxy disks, attributing the increase of sigma with redshift to the higher energy injected by supernovae due to the elevated star-formation rate in high-$z$ galaxies. This supernova-driven model suggests that turbulence is lower in galaxies with lower stellar mass compared to those with higher stellar mass. Additionally, it forecasts the evolution of sigma in Milky-Way like progenitors.

Measurements of Natural Turbulence During the BOLT II Flight Experiment

A Mach 6.0 flight experiment was performed to characterize the turbulent skin friction and heat flux associated with natural transition for vehicle-length Reynolds numbers up to 45 million. This boundary-layer turbulence flight, termed BOLT II, was the second in a series coordinated by the Air Force Office of Scientific Research. Surface heat flux, skin friction, and pressure fluctuation spectra were acquired to characterize the transition process. The test geometry used concave curvature and swept leading edges to introduce a boundary layer with stationary laminar vortex streaks, competing transition mechanisms, and complex early turbulence. The analyses also showed that the spatial evolution of turbulence varied with respect to the location of the vortex heating streaks. Prominent overshoots were observed in the early turbulence within the streak. Turbulence data was collected for Reynolds numbers ReL up to 45×106. A common Rex=12×106 was identified as the start of equilibrium turbulence for the data presented. Conjugate heat transfer simulations, both laminar and turbulent, agreed well with the experimental data, including the laminar leading edge. The Reynolds analogy ratios based on the curve fits to the data, including compressibility, were generally between 0.9 and 1.0. The observed variations were likely the result of the spatial separation of the sensors and different definitions of Stanton number normalization between flight and theory.

Direct observation of atmospheric turbulence with a video-rate wide-field wavefront sensor

Turbulence is a complex and chaotic state of fluid motion. Atmospheric turbulence within the Earth’s atmosphere poses fundamental challenges for applications such as remote sensing, free-space optical communications and astronomical observation due to its rapid evolution across temporal and spatial scales. Conventional methods for studying atmospheric turbulence face hurdles in capturing the wide-field distribution of turbulence due to its transparency and anisoplanatism. Here we develop a light-field-based plug-and-play wide-field wavefront sensor (WWS), facilitating the direct observation of atmospheric turbulence over 1,100 arcsec at 30 Hz. The experimental measurements agreed with the von Kármán turbulence model, further verified using a differential image motion monitor. Attached to an 80 cm telescope, our WWS enables clear turbulence profiling of three layers below an altitude of 750 m and high-resolution aberration-corrected imaging without additional deformable mirrors. The WWS also enables prediction of the evolution of turbulence dynamics within 33 ms using a convolutional recurrent neural network with wide-field measurements, leading to more accurate pre-compensation of turbulence-induced errors during free-space optical communication. Wide-field sensing of dynamic turbulence wavefronts provides new opportunities for studying the evolution of turbulence in the broad field of atmospheric optics.

Understanding the radio luminosity function of star-forming galaxies and its cosmological evolution

ABSTRACT We explore the redshift evolution of the radio luminosity function (RLF) of star-forming galaxies using galform, a semi-analytic model of galaxy formation and a dynamo model of the magnetic field evolving in a galaxy. Assuming energy equipartition between the magnetic field and cosmic rays, we derive the synchrotron luminosity of each sample galaxy. In a model where the turbulent speed is correlated with the star formation rate, the RLF is in fair agreement with observations in the redshift range 0 ≤ z ≤ 2. At larger redshifts, the structure of galaxies, their interstellar matter, and turbulence appear to be rather different from those at z ≲ 2, so that the turbulence and magnetic field models applicable at low redshifts become inadequate. The strong redshift evolution of the RLF at 0 ≤ z ≤ 2 can be attributed to an increased number, at high redshift, of galaxies with large disc volumes and strong magnetic fields. On the other hand, in models where the turbulent speed is a constant or an explicit function of z, the observed redshift evolution of the RLF is poorly captured. The evolution of the interstellar turbulence and outflow parameters appear to be major (but not the only) drivers of the RLF changes. We find that both the small- and large-scale magnetic fields contribute to the RLF but the small-scale field dominates at high redshifts. Polarization observations will therefore be important to distinguish these two components and understand better the evolution of galaxies and their non-thermal constituents.

Assessment of synthetic turbulence of stably stratified atmospheric boundary layers for LES

This work studies the evolution of turbulence in a Stable Boundary Layer (SBL) in Large-Eddy Simulations (LES) when a synthetic turbulence field of velocity and temperature is used as initial condition and as well as precursor. Following common approaches found in the literature, initial fields of different characteristics are created and their evolution in the LES is evaluated in order to assess the ability of the synthetically generated turbulence to represent a snapshot of SBL turbulence. The study is carried out with two modelling cases, a forested site as well as the GABLS benchmark [4]. In both cases, the usage of a turbulent SBL as an initial condition proved advantageous to reach a faster convergence presenting an opportunity for computational savings. Yet, the very different turbulence conditions of the modelling setups produce varying results with regard to the type of velocity and temperature fluctuations. Likewise, the usage of a precursor was shown able to represent the flow in a successor LES although with varying reliability, dependent on the background turbulence and the stratification level, that suppresses velocity fluctuations and could lead to the misrepresentation of turbulence level.

Optical turbulence profiling at the Table Mountain Facility with the Laser Communication Relay Demonstration GEO downlink

We report the first measurement of the atmospheric optical turbulence profile using the transmitted beam from a satellite laser communication terminal. A ring image next generation scintillation sensor (RINGSS) instrument for turbulence profiling, as described in Tokovinin [MNRAS 502, 747 (2021)10.1093/mnras/staa4049], was deployed at the NASA/Jet Propulsion Laboratory’s Table Mountain Facility (TMF) in California. The optical turbulence profile was measured with the downlink optical beam from the Laser Communication Relay Demonstration (LCRD) geostationary satellite. LCRD conducts links with the Optical Communication Telescope Laboratory ground station and the RINGSS instrument was co-located at TMF to conduct measurements. Turbulence profiles were measured at day and night and atmospheric coherence lengths were compared with other turbulence monitors such as a solar scintillometer and Polaris motion monitor. RINGSS sensitivity to boundary layer turbulence, a feature not provided by many profilers, is also shown to agree with a boundary layer scintillometer at TMF (R = 0.85). Diurnal evolution of optical turbulence and measured profiles are presented. The correlation of RINGSS with other turbulence monitors (R = 0.75 − 0.86) demonstrates the concept of free-space optical communications turbulence profiling, which could be adopted as a way to support optical ground stations in a future Geostationary feeder link network. These results also provide further evidence that RINGSS, a relatively new instrument concept, correlates well with other instruments in daytime and nighttime turbulence.

A mean flow velocity estimation scheme based on flow field characteristics and distribution point optimization for carbon monitoring in coal-fired power plants: A numerical study

CO2 online monitoring provides a method to obtain carbon emissions by directly quantifying the flue gas flow rate and CO2 concentration. However, significant flow rate measurement errors arise due to the complexity of turbulence in large-diameter stacks. To address the issue, this study utilizes turbulence numerical simulation combined with mean velocity estimation error analysis to investigate the flow field of typical stacks in coal-fired power plants. The simulation results demonstrated that the evolution of turbulence exaggerates velocities. The flow field exhibits stable turbulence characteristics in a single-introduced stack, while in the double-introduced stack, the flow field dynamically evolves due to asymmetric collisions and abrupt expansions. Furthermore, the effects of load and temperature on the estimation error of flow velocity are established. The optimum monitoring height, the ideal chord angle and the stepped number of deployment points based on the log-linear method are determined. Within the single-introduced stack, a correction factor is introduced and a corresponding formula is established that links estimation errors with monitoring heights. This resulted in a dramatic reduction of the maximum estimation error from 14% to 0.3%. Finally, the systematic and simplified optimization scheme for estimating mean flow velocity is summarised, which provides a powerful reference for flow rate measurement for online CO2 monitoring in coal-fired power plants.

Trailing vortex at drifting ship hull: a numerical study on wandering and turbulence

ABSTRACT Trailing vortices are commonly associated with so-called contrails in the sky. These show instability phenomena which manifest in transverse motions and sudden thickness changes. Aircraft aerodynamics considers this so-called far field whereas for naval hydrodynamics the near-field is of dominating interest. For the latter, vortices are intensively investigated at the propeller, but they emerge also at manoeuvring ship hulls or blunt stern shapes. And this is studied within the current paper: the major trailing vortex next to the KVLCC2 hull at large drift incidence. Numerical simulations with the SST-based IDDES model are conducted with OpenFOAM. The target is to reveal details of the vortex centre flow like the evolution of turbulence and the characteristics and consequences of vortex wandering. The results reveal a low-frequency broadband wandering motion next to a broad turbulent inertial subrange and that about two thirds of resolved TKE can be attributed to wandering.

Pickup Ion Modulation on Plateau-like Turbulence in the Martian Magnetosheath

The distribution of magnetic energy across scales, represented by the turbulence spectrum, provides insights into magnetic field dynamics in astrophysical and space plasma. While the Earth’s magnetosheath exhibits a conventional two-slope spectrum, the Martian magnetosheath often displays a prominent plateau-like spectrum. However, the underlying physical mechanism remains unresolved. Based on MAVEN observations, we present appealing evidence of pickup ions (PUIs) modulating the plateau-like spectrum through proton cyclotron waves (PCWs). PCWs, driven by unstable pickup H+ ion distributions, significantly influence the formation of plateau-like spectra. Both case and statistical studies suggest that the spectral evolution is affected by the relative abundance of pickup O+ ions. A substantial presence of pickup O+ ions can suppress PCWs driven by pickup H+ ions, resulting in a decline in the slope of the plateau spectrum. Particle-in-cell simulations confirm the role of PUI-modulated PCWs in the plateau-range energy injection. Our results provide new insight into the impact of PUIs on magnetic turbulence evolution and associated energy transfer processes in space and astrophysical plasma.

A novel attention enhanced deep neural network for hypersonic spatiotemporal turbulence prediction

High Reynolds number turbulent flow of hypersonic vehicles exhibits multi-scale flow structures and non-equilibrium high-frequency characteristics, presenting a significant challenge for accurate prediction. A deep neural network integrated with attention mechanism as a reduced order model for hypersonic turbulent flow is proposed, which is capable of capturing spatiotemporal characteristics from high-dimensional numerical turbulent data directly. The network model leverages encoder–decoder architecture where the encoder captures high-level semantic information of input flow field, Convolutional Long Short-Term Memory network learns low-dimensional characteristic evolution, and the decoder generates pixel-level multi-channel flow field information. Additionally, skip connection structure is introduced at the decoding stage to enhance feature fusion while incorporating Dual-Attention-Block that automatically adjusts weights to capture spatial imbalances in turbulence distribution. Through evaluating the time generalization ability, the neural network effectively learns the evolution of multi-scale high-frequency turbulence characteristics. It enables rapid prediction of high Reynolds number turbulence evolution over time with reasonable accuracy while maintaining excellent computational efficiency.

Evolution of the Interplanetary Turbulence and the Associated Turbulence Anisotropy in the Outer Heliosphere: VOYAGER 2 Observations

We study the radial evolution of the inertial-range solar wind plasma turbulence and its anisotropy in the outer heliosphere. We use magnetic field ( B ) measurements from the Voyager 2 spacecraft for heliocentric distances R from 1 to 33 au. We find that the perpendicular and trace power spectral densities (PSDs) of the magnetic field ( EB⊥ and EBTr ) still follow a Kolmogorov-like spectrum until 33 au. The parallel magnetic field PSD, EB∥ , transits from a power-law index of −2 to −5/3 as the distance crosses R ∼ 10 au. The PSD at frequencies 0.01 Hz < f < 0.2 Hz flattens at R > 20 au, gradually approaching an f −1 spectrum, probably due to instrument noise. At 0.002 Hz < f < 0.1 Hz, quasi-parallel propagation dominates at 1 au < R < 7 au, with quasi-perpendicular propagation gradually emerging at R > 5 au. For R > 7 au, oblique propagation becomes the primary mode of propagation. At smaller frequencies of f < 0.01 Hz, EB⊥ increases with propagation angle at 1 au < R < 5 au, and in contrast decreases with propagation angle at R > 5 au due to the enhanced power level at propagation angles smaller than 20°. Such enhancement may derive from the injection of wave energy from the pickup ion source into the background turbulent cascade, and the injected wave energy is transferred across scales without leaving local enhancements in EB⊥ or EBTr .

Nonlinear Wave Damping by Kelvin–Helmholtz Instability-induced Turbulence

Magnetohydrodynamic kink waves naturally form as a consequence of perturbations to a structured medium, for example, transverse oscillations of coronal loops. Linear theory has provided many insights into the evolution of linear oscillations, and results from these models are often applied to infer information about the solar corona from observed wave periods and damping times. However, simulations show that nonlinear kink waves can host the Kelvin–Helmholtz instability (KHI), which subsequently creates turbulence in the loop, dynamics that are beyond linear models. In this paper we investigate the evolution of KHI-induced turbulence on the surface of a flux tube where a nonlinear fundamental kink mode has been excited. We control our numerical experiment so that we induce the KHI without exciting resonant absorption. We find two stages in the KHI turbulence dynamics. In the first stage, we show that the classic model of a KHI turbulent layer growing at ∝t is applicable. We adapt this model to make accurate predictions of the damping of the oscillation and turbulent heating as a consequence of the KHI dynamics. In the second stage, the now dominant turbulent motions are undergoing decay. We find that the classic model of energy decay proportional to t −2 approximately holds and provides an accurate prediction of the heating in this phase. Our results show that we can develop simple models for the turbulent evolution of a nonlinear kink wave, but the damping profiles produced are distinct from those of linear theory that are commonly used to confront theory and observations.

Evolution of small-scale turbulence at large Richardson numbers

Abstract. The theory of stratified turbulent flow developed earlier by the authors is applied to data from different areas of the ocean. It is shown that turbulence can be amplified and supported even at large gradient Richardson numbers. The cause of that is the exchange between kinetic and potential energies of turbulence. Using the profiles of Brunt–Väisälä frequency and vertical current shear given in Forryan et al. (2013), the profiles of the kinetic energy dissipation rate are calculated. The results are in reasonable agreement with the experimental data.