Vertical Shear Of Horizontal Velocity Research Articles

Global Observations of Rotary-With-Depth Shear Spectra

Abstract Internal waves are predominantly generated by winds, tide/topography interactions and balanced flow/topography interactions. Observations of vertical shear of horizontal velocity (uz, vz) from LADCP profiles conducted during GO-SHIP hydrographic surveys, as well as vessel-mounted sonars, are used to interpret these signals. Vertical directionality of intermediate-wavenumber [λz ~ 𝒪(100 m)] internal waves is inferred in this study from rotary-with-depth shears. Total shear variance and vertical asymmetry ratio (Ω), i.e. the normalized difference between downward- and upward-propagating intermediate wavenumber shear variance, where Ω > 0 (< 0) indicates excess downgoing (upgoing) shear variance, are calculated for three depth ranges: 200-600 m, 600 m to 1000 mab (meters above bottom), and below 1000 mab. Globally, downgoing (clockwise-with-depth in the northern hemisphere) exceeds upgoing (counterclockwise-with-depth in the northern hemisphere) shear variance by 30% in the upper 600 m of the water column (corresponding to the globally averaged asymmetry ratio of = 0.13), with a near-equal distribution below 600-m depth ( ~ 0). Downgoing shear variance in the upper water column dominates at all latitudes. There is no statistically significant correlation between the global distribution of Ω and internal wave generation, pointing to an important role for processes that re-distribute energy within the internal wave continuum on wavelengths of 𝒪(100 m).

Horizontal and vertical spreading of dye in the coastal ocean of the northern Mid-Atlantic bight

The paper investigates the horizontal and vertical spreading of a neutrally-buoyant chemical tracer (rhodamine) that was released into the surface mixed layer in the coastal ocean. Rhodamine concentrations from the dye release experiment were combined with observations of water column properties and velocity measurements from the high-frequency radar (HFR) and ship-based ADCP in order to investigate and interpret the downward penetration of dye from the mixed layer into the stratified part of the water column and to quantify the horizontal diffusivity associated with the lateral dye spreading. Of the total amount of dye encountered during the 33-h long survey, 99% was observed within the mixed layer, suggesting that the downward penetration of dye from the mixed layer into the pycnocline is a slow process that occurs on the time scale of at least multiple days. The observed elevated dye concentrations below the mixed layer were always co-located with the elevated concentrations within the mixed layer. However, the distribution of dye below the mixed layer was patchy, and the below-mixed-layer dye concentrations were poorly correlated with those within the mixed layer. Combined with the absence of strong vertical shear of horizontal velocity across the base of the mixed layer, this suggests that the observed dye could have been ejected from the mixed layer earlier and at a different location, and then advected to the observed location by the horizontal currents below the mixed layer. The vertical diffusivity in the mixed layer is estimated to be approximately 7x10−4m2s, about two orders of magnitude larger than the diffusivity across the base of the mixed layer, which is 5x10−6m2s. Lateral spread of dye was found to be well represented by the HFR velocities (with roughly 2-km resolution) with the added small-scale turbulent diffusivity of 5 m2s.Plain Language Summary.The top part of the water column, called the surface mixed layer, is well mixed to a nearly uniform density. Below lays the pycnocline where density changes rapidly with depth. The exchange of water and properties between the mixed layer and pycnocline is an important but poorly understood oceanographic process and is the main subject of the current observational study. Specifically, this paper describes and interprets the initial 36 h of the vertical and horizontal spreading of a dye plume, released into the surface mixed layer of the coastal ocean south of Martha's Vineyard, MA. Our results indicated that the ejection and penetration of dye down from the mixed layer is a slow process that occurs over a time scales longer than multiple days. The episodic nature of the downward dye ejection from the mixed layer and the resulting patchy distribution of the subsurface dye is another important finding from this work, which has far-reaching implications for the parameterization of these small-scale vertical exchange processes in numerical models. The vertical diffusivity within the mixed layer (7x10−4m2s) is estimated to be about two orders of magnitude larger than the diffusivity across the base of the mixed layer (5x10−6m2s). Finally, the lateral spreading of the dye plume was found to be well represented by advection by the high-frequency-radar-based velocities with the added small-scale turbulent diffusivity of 5 m2s – the value that is in line with our prior estimates for this coastal region, but is larger than many prior estimates from different regions of the ocean.

Observing and quantifying ocean flow properties using drifters with drogues at different depths

AbstractThis paper presents analyses of drifters with drogues at different depths – 1, 10, 30, 50 m – that were deployed in the Mediterranean Sea to investigate frontal subduction and upwelling. Drifter trajectories were used to estimate divergence, vorticity, vertical velocity, and finite-size Lyapunov exponents (FTLEs), and to investigate the balance of terms in the vorticity equation. The divergence and vorticity are O(f) and change sign along trajectories. Vertical velocity is O(1 mm/s), increases with depth, indicates predominant upwelling with isolated downwelling events, and sometimes changes sign between 1 and 50 m. Vortex stretching is one of, but not the only, significant term in the vorticity balance. 2D FTLEs are 2 × 10−51/s after 1 day, twice larger than in a 400-m-resolution numerical model. 3D FTLEs are 50% larger than 2D FTLEs and are dominated by the vertical shear of horizontal velocity. Bootstrapping suggests uncertainty levels of ~10% of the time-mean absolute values for divergence and vorticity. Analysis of simulated drifters in a model suggests that drifter-based estimates of divergence and vorticity are close to the Eulerian model estimates, except when drifters get aligned into long filaments. Drifter-based vertical velocity is close to the Eulerian model estimates at 1 m but differs at deeper depths. The errors in the vertical velocity are largely due to the lateral separation between drifters at different depths, and partially due to only measuring at 4 depths. Overall, this paper demonstrates how drifters, heretofore restricted to 2D near-surface observations, can be used to learn about 3D flow properties throughout the upper layer of the water column.

Evolution of the Velocity Structure in the Diurnal Warm Layer

AbstractThe daily formation of near-surface ocean stratification caused by penetrating solar radiation modifies heat fluxes through the air–sea interface, turbulence dissipation in the mixed layer, and the vertical profile of lateral transport. The transport is altered because momentum from wind is trapped in a thin near-surface layer, the diurnal warm layer. We investigate the dynamics of this layer, with particular attention to the vertical shear of horizontal velocity. We first develop a quantitative link between the near-surface shear components that relates the crosswind component to the inertial turning of the along-wind component. Three days of high-resolution velocity observations confirm this relation. Clear colocation of shear and stratification with Richardson numbers near 0.25 indicate marginal instability. Idealized numerical modeling is then invoked to extrapolate below the observed wind speeds. This modeling, together with a simple energetic scaling analysis, provides a rule of thumb that the diurnal shear evolves differently above and below a 2 m s−1 wind speed, with limited sensitivity of this threshold to latitude and mean net surface heat flux. Only above this wind speed is the energy input sufficient to overcome the stabilizing buoyancy flux and thereby induce marginal instability. The differing shear regimes explain differences in the timing and magnitude of diurnal sea surface temperature anomalies.

Formation of interleaving layers in the Bay of Bengal

Observations of the upper 200 m of the strongly stratified Bay of Bengal reveal a host of interleaving layers of watermass properties. The features appear as isopycnal spice anomalies and form multiple, parallel, ∼10 m thin layers, that are coherent over horizontal scales of 30–80 km. They are coincident with anomalies in density stratification and in some cases, with the vertical shear of horizontal velocity, but are not aligned with isopycnals. The cross-isopycnal slopes of these prominent features are O(10−4) and are, on average, 5 to 10 times smaller than the expected slopes of passive tracer anomalies due to mesoscale stirring. We present two alternate mechanisms by which such interleaving layers can be created from existing lateral spice gradients: (i) stirring by vertically sheared submesoscale eddies, and (ii) near-inertial wave shear. A numerical simulation of a density (and spice) front, based on observations of a narrow and fast jet, develops a submesoscale vortex that produces spice layering similar to our observations. The layering suggests that even a weak vertical diffusivity would greatly enhance the horizontal mixing of spice at submesoscales, the scales of the proposed processes, through shear dispersion. The analysis of the observations draws attention to the prevalence of submesoscale dynamics and NIWs with unusually high vertical wavenumbers in the Bay of Bengal.

Temporal and spatial characteristics of potential energy anomaly in Lake Taihu.

In this study, water temperature and meteorological data in Lake Taihu from June 11 to July 6, 2013, are collected to calibrate and verify the unstructured grid finite-volume community ocean model (FVCOM) coupled with a heat exchange module. The spatial and temporal variations of potential energy anomalies (PEA) in the lake, simulated by the calibrated FVCOM, are analyzed to explore the stratification and de-stratification processes in water body. The temporal variation of PEA primarily follows the diurnal cycles of solar radiation, while the spatial heterogeneity of PEA is jointly determined by solar radiation and vertical shear of horizontal velocity coupled with the topography of the lake. The maxima of PEA in the lake are not greater than 4J/m3 in the summer and even smaller along shore regions and near the Pingtaishan station. This study is helpful to improve understanding of the effect of physical processes on the algae bloom in Lake Taihu.

Mesoscale mixing of the Denmark Strait Overflow in the Irminger Basin

The Denmark Strait Overflow (DSO) is a major export route for dense waters from the Nordic Seas forming the lower limb of the Atlantic Meridional Overturning Circulation, an important element of the climate system. Mixing processes along the DSO pathway influence its volume transport and properties contributing to the variability of the deep overturning circulation. They are poorly sampled by observations, however, which hinders development of a proper DSO representation in global circulation models. We employ a high resolution regional ocean model of the Irminger Basin to quantify impact of the mesoscale flows on DSO mixing focusing on geographical localization and the time–modulation of water property changes. The model reproduces the observed bulk warming of the DSO plume 100–200 km downstream of the Denmark Strait sill. It also reveals that mesoscale variability of the overflow (‘DSO-eddies’, of 20–30 km extent and a time scale of 2–5 day) modulates water property changes and turbulent mixing, diagnosed with the vertical shear of horizontal velocity and the eddy heat flux divergence. The space–time localization of the DSO mixing and warming and the role of coherent mesoscale structures should be explored by turbulence measurements and factored into the coarse circulation models.

The nonlinear nature of barotropic currents in oceans

The structure of the barotropic component of oceanic currents is discussed. First, we present observational evidence against the absence of the vertical shear of horizontal velocity in barotropic flows. We then discuss the Taylor-Proudman theorem, which we base our presumption on. We show that this theorem crudely neglects nonlinear terms of fluid motion equations either through geostrophic approximation or directly through a scale analysis of the vorticity transport equation. However, these terms serve as a mechanism allowing for the vertical shear of horizontal velocity.

Dynamics of stratified turbulence decaying from a high buoyancy Reynolds number

We present direct numerical simulations (DNS) of unforced stratified turbulence with the objective of testing the strongly stratified turbulence theory. According to this theory the characteristic vertical scale of the turbulence is given by $\ell _{v}\sim u_{h}/N$, where $u_{h}$ is the horizontal velocity scale and $N$ the Brunt–Väisälä frequency. Combined with the hypothesis of the energy dissipation rate scaling as ${\it\epsilon}\sim u_{h}^{3}/\ell _{h}$, this theory predicts inertial range scalings for the horizontal spectrum of horizontal kinetic energy and of potential energy, according to $E(k_{h})\propto k_{h}^{-5/3}$. We begin by presenting a scaling analysis of the horizontal vorticity equation from which we recover the result regarding the vertical scale, $\ell _{v}\sim u_{h}/N$, highlighting in the process the important dynamical role of large-scale vertical shear of horizontal velocity. We then present the results from decaying DNS, which show a good agreement with aspects of the theory. In particular, the vertical Froude number is found to reach a constant plateau in time, of the form $Fr_{v}=u_{h}/(N\ell _{v})=C$ with $C=O(1)$ in all the runs. The derivation of the dissipation scaling ${\it\epsilon}\sim u_{h}^{3}/\ell _{h}$ at low Reynolds number in the context of decaying stratified turbulence highlights that the same scaling holds at high $\mathscr{R}=ReFr_{h}^{2}\gg 1$ as well as at low $\mathscr{R}\ll 1$, which is known (see Brethouwer et al., J. Fluid Mech., vol. 585, 2007, pp. 343–368) but not sufficiently emphasized in recent literature. We find evidence in our DNS of the dissipation scaling holding at $\mathscr{R}=O(1)$, which we interpret as being in the viscous regime. We also find ${\it\epsilon}_{k}\sim u_{h}^{3}/\ell _{h}$ and ${\it\epsilon}_{p}\sim u_{h}^{3}/\ell _{h}$ (with ${\it\epsilon}={\it\epsilon}_{k}+{\it\epsilon}_{p}$), in our high-resolution run at earlier times corresponding to $\mathscr{R}=O(10)$, which is in the transition between the strongly stratified and the viscous regimes. The horizontal spectrum of horizontal kinetic energy collapses in time using the scaling $E_{h}(k_{h})=C_{1}{\it\epsilon}_{k}^{2/3}k_{h}^{-5/3}$ and the horizontal potential energy spectrum is well described by $E_{p}(k_{h})=C_{2}{\it\epsilon}_{p}{\it\epsilon}_{k}^{-1/3}k_{h}^{-5/3}$. The presence of an inertial range in the horizontal direction is confirmed by the constancy of the energy flux spectrum over narrow ranges of $k_{h}$. However, the vertical energy spectrum is found to differ significantly from the expected $E_{h}(k_{v})\sim N^{2}k_{v}^{-3}$ scaling, showing that $Fr_{v}$ is not of order unity on a scale-by-scale basis, thus providing motivation for further investigation of the vertical structure of stratified turbulence.

Eddies in the Red Sea: A statistical and dynamical study

AbstractSea level anomaly (SLA) data spanning 1992–2012 were analyzed to study the statistical properties of eddies in the Red Sea. An algorithm that identifies winding angles was employed to detect 4998 eddies propagating along 938 unique eddy tracks. Statistics suggest that eddies are generated across the entire Red Sea but that they are prevalent in certain regions. A high number of eddies is found in the central basin between 18°N and 24°N. More than 87% of the detected eddies have a radius ranging from 50 to 135 km. Both the intensity and relative vorticity scale of these eddies decrease as the eddy radii increase. The averaged eddy lifespan is approximately 6 weeks. AEs and cyclonic eddies (CEs) have different deformation features, and those with stronger intensities are less deformed and more circular. Analysis of long‐lived eddies suggests that they are likely to appear in the central basin with AEs tending to move northward. In addition, their eddy kinetic energy (EKE) increases gradually throughout their lifespans. The annual cycles of CEs and AEs differ, although both exhibit significant seasonal cycles of intensity with the winter and summer peaks appearing in February and August, respectively. The seasonal cycle of EKE is negatively correlated with stratification but positively correlated with vertical shear of horizontal velocity and eddy growth rate, suggesting that the generation of baroclinic instability is responsible for the activities of eddies in the Red Sea.

Estimates of the turbulent kinetic energy budget in the oceanic convective boundary layer

The terms of the steady-state turbulent kinetic energy (TKE) budget in the oceanic convective boundary layer (CBL) are estimated by use of microstructure data obtained over the continental shelf of the East China Sea. The dissipation term is calculated from the micro-scale vertical shear of horizontal velocity measured directly using a freely-falling microstructure profiler, whereas the buoyancy flux and shear production terms are estimated indirectly by integrating vertically the one-dimensional conservation equation of density and by applying similarity theory, respectively. The transport term, calculated as the residual of the other three terms, vertically redistributes the TKE from the upper half of the CBL to the lower half, consistent with the TKE budgets in the atmospheric CBL and in shear-free and slightly-sheared CBLs simulated by large eddy-simulation models. The relatively large contribution of the transport term to the TKE budget shows that a local equilibrium form of the TKE equation is not appropriate for the TKE budget in the oceanic CBL.

Assessing shelf mixing using CTD, ADCP, and free falling shear probe turbulence data

CTD, ADCP and free-falling microstructure profiler data from Thermaikos Gulf of Northern Aegean Sea in Greece are analyzed in order to (a) gain an insight in the vertical diffusion processes of the area and (b) compare the methods of vertical diffusivity assessment based on microstructure profiler shear data and on potential density overturns. The analysis reveals the presence of mixing events at the top mixed layer as well as above the upper thermocline boundary. It is consistent with a notable change in the susceptibility of the water column to turbulent events, within a month's period as well as convective instability possibly related to riverine discharge. The comparison of the profiles of vertical shear of horizontal velocity and of density presumes isotropy of the turbulent field.

Observations of the structure of turbulent mixing across the Kuroshio

The mean structure of turbulence intensity across the Kuroshio in spring is presented by compositing microstructure profiles on a stream coordinate. The composite mean of turbulent energy dissipation rate was high near fronts on both cyclonic and anticyclonic sides. On the cyclonic side, > 10−8 W kg−1 (vertical diffusivity of > 3 × 10−5 m2 s−1) was observed in the region of strong vertical shear of geostrophic velocity. Depth‐averaged within the depth range 50–150 m (150–250 m) was significantly higher at 0 to 50 km (−25 to 50 km) compared with >50 km from the axis. Although lower than on the cyclonic side, at depths of 50–150 m on the anticyclonic side near the front was again enhanced. On this side, the total vertical shear of horizontal velocity was strong, whereas the geostrophic shear was weak.

Effects of vertical mixing parameterization on the mixed layer depth over the North Pacific in a global OGCM

We present MLD variability over the North Pacific Ocean in a global ocean general circulation model and impacts of three different vertical mixing schemes on it, based on statistical measures (annual mean difference, root-mean-square difference and correlation coefficient). The constant vertical mixing scheme tends to underestimate MLD over the whole basin. The Pacanowski-Philander scheme tends to overestimate MLD (> 20 m) in the mid- to high latitude during summer, implying that vertical mixing in the mid- to high latitude may not be represented properly by simple internal mixing mechanisms such as stratification or vertical shear of horizontal velocity. On the other hand, the new vertical mixing scheme (Noh et al. 2002) gives the most consistent MLD and its seasonal and spatial variability when compared with observation. These results suggest that parameterization of vertical mixing has significant effects on simulation of the seasonal and spatial variability of MLD over the North Pacific Ocean.

Temporal and spatial variability of vertical salt flux in a highly stratified estuary

The temporal and spatial variability of vertical salt flux in the Fraser River Estuary, British Columbia, was investigated observationally, using several different direct and indirect indicators of buoyancy flux. Data were collected from the estuary using shipboard instrumentation, primarily an acoustic Doppler current profiler and a towed conductivity‐temperature‐depth unit. Direct estimates of buoyancy flux were made from along‐channel control volume analyses and from measurements of overturn scales. The spatial and temporal evolution of the salt wedge structure through a tidal cycle was evaluated using the results of these buoyancy flux calculations, as well as gradient Richardson number, Froude number, and stratification profiles. Observations indicate that buoyancy flux is driven primarily by interfacial stress, and not bottom stress, as is common in many estuaries. Vertical salt flux, as opposed to seaward advection of high‐salinity fluid, was found to be the dominant mechanism responsible for removal of salt from the estuarine channel during each daily tidal cycle. Buoyancy flux was highly variable in time and space, however, with vertical salt flux during ebb tides on the order of 2 to 3 times greater than that estimated during floods. This is due to an increase in the vertical shear of horizontal velocity and a sharp increase in stratification, which was observed during early ebb. Enhanced mixing was observed spatially within a region dominated by a channel constriction in which the channel narrows by approximately 25%.

A Study of Richardson Number and Instability in Moist Saturated Flow

AbstractIn this paper, we derived the Ri equations in dry and moist saturated atmosphere. A rainfall case which occurred in Northern China is numerically simulated, and the model output data is used to calculate and analyze comparatively the terms of Ri equations in dry air and moist saturated flow. The analysis shows that the vertical shear of horizontal velocity dominates the influence on Ri change and instability in dry process, whereas in moist case, the influence of numerator of Ri (i.e., Brunt‐Vaisala Frequency, named as BVF) on Ri change and instability can reach up to the same magnitude order as the denominator of Ri.Since BVF has very important influence on instability in moist case, we look for the expression of BVF which is more appropriate for the real moist case. Thus Ri is modified, so that we can estimate instability in moist process. It is found that, due to considering the virtual temperature effect and the change of total water mixing ratio (i.e., part liquid water is dropped out the parcel), the stability in rainy region is effectively decreased. Therefore, the modified moist Ri formula may be more appropriate to diagnose the instability in rainy region.

Global mapping of diapycnal diffusivity in the deep ocean based on the results of expendable current profiler (XCP) surveys

Based on the results of the extensive XCP surveys in the North Pacific, we first examine the empirical relationship between the estimated diapycnal diffusivity in the thermocline and the numerically predicted, available energy density of the semidiurnal internal tide (major energy source for diapycnal diffusivity) at each location. The diapycnal diffusivity is estimated by applying the parameterization of Gregg (1989) to the fine‐scale vertical shear of horizontal velocity measured by XCP. Next, the numerically predicted energy density of the semidiurnal internal tide at each longitude and latitude in the world's oceans is incorporated into the resulting empirical relationship to obtain the global distribution of diapycnal diffusivity in the thermocline. This model predicts that strong diapycnal mixing (mixing hotspot) is limited to the prominent topographic features at latitudes between 20° and 30°.

Physical oceanographic conditions during GasEx‐2001

GasEx‐2001 is a study of air‐sea gas exchange in a region of CO2 outgassing. The bulk of the experiment followed a drifting array of near‐surface instruments deployed during the second half of February 2001 just south of the equator in the central Pacific Ocean. Physical oceanographic conditions including local currents, the seasonal cycle, Kelvin waves, and tropical instability waves are described using shipboard data and a variety of other data sources to set the large‐scale oceanographic context for GasEx‐2001. Local physical oceanographic conditions during GasEx‐2001 are then analyzed using shipboard data and a simple one‐dimensional mixed layer model. The thermocline shoals about 13 m over the 15‐day experiment, implying an upwelling rate of 1 × 10−5 m s−1. Zonal velocity is surface‐intensified and westward, with vertical shear mostly through the thermocline. Meridional velocity is also strongly sheared with a maximum equatorward flow in the thermocline that is much reduced by 17‐m depth. The mixed layer model exhibits more near‐surface warming over the course of the experiment than is observed. Prescribing upwelling in the model closes the heat budget within error estimates. Entrainment at the base of the mixed layer plays a limited role in the mixed layer budgets of carbon and other water properties. Vertical shear of horizontal velocity within the mixed layer and slippage of the array through the surface water also have small (but uncertain) roles in these budgets.

Latitudinal dependence of diapycnal diffusivity in the thermocline estimated using a finescale parameterization

The spatial distribution of diapycnal diffusivity in the thermocline over a large area in the interior of the North Pacific is obtained by incorporating the finescale vertical shear of horizontal velocity measured by expendable current profilers into the empirical formula proposed by Gregg [1989]. It is clearly shown that diapycnal diffusivity in the North Pacific strongly depends on the latitude. For example, the estimated diapycnal diffusivities near the Hawaiian Ridge and the Izu‐Ogasawara Ridge exceed 10−4 m2 s−1, whereas those near the Aleutian Ridge and the Emperor Seamounts are of the order of 0.1 × 10−4 m2 s−1, even though the available semidiurnal internal tidal energy is similar among all of these prominent topographic features. The observed results are consistent with the numerical prediction that the cascade of internal tidal energy down to dissipation scales is dominated by parametric subharmonic instability which is expected to occur only below 30°N.

Comparison of methods of estimating mean synoptic current structure in “stream coordinates” reference frames with an example from the Antarctic Circumpolar Current

Stream coordinates techniques, that is, methods of deriving the mean “synoptic” structures of narrow meandering ocean currents from Eulerian measurements, have been in use for nearly two decades and have resulted in improvements in our understanding of the dynamics and transports of such currents. A 2-year experiment in the Sub-Antarctic Front (SAF) southwest of Tasmania, involving overlapping arrays of inverted echo sounders and horizontal electric field recorders, has provided an opportunity to test various stream coordinates methods. The methods differ significantly in how well, or even if, they can reveal divergence or convergence of the meandering current, and whether they accurately reproduce the current's horizontal structure and transport. Cross-stream distance was determined either via a frozen-field assumption or as the distance to an optimally interpolated (OI) origin contour; downstream direction was determined either as the local direction which maximized the vertical shear of horizontal velocity or as the tangent line to the OI mapped core contour. All combinations of these distance and direction definitions were tested. The use of a frozen field assumption in determining cross-stream distance yields overly smooth along-stream velocity cross-sections and overestimated transports. The vertical shear definition of downstream direction results in a false rotation of cross-stream flows into along-stream flows near the flanks of the current. The preferred methods define the horizontal location of the front with 2-D arrays of instruments (e.g., inverted echo sounders or moored current meters). Methods employing the assumptions of a meandering “frozen-field” baroclinic structure or the use of the local vertical shear of the horizontal velocity to determine the downstream direction should be avoided, if possible, particularly in the SAF.