Horizontal Eddies Research Articles

The Vertical Structure of Turbulence Kinetic Energy Near the Arctic Sea‐Ice Surface

AbstractAtmospheric turbulence over the Arctic sea‐ice surface has been understudied due to the lack of observational data. In this study, we focus on the turbulence kinetic energy (TKE) over sea ice and distinguish its two different vertical structures, the “Surface” type and the “Elevated” type, using observations during the Multidisciplinary drifting Observatory for the Study of Arctic Climate expedition (MOSAiC). The “Surface” type has the maximum TKE near the surface (at 2 m), while the “Elevated” type has the maximum TKE at a higher level (6 m). The TKE budget analysis indicates that the “Elevated” type is caused by the increased shear production of TKE at 6 m. In addition, spectral analysis reveals that the contribution to TKE by horizontal large eddies is enhanced in the “Elevated” type. Finally, how the vertical structure of TKE affects the parameterization of turbulent momentum flux is discussed.

Wave-driven current and vortex patterns at an open beach: Insights from phase-resolving numerical computations and Lagrangian measurements

Wave-driven currents have a substantial impact on local circulation patterns in and across the surf zone, and are responsible for cross-shore and longshore exchange of mass and momentum over a broad range of spatial and temporal scales. Nearshore currents may drive sediment transport, lead to beach erosion, and also affect the spread of bacteria and other marine microorganisms, as well as the distribution of pollutants such as chemicals and microplastics. In addition, surf zone currents can cause hazardous conditions for beach-goers in the form of rip currents.It is known from previous work (Chen et al., 2003; Feddersen et al., 2011; Hally-Rosendahl and Feddersen, 2016) that Boussinesq-type models in combination with appropriate boundary conditions and wave breaking capabilities can function as powerful tools for the analysis of circulation patterns in the surf zone. In the present work, data from a recent field campaign reported on in Bjørnestad et al. (2021) are used to further validate the capability of Boussinesq systems to simulate nearshore dynamics.The numerical model is then used to study the influence of tidal elevation, peak direction and directional spread of the incoming wavefield on the quantity, extent, and circulatory magnitude of the nearshore circulation. In addition, fundamental features such as horizontal eddies are investigated, and comparisons are made to solid-body rotation and irrotational vortices.Overall, it is observed that local variations in the bathymetry across the surf zone are the controlling factor regarding the size of these circulations, and an increasing tidal level, which can be seen as a uniform offset to the bathymetry, favors the generation of larger vortex patterns. For a given tidal stage, the directional spread of the incoming wavefield has the most pronounced influence on the size and strength of the nearshore eddies while the peak direction has the strongest effect on the total number of circulations.

THE ROLE OF BOTTOM MESO-SCALE DYNAMICS IN CONTOURITE FORMATION IN THE ARGENTINE BASIN

The Argentine Basin is a deep-sea basin located in the South Atlantic Ocean that contains sedimentary deposits derived from different provenances. It is characterized by complex ocean dynamics encompassing diverse spatial and temporal dimensions. The northward subantarctic Malvinas Current and southward subtropical Brazil Current converge at the western margin of the Argentine Basin, resulting in the formation of the Brazil-Malvinas Confluence. Bottom currents, particularly currents flowing alongslope and horizontal eddies, are crucial in shaping the seafloor and in the formation of sedimentary features (e.g. contourites). The poorly understood strength and variability of bottom currents leave the processes that control sedimentation in deep environments unclear. High-resolution (1/12°) reanalysis was used to analyze near-bottom flows and bottom dynamics were compared with seafloor sedimentary characteristics obtained from geophysical datasets and sediment cores. High speeds, up to 3.5 m/s at the surfa ce and up to 1.4 m/s at the bottom, reveal the presence of intense flows in this area. The Zapiola Drift, an approx. 1,200 m high sedimentary deposit located in the central part of the Argentine Basin, is bounded by a zone of high bottom eddy kinetic energy (EKE) that resulted in the erosion of the seafloor and in the accumulation of sandy mud. The Malvinas Current is distinguished by strong and constant currents flowing northwards along the continental slope and by minimal EKE at the bottom. The area of the continental slope along which the Malvinas Current flows corresponds to a contourite terrace, a relatively flat surface composed almost entirely of sandy sediments and with abundant erosional features. The regions of highest EKE activity in the bottom layer is the overshoot of the Brazil-Malvinas Confluence and the Abyssal Plain. Our study highlights the impact of bottom current dynamics on contouritic sedimentation. In some regions, sedimentation is influenced by sporadic processes that occur between intense and weak flow events over time, which are considered intermittent processes. While sedimentation in other areas is controlled by constant flows. A better understanding of the strength and variability of bottom currents will improve paleoceanographic reconstructions based on the sedimentary record.

Wave Breaking Eddies And Transient Rip Current Dynamics In Large-Scale Wave Basin Experiments

Rip currents transport contaminants, nutrients, larvae, and, unfortunately, occasionally even swimmers between the surf zone and inner shelf. Transient rip currents are ephemeral ejections associated with surfzone eddies that are ubiquitous even on alongshore-uniform beaches. During directionally spread wave conditions, depth-limited breaking along finite-length regions, known as short-crested breaking, leads to spatial variation in the breaking force and corresponding vertical vorticity input to the water column. An inverse energy cascade from the injected vorticity may result in larger scale horizontal surfzone eddies, consistent with two-dimensional turbulence. These large-scale eddies enhance dispersion within the surf zone and may mutually advect offshore as a transient rip current. While this hypothesis is widely discussed in the literature, we do not have strong observational evidence for the processes connecting the wave field to the formation of large-scale horizontal eddies. To overcome the challenges of isolating and measuring the processes leading to transient rip currents in the field, we examined these processes in large-scale laboratory experiments.

Role of three-dimensional vortex motions on horizontal eddies in an open-channel cavity

Lateral cavities are a popular object of study in hydraulic research as they are widely found in rivers and hydraulic facilities and significantly impact flow patterns, sediment transport, and water quality in aquatic ecosystems. While the effects of open-channel cavities on various aspects including characteristics of three-dimensional structures have been extensively studied, the role of vertical flow structures in the cavity has not been focused on. This study examines the relationship between the shallowness parameter and the three-dimensional flow effects on the dynamics of an open-channel lateral cavity flow with horizontal vortex motion, comparing the conventional two-dimensional model (2DC), advanced depth-integrated models including general bottom velocity calculation method (GBVC) with the ability to consider vertical flow structures, simplified bottom velocity calculation method with the shallow water assumption (SBVC), a three-dimensional model (3DC), and experimental data. The comparison results demonstrate that the three-dimensional flow effect significantly impacts the velocity distribution and vortex evolution in the cavity. The GBVC model demonstrates a good agreement with the flow patterns by the 3DC model and experimental results in the cavity, whereas the 2DC and SBVC models are unsuitable for deep-water conditions.

Two-dimensional inverse energy cascade in a laboratory surf zone for varying wave directional spread

Surfzone eddies enhance the dispersion and transport of contaminants, bacteria, and larvae across the nearshore, altering coastal water quality and ecosystem health. During directionally spread wave conditions, vertical vortices (horizontal eddies) are injected near the ends of breaking crests. Energy associated with these eddies may be transferred to larger-scale, low-frequency rotational motions through an inverse energy cascade, consistent with two-dimensional turbulence. However, our understanding of the relationships between the wave conditions and the dynamics and energetics of low-frequency surfzone eddies are largely based on numerical modeling. Here, we test these relationships with remotely sensed and in situ observations from large-scale directional wave basin experiments with varying wave conditions over alongshore-uniform barred bathymetry. Surface velocities derived with particle image velocimetry were employed to assess the spatial scales of low-frequency surfzone eddies and compute structure functions with alongshore velocities. Second-order structure functions for directionally spread waves (σθ≥10°) are consistent with energy flux to larger or smaller length scales, while normally incident, unidirectional waves do not display this behavior. Third-order structure functions suggest that the surfzone flows exhibit a bidirectional energy cascade—a direct cascade to smaller and inverse cascade to larger length scales—during large directional spreads waves (σθ≥18°). However, there is not decisive evidence of an inverse energy cascade for moderate directional spreads (σθ=10°). Energy flux varies by cross-shore location and increases with increasing directional spread and wave height. Eddy decorrelation length scales weakly depend on wave directional spread. These findings advance our understanding of the dynamics linking wave breaking to large-scale rotational motions that enhance mixing and lead to rip currents, important conduits for cross-shore material exchange.

Observations of two-dimensional turbulence in the surfzone

Low-frequency, many-minute-period horizontal surfzone eddies are an important mechanism for the dispersion of material, transporting larvae, pollutants, sediment, and swimmers both across and along the nearshore. Previous numerical, laboratory, and field observations on alongshore uniform bathymetry with no or roughly uniform mean background flows suggest that the low-frequency eddies may be the result of a two-dimensional inverse energy cascade that transfers energy from relatively small spatial-scale vorticity injected by depth limited breaking waves to larger and larger spatial scales. Here, using remotely sensed high-spatial resolution estimates of currents, those results are extended to surfzones with strong complex mean circulation patterns [flows O(1 m/s)] owing to nonuniform bathymetry. Similar to previous results, wavenumber spectra and second-order structure functions calculated from the observations are consistent with a two-dimensional inverse energy cascade. The size of the largest eddies is shown to depend on the surfzone width and the spatial scales of the mean currents. Third-order structure functions also are consistent with an inverse cascade for spatial scales greater than ∼50 m. At smaller scales, the third-order structure functions suggest a mixture of inverse and forward cascades.

Experimental and numerical assessment of hydraulic characteristic of a new semi-frustum weir in the pool-weir fishway

The characteristics of the flow in pool-weir fishways is highly dependent on the geometry of the weir. This study proposed a new semi-frustum weir to the pool-weir fishway for the first time, the hydraulic performances of which was investigated by using both experimental and numerical methods. The lab experiments were performed on a flume with four weirs set on flume's bed at an equal spacing of 0.15 m, three-dimensional velocities were measured in almost the whole surface and at three levels of pool 2 under flow rates ranging from 25 to 45 L/s. Subsequently, a three-dimensional numerical simulation of the flow was conducted using the experimental data obtained to calibrate a significant model based on the finite volume method, including the Reynolds-averaged Navier-Stokes (RANS) equations coupled with the standard k-ε turbulence model and a VOF free-surface elevation method. Both the measured and simulated results show that the semi-frustum weir is effective in smoothing flow and dissipating water energy, and there exist two different flow regions in the flow: a direct flow region characterized by maximum velocities, and a recirculation region defined by low velocities and horizontal eddies. Moreover, the sensitivity of flow velocities and turbulences with bed slope, R/r (top radius/base radius) and pool spacing at invariant flow rate of 35 L/s, were evaluated with respect to velocity and turbulent kinetic energy, respectively. The fishway is found to perform better with a smaller bed slope and radius ratio, but with a larger pool spacing. Though the proposed semi-frustum weir in the pool-weir fishway is believed to provide suitable flow conditions for the upstream-moving of the fish at prescribed discharge and bed slope, more simulations are needed to be conducted on this kind of fishway with turning pools included to extend the fishway's application.

Exchange of water and contaminants between the Strait of Istanbul and the Golden Horn

The Golden Horn (Estuary) is a hotspot for marine pollution because of its close proximity to the Strait of Istanbul (Strait) with dense maritime traffic and high pollution risk of oil spill. Transport and fate of water and contaminants in Strait and Estuary are analyzed by three-dimensional numerical models. Eddies forming at the Golden Horn junction (Junction), either on a single layer or distributed over the entire water column, block the water exchange partly or entirely across the Junction. In case of an oil spill in adjacent waters, the size and distribution of eddies at Junction control the transport and fate of contaminants inside Estuary. Using twenty test cases, the exchange flows at Junction are classified in four types based on sea level difference between north and south boundaries of Strait and Reynolds number of surface flow. Eddies may prevent the natural water exchange between Strait and Estuary but also block the contaminants penetrating to Estuary. Under predominant conditions of mild and moderate southward net flow in Strait, surface waters enter Estuary. During very strong southward flow, Junction is blocked to Black Sea water and surface contaminants. Strait hydrodynamics control water exchange with Estuary through eddy formation. When horizontal eddies are formed at Junction, their size and distribution control the transport and fate of contaminants in branching inlets and estuaries by blocking the water exchange either entirely or partly in specific layers.

Statistics of single and multiple floaters in experiments of surface wave turbulence

We present laboratory experiments of surface wave turbulence excited by paddles in the deep water regime. The free surface is seeded with buoyant particles that are advected and dispersed by the flow. Positions and velocities of the floaters are measured using particle tracking velocimetry. We study the statistics of velocity and acceleration of the particles, mean vertical displacements, single-particle horizontal dispersion, and the phenomenon of preferential concentration. Using a simple model together with the experimental data, we show that the time evolution of the particles has three characteristic processes that dominate the dynamics at different times: drag by surface waves at early times, trapping by horizontal eddies at intermediate times, and advection by a large-scale mean circulation at late times.

Turbulence decay in the density-stratified intracluster medium

Abstract Turbulence evolution in a density-stratified medium differs from that of homogeneous isotropic turbulence described by the Kolmogorov picture. We evaluate the degree of this effect in the intracluster medium (ICM) with hydrodynamical simulations. We find that the buoyancy effect induced by ICM density stratification introduces qualitative changes to the turbulence energy evolution, morphology, and the density fluctuation–turbulence Mach number relation, and likely explains the radial dependence of the ICM turbulence amplitude as found previously in cosmological simulations. A new channel of energy flow between the kinetic and the potential energy is opened up by buoyancy. When the gravitational potential is kept constant with time, this energy flow leaves oscillations to the energy evolution, and leads to a balanced state of the two energies where both asymptote to power-law time evolution with slopes shallower than that for the turbulence kinetic energy of homogeneous isotropic turbulence. We discuss that the energy evolution can differ more significantly from that of homogeneous isotropic turbulence when there is a time variation of the gravitational potential. Morphologically, ICM turbulence can show a layered vertical structure and large horizontal vortical eddies in the central regions with the greatest density stratification. In addition, we find that the coefficient in the linear density fluctuation–turbulence Mach number relation caused by density stratification is in general a variable with position and time.

The suppression of surfzone cross‐shore mixing by alongshore currents

AbstractMixing by horizontal surfzone eddies is important to the cross‐shore exchange of material through the surfzone. Surfzone cross‐shore mixing for normally and obliquely incident waves, with very similar incident significant wave heights and directional spreads, is quantified using Boussinesq modeled drifter trajectories. For t < 100 s, surfzone cross‐shore diffusivities K(t) are independent of incident wave angle owing to similar eddy velocities m s−1. For 600 < t < 10,000 s, K(t) is maximum for normally incident waves and decreases with incident wave angle. Thus, the mixing parameterization is not completely applicable to the surfzone, because and LE do not change for these experiments. Reduced mixing for obliquely incident waves results from large eddies (wavelengths >200 m) propagating at a velocity C different than the mean current velocity V(x)—the same mechanism that reduces mixing for mesoscale eddies.

Spatial and Temporal Growth of Perturbations in Open-Channel Viscous Transverse Shear Flow

AbstractThe comparison between spatial and temporal growth of perturbations in a shear layer is revisited for the case of a viscous open-channel flow with velocity inflection. Turbulence is characterized by two distinct scales: a subdepth turbulence associated with the bed shear stress and a large-scale turbulence associated with the large horizontal eddies that develop in the shear layer. Temporal and spatial linear stability analyses are performed. The base flow is assumed to be affected only by the subdepth scale turbulence. Therefore, the base flow represents not the average flow but the flow completely free of the effect of the instability of the shear layer. Temporal and spatial approaches present less discrepancy in the viscous than in the previously analyzed in-viscous case. In particular, the phase velocity was found to be strongly correlated to the frequency in both the temporal and spatial approaches.

Bathymetric controls on very low frequency rip current motions

McCarroll, R.J.; Brander, R.W., and Turner, I.L., 2016. Bathymetric controls on very low frequency rip current motions. In: Vila-Concejo, A.; Bruce, E.; Kennedy, D.M., and McCarroll, R.J. (eds.), Proceedings of the 14th International Coastal Symposium (Sydney, Australia). Journal of Coastal Research, Special Issue, No. 75, pp. 418-422. Coconut Creek (Florida), ISSN 0749-0208.Time-averaged mean rip currents are forced by persistent gradients in dissipation over shallow bars and deep rip channels. Time-variable horizontal surfzone eddies, at the ∼10 min or very low frequency (VLF) range, are forced by stochastic wave breaking injecting vortical energy into the surfzone. Previous observations note that deep channel rips have greater variability of velocity while shallow channel rips exhibit greater variability in trajectory, this suggests a continuum of flow states that at present are poorly understood. This paper investigates the degree of bathymetric control on VLF motions illustrating how VLF motions manifest on different morphologies. Three field sites are investigated using low-pass filtered: (i) mean velocity; (ii) variable eddy velocity; (iii) directional standard deviation; and (iv) instantaneous vorticity. A VLF flow-type parameter is introduced to differentiate flow regimes, based on degree of bathymetric control. A novel classification scheme is introduced: (i) strong bathymetric control, with high mean velocities and rip cell oscillation; (ii) moderate control, with high mean velocities and variable VLF trajectories; and (iii) weak control, with low mean velocities and mobile eddies. Level of bathymetric control may be related to channel orientation, in addition to relative depth. This study improves our understanding of rip flow variability over short times frames, with implications for sediment transport and beach safety.

A numerical study on the density driven circulation in the Yellow Sea Cold Water Mass

The circulation of Yellow Sea Cold Water Mass (YSCWM) in the Southern Yellow Sea is investigated using a diagnostic 2D MITgcm model. The resolution of the computational grid is 900 m in the horizontal and 2 m in the vertical where an initial temperature distribution corresponding to a typical measured Yellow Sea Cold Water Mass was applied. The existence of YSCWM that causes fluid density difference, is shown to produce counter-rotating cyclonic horizontal eddies in the surface layer: the inner one is anti-cyclonic (clockwise) and relatively weaker (8–10 cm s−1) while the outer one is cyclonic (anti-clockwise) and much stronger (15–20 cm s−1). This result is consistent with the surface pattern observed by Pang et al. (2004), who has shown that a mesoscale anti-cyclonic eddy (clockwise) exists in the upper layer of central southern Yellow Sea, and a basin-scale cyclonic (anticlockwise) gyre lies outside of the anti-cyclonic eddy, based on the trajectories and drifting velocities of 23 drifters. Below the thermocline, there is an anti-cyclonic (clockwise) circulation. This complex current eddy system is considered to be capable of trapping suspended sediments and depositing them near the front between YSCWM and the coastal waters off the Subei coast, providing an explanation on the sediment depth and size distribution of mud patches in the Southern Yellow Sea. Moreover, sensitive test scenarios indicate that variations of bottom friction do not substantially change the main features of the circulation structure, but will reduce the bottom current velocity, increase the surface current velocity and weaken the upwelling around the frontal area.

Detached eddy simulation of shallow mixing layer development between parallel streams

Results of a high resolution Detached Eddy Simulation (DES) are used to characterize the evolution of a shallow mixing layer developing between two parallel streams in a long open channel with a smooth flat bed and medium size dunes. The study discusses the vertical non-uniformity in the mixing layer structure and provides a quantitative characterization of the growth of the large-scale quasi two-dimensional (2D) coherent structures with the distance from the splitter plate. Results show that in streamwise sections situated between 75D (D is the channel depth) and 150D from the splitter plate, the width of the mixing layer close to the free surface is 20–30% more than the width in the near-bed region. This is mostly because of the tilting of the mixing layer interface on the low-speed side toward the low speed stream as the free surface is approached. Power spectra of the horizontal velocity components near the free surface show the presence of a −3 subrange, corresponding to inverse energy cascade in two-dimensional turbulence, at streamwise locations situated more than 10D from the splitter plate, consistent with the presence of large-scale quasi 2D horizontal eddies and the transfer of energy (inverse energy cascade) from the smaller scales toward these eddies. Consistent with visualizations of the mass transport of a passive scalar within the mixing layer, close to the free surface, the estimated streamwise length of the quasi 2D mixing layer eddies is about 2.5–3.0 times larger than the local width of the mixing layer. The presence of large-scale roughness elements in the form of an array of two-dimensional dunes with a maximum height of 0.25D (D is the channel depth) induces a much more rapid and larger shift of the centerline of the mixing layer due to the increased influence of the bottom roughness.

On the nonlinear development of shear layers in partially vegetated channels

A predictive theory is developed to investigate the nonlinear instability regime of perturbed shear layers in open-channel flows with lateral vegetation. The turbulence is characterized by two distinct scales: a sub-depth turbulence which is associated with the bed shear stress and a large-scale turbulence associated with the large horizontal eddies which develop in the shear layer. The sub-depth turbulence is modeled by assuming a logarithmic vertical distribution of the velocity. Meanwhile, an analogous model for the large-scale turbulence requires the estimation of the transverse velocity profile in the nonlinear state because the growth of the large-scale disturbances expands the shear layer and modifies the velocity distribution across the channel. The nonlinear growth of the disturbances is limited, however, because solid boundaries in the channel play stabilizing mechanisms which lock the amplitude of the large-scale disturbances into a finite-equilibrium state, for which a corresponding transverse velocity profile is determined. A weakly nonlinear stability analysis is performed and the results are validated using experimental data from previous works.

The Generation of Surfzone Eddies in a Strong Alongshore Current

AbstractThe surfzone contains energetic two-dimensional horizontal eddies with length scale larger than the water depth. Yet, the dominant eddy generation mechanism is not understood. The wave-resolving model funwaveC is used to simulate surfzone eddies in four case examples, from the SandyDuck field experiment, that had alongshore uniform bathymetry. The funwaveC model is initialized with the observed bathymetry and the incident wave field in 8-m depth and reproduces the observed cross-shore structure of significant wave height and mean alongshore current. Within the surfzone, the wave-resolving funwaveC-modeled E(f, ky) spectra and the bulk (frequency and ky integrated) rotational velocities are consistent with the observations below the sea–swell band (<0.05 Hz), demonstrating that the model can be used to diagnose surfzone eddy generation mechanisms. In the mean-squared perturbation vorticity budget, the breaking wave vorticity forcing term is orders of magnitude larger than the shear instability generation term. Thus, surfzone eddies (vorticity) generally are not generated through a shear instability, with possible exceptions for very narrow banded in frequency and direction and highly obliquely large incident waves. The alongshore wavenumber spectra of breaking wave vorticity forcing is broad with the majority (>80%) of vorticity forcing occurring at short alongshore scales <20 m. However, the alongshore wavenumber spectra of vorticity is red, which may be due to a 2D turbulence inverse energy cascade bringing energy to longer wavelengths or may result from an amplified vorticity response to direct forcing at smaller ky.

First direct evidence that breaking waves cause horizontal eddies

As ocean waves pass from deeper water into the shallow coastal regions, they begin to break, churning up the surf zone waters. At the edges of the crests of the breaking waves, horizontally rotating eddies (vertical vortices) are generated, converting some of the waves' kinetic energy into turbulence. These horizontally rotating eddies are an important mechanism for dispersing nutrients, larvae, bacteria, sediments, and other suspended objects along the coastline.

Vorticity generation by short‐crested wave breaking

Eddies and vortices associated with breaking waves rapidly disperse pollution, nutrients, and terrestrial material along the coast. Although theory and numerical models suggest that vorticity is generated near the ends of a breaking wave crest, this hypothesis has not been tested in the field. Here we report the first observations of wave‐generated vertical vorticity (e.g., horizontal eddies), and find that individual short‐crested breaking waves generate significant vorticity [O(0.01 s−1)] in the surfzone. Left‐ and right‐handed wave ends generate vorticity of opposite sign, consistent with theory. In contrast to theory, the observed vorticity also increases inside the breaking crest, possibly owing to onshore advection of vorticity generated at previous stages of breaking or from the shape of the breaking region. Short‐crested breaking transferred energy from incident waves to lower frequency rotational motions that are a primary mechanism for dispersion near the shoreline.