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DOE OSTI2022

Extended Barton–Bandis model for rock joints under cyclic loading: Formulation and implicit algorithm

In this paper, the Barton–Bandis model for rock joints is extended to cyclic loading conditions, without any new material parameter. Also developed herein is an implicit solution algorithm for the extended Barton–Bandis model, which can also be used for the original Barton–Bandis model for which an implicit algorithm has been unavailable. To this end, we first cast the Barton–Bandis model into an incremental elasto-plastic framework, deriving an expression for the elastic shear stiffness being consistent with the original model formulation. We then extend the model formulation to cyclic loading conditions, incorporating the dependence of shear stress and dilation on the joint position and the shearing direction. The extension is achieved by introducing a few state-dependent variables which can be calculated with the existing material parameters. For robust and accurate utilization of the model, we also develop an implicit algorithm based on return mapping, which is unconditionally stable and guarantees the satisfaction of the strength criterion. We verify that the proposed model formulation and algorithm produce virtually the same results as the original Barton–Bandis model under monotonic shearing conditions. Here, we then validate the extended Barton–Bandis model against experimental data on natural rock joints under cycling loading conditions. The present work thus enables the Barton–Bandis model, which has been exceptionally popular in research and practice, to be applicable to a wider range of problems in rock mechanics and rock engineering.

58 GEOSCIENCES↗

DOE OSTI2020

Rheological behavior of neat and carbon fiber-reinforced poly(ether ketone ketone) for extrusion deposition additive manufacturing

To develop new materials for extrusion additive manufacturing (AM) systems, a fundamental understanding of rheological properties is essential to correlate the effect of processing on material structure and its properties. In this work, the rheological properties of five different grades of neat and carbon fiber (CF)-reinforced poly(ether ketone ketone) are reported. Rheological properties are essential to understand the effect of reinforcing fibers and AM process parameters such as time, temperature, environment, and shear rate on flow behavior during processing. Small-amplitude oscillatory shear tests and steady shear tests indicated neat grades to exhibit less increase in viscosity over time when processed in air than the CF-filled grades. The filled grades showed greater shear thinning and lower sensitivity to temperature. Altogether, this rheological analysis provides a broad framework for determining appropriate processing conditions for extrusion deposition AM of such high-temperature polymer systems.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Predicted viscosity of liquid HMX up to 40 GPa

Viscous flow serves as a significant heating mechanism during the formation of hot spots, but the shear viscosity which determines this response is poorly characterized for most high explosives. Most recently, a model was proposed for the shear viscosity of liquid HMX (1,3,5,7-tetranitro-1,3,5,7-tetrazocane) that was fit to pressures reaching 5 GPa, but this work uncovered uncertainties in the viscosity at 0 GPa and remains untested at higher pressures. We use molecular dynamics (MD) simulations and the Green-Kubo formalism to predict the temperature- and pressure-dependent shear viscosity of HMX over the pressure interval 0 GPa≤P≤40 GPa. Reassessment of the viscosity at 0 GPa rules out several potential explanations for discrepancies between earlier reports; we attribute these differences to details of MD trajectory integration impacting molecular flexibility. The shear viscosity of HMX exhibits an Arrhenius temperature dependence at each pressure considered, with exponential prefactor and activation energy terms that are also strong functions of pressure. An analytic form for the viscosity is developed based on an extension of the well-known Andrade equation that simultaneously captures the temperature and pressure dependencies in the MD data up to 40 GPa. Comparison against a recently developed model for the viscosity of liquid RDX (1,3,5-trinitro-1,3,5-triazinane) shows that both materials exhibit similar functional dependencies with the viscosity of HMX being higher by roughly an order of magnitude at a given temperature-pressure state.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Projected changes to severe thunderstorm environments as a result of twenty-first century warming from RegCM CORDEX-CORE simulations

Hazardous weather related to the occurrence of severe thunderstorms including tornadoes, high-winds, and hail cause significant damage globally to life and property every year. Yet the impact on these storms from a warming climate remains a difficult task due to their transient nature. Here, we investigate the change in large-scale environments in which severe thunderstorms form during twenty-first century warming (RCP2.6 and RCP8.5) in a group of RegCM CORDEX-CORE simulations. Severe potential is measured in terms of Convective Available Potential Energy (CAPE) and vertical wind-shear during the severe seasons in three regions which are known to currently be prone to severe hazards: North America, subtropical South America, and eastern India and Bangladesh. In every region, environments supportive for severe thunderstorms are projected to increase during the warm season months in both the RCP2.6 and RCP8.5 scenarios during the twenty-first century. The number of days supportive for severe thunderstorms increases by several days per season over the vast majority of each region by the end of the century. Analyzing the CAPE and shear trends during the twenty-first century, we find seasonally and regionally specific changes driving the increased severe potential. Twenty-first century surface warming is clearly driving a robust increase in CAPE in all regions, however poleward displacement of vertical shear in the future leads to the displacement of severe environments over North America and South America. The results found here relate that severe impacts in the future cannot be generalized globally, and that regionally specific changes in vertical shear may drive future movement of regions prone to severe weather.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2021

Significant disparity of non-basal dislocation activities in hot-rolled highly-textured Mg and Mg-3Al-1Zn alloy under tension

It is well-established that Mg-3Al-1Zn (AZ31) alloy exhibits much better tensile ductility than pure Mg. However, the underlying mechanisms for such difference still remain relatively unexplored at the dislocation level. In this work, we deformed hot-rolled highly-textured pure Mg and AZ31 samples with similar initial microstructures (i.e., grain size and texture) under tension along the rolling direction. Apparent shear banding was only observed in the pure Mg samples from the early stage of the deformation. Shear bands could act as easy paths for crack propagation, leading to low ductility in pure Mg. Apparent shear banding was not noted in deformed AZ31 samples. We then investigated the deformation mechanisms at the dislocation level using transmission electron microscopy. Systematic tilting experiments and statistical analyses of multiple grains at different strain levels revealed a significant disparity of non-basal dislocation activities between pure Mg and AZ31. For pure Mg, dislocations were activated since the early stage of plastic deformation. For AZ31, dislocations were mostly absent at all strain levels, even in the strain-to-failure samples. Non-basal dislocations, including prismatic and pyramidal dislocations, were observed. The promotion of the non-basal dislocation activities and the suppression of dislocations in AZ31 are expected to offer more sustainable hardening, which could elucidate the absence of apparent shear banding and much-improved ductility in AZ31 compared to pure Mg.

Zhao, Dexin↗

DOE OSTI2022

Unveiling the origins of work-hardening enhancement and mechanical instability in laser shock peened titanium

Laser shock-peening (LSP) produces complex gradients in microstructures and residual stresses, which enables fabrication of metallic engineering components with superior mechanical properties. In this work, we use non-destructive and spatially resolved high-energy X-ray diffraction (HE-XRD) to investigate the influences of LSP on microstructure, surface topography, and residual stress for high purity titanium plates. LSP is found to produce large compressive in-plane residual stresses near the peened surface which monotonically decay to zero about 2.5 mm below the surface. These properties were also tracked during in-situ tensile loading, allowing stress partitioning and work-hardening rates to be measured as a function of depth. The surface region is found to have the highest work-hardening rate and remain mechanically stable up to sample failure. In addition, a crystal rigid rotation along a transversal axis of about 27 & nbsp; was observed at large applied strain near the surface region, which is attributed to the formation of denser dispersed shear bands. Furthermore, a sudden drop in tensile stress was observed at a depth of similar to 160 mu m from the LSP surface, indicating the formation of a localized mechanical instability zone (LMIZ). The origin of this LMIZ could be attributed to the increase in shear stress induced by a load transfer from LSP surface due to the formation of denser dispersed shear bands. These observations indicate a localized transition in deformation behavior has occurred from dispersed shear banding to LMIZ and homogeneous deformation.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Energetics of the nucleation and glide of disconnection modes in symmetric tilt grain boundaries

Grain boundaries (GBs) evolve by the nucleation and glide of disconnections, which are dislocations with a step character. In this work, motivated by recent success in predicting GB properties such as the shear coupling factor and mobility from the intrinsic properties of disconnections, we develop a systematic method to calculate the energy barriers for the nucleation and glide of individual disconnection modes under arbitrary driving forces and a quasi-2D setting. This method combines tools from bicrystallography to enumerate disconnection modes and the Nudged elastic band (NEB) method to calculate their energetics, yielding minimum energy paths and atomistic mechanisms for the nucleation and glide of each disconnection mode. We apply the method to accurately predict shear coupling factors of $[001]$ symmetric tilt grain boundaries in Cu. Particular attention is paid to the boundaries where the dislocation-based disconnection nucleation model produces incorrect nucleation barriers. We demonstrate that the method can accurately compute energy barriers and predict shear-coupling factors in the low-temperature regime. For certain disconnection modes in which the assumptions underlying our method do not hold, we report upper bounds on the energy barriers for disconnection nucleation and glide. In addition, the NEB trajectories reveal interesting phenomena such as the dissociation of a higher energy mode into lower energy modes, and in some cases, shear coupling being mediated by partial disconnections, wherein the GB structure temporarily changes to a metastable state before reverting back to its original structure. Graphical abstract

36 MATERIALS SCIENCE↗

DOE OSTI2020

Single crystal yield criterion for chromium based on atomistic studies of isolated 1/2[111] screw dislocations

Using the recently developed Bond Order Potential for Cr, we investigate the mobility of isolated 1/2[111] screw dislocations under stress at 0 K. These studies provide the dependence of the critical resolved shear stress (i.e., the Peierls stress) on the orientation of the maximum resolved shear stress plane and on the shear stress perpendicular to the slip direction. Similar studies are made for loading in tension and compression to show that the onset of yielding in Cr single crystals can be described using a combination of the shear stresses parallel and perpendicular to the slip direction. Based on these results, we develop a single crystal yield criterion for Cr that includes all non-Schmid contributions to the Peierls stress. This criterion is used to predict the shape of the yield surface and compare it with the regular Tresca's hexagon arising from the Schmid law. For all directions of uniaxial load, the criterion is used to quantify the character and magnitude of the tension-compression asymmetry.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Anomalous elastic behavior of tantalum at high pressures: Experimental and theoretical studies

Elastic wave velocities of polycrystalline tantalum have been measured up to 13.6 GPa at room temperature using ultrasonic interferometry technique in a multi-anvil apparatus. The bulk and shear moduli, as well as their pressure derivatives are obtained using Eulerian 3rd order finite strain equations, yielding K S0 = 193.9(29) GPa, G 0 = 69.3(10) GPa, K S0' = 3.18(5) and G 0' = 0.88(1). Here the Steinberg-Guinan yield stress model is examined using the current shear modulus and its pressure derivative, where a slightly lower A 0 = 0.0127 GPa –1 compared to previous studies is obtained. First-principles calculations on the elasticity of tantalum have also been performed up to 200 GPa. Anomalous softening of the elastic shear constant C 44 and shear wave velocity V S is observed between 80– 180 GPa, whereas the anisotropy shows a softening-stiffening behavior with increasing pressure and reaches a minimum at around 150 GPa. Such anomalies might commonly originate from the nesting of Fermi surface for Group VB metals.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Non-local model for surface tension in fluid-fluid simulations

We propose a non-local model for surface tension obtained in the form of an integral of a molecular-force-like function with support 3.5e added to the Navier-Stokes momentum conservation equation. We demonstrate analytically and numerically that with the non-local model interfaces with a radius of curvature larger than the support length behave macroscopically and microscopically, otherwise. For static droplets, the pressure difference Pe,in - Pe,out satisfies the Young-Laplace law for droplet radius greater than 3.5e and other- wise deviates from the Young-Laplace law. The latter indicates that the surface tension in the proposed model decreases with decreasing radius of curvature, which agrees with molecular dynamics and experimental studies of nanodroplets. Using the non-local model we perform numerical simulations of droplets under dynamic conditions, including a rising droplet, a droplet in shear flow, and two colliding droplets in shear flow, and compare results with a standard Navier-Stokes model subject to the Young-Laplace boundary condition at the fluid-fluid interface implemented via the Conservative Level Set (CLS) method. We find good agreement with existing numerical methods and analytical results for a rising macroscopic droplet and a droplet in a shear flow. For colliding droplets in shear flow, the non- local model converges (with respect to the grid size) to the correct behavior, including sliding, coalescence, and merging and breaking of two droplets depending on the capillary number. In contrast, we find that the results of the CLS model are highly grid-size dependent.

Howard, Amanda A.↗

DOE OSTI2020

Active- and transfer-learning applied to microscale-macroscale coupling to simulate viscoelastic flows

Active- and transfer-learning are applied to microscale dynamics of polymer flows for the multiscale discovery of effective constitutive approximations required in viscoelastic flow simulation. The result is macroscopic rheology directly connected to a microstructural model. Micro and macroscale simulations are adaptively coupled by means of Gaussian process regression (GPR) to run the expensive microscale computations only as necessary. This multiscale method is demonstrated with flows of a polymer solution as a model system. At the microscale level dissipative particle dynamics (DPD) is employed to model the fluid as a suspension of bead-spring micro-structures subjected to steady shear flow. The results yield the non-Newtonian viscosity and the first normal stress difference at strain rates as training data used in a GPR model. DPD parameters are calibrated with respect to experimental data for a real polymer solution. Compliance with these data requires adjustment of the DPD model's cutoff radius, which then becomes a function of the second invariant of the strain rate tensor. The FENE-P model is chosen for the macroscale description using the spectral element method (SEM) to simulate channel flow and flow past a circular cylinder. The DPD results at the lowest possible shear strain rate yield an estimate of the zero-shear rate viscosity, which allows the initiation of the macroscale flow by SEM as a Newtonian fluid. The resulting strain-rate field is surveyed to determine additional shear strain rate sampling points for the DPD system. This new information allows an initial fitting of parameters of the constitutive equation followed by new SEM simulations at the macroscale. Additionally, guided by active-learning GPR to select new sampling points, this process continues until convergence is achieved. The effectiveness of this new simulation paradigm for viscoelastic flows is tested with different macroscale operating conditions. The effective closure learned in the channel simulation is then transferred directly to the flow past a circular cylinder at low Reynolds number, where the results show that only two additional DPD simulations are required to achieve a satisfactory constitutive model. With an increase of the Reynolds number, the active-learning scheme automatically detects the inaccuracy of the learned constitutive model, and initiates additional DPD simulations for the extra data needed to once again close the microscale-macroscale coupled system. This new paradigm of active- and transfer-learning for multiscale modeling is readily applicable to other microscale-macroscale coupled simulations of complex fluids and other materials. Furthermore, the coupling between microscale and macroscale solvers can be seamlessly implemented with our open source multiscale universal interface (MUI) library.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Periodic boundary conditions for arbitrary deformations in molecular dynamics simulations

A generalization of the Lees-Edwards periodic boundary conditions (gLE-PBC) for molecular dynamics (MD) simulations is developed to allow for arbitrary deformations to be applied to the domain. The gLE-PBC domain remains a rectangular cuboid regardless of the applied deformation in contrast with the Lagrangian-rhomboid periodic boundary conditions (LR-PBC) where the domain deforms according to the applied deformation. Furthermore, the kinematics of gLE-PBC are validated against pure shear. The gLE-PBC method for interacting systems is then validated against the LR-PBC method and analytical solutions for a solid under isotropic compression, one-dimensional shearing, three-dimensional extension and shearing and for a liquid under Couette flow. Bulk physical properties extracted from the gLE-PBC simulations agree well with values calculated from equilibrium MD simulations. Three dimensional shearing and a deformation with a full velocity gradient matrix are also simulated, showing the range of problems gLE-PBC can explore.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2024

Microstructure and mechanical properties of ultrasonic spot welding of AA7075-T6 and A380 casting aluminum alloy

Ultrasonic spot welding (USW) was employed to join AA7075-T6 and casting Al alloy A380. Under a constant welding power, the influence of the welding time duration (from 1 s to 3 s) on peak temperature, microstructure, hardness, and mechanical strength of the joints were studied. It was found that the peak temperature increased with welding time. A sound solid-state metallurgical bonding was obtained at the joint interface. The cracks occurred at the edge of the joints were eventually eliminated as the welding time increased. A layer of refined grains formed in A380 adjacent to the bonding line. Further, hardness reduction occurred in AA7075 at the joint interface and the degree of hardness reduction and the volume increased with the peak temperature. By increasing welding time, lap shear tensile tests show that the peak load increased from 5.3 kN to 6.55 kN. The corresponding interfacial shear strength ranged from 96.29 MPa to 99.72 MPa, lower than the shear strength of both base materials (331 MPa for AA7075 and 185 MPa for A380). All joint samples exhibited interfacial fracture after lap shear tensile testing, with a thin layer of A380 remnant attached to AA7075 at the center of the fractured surface.

36 MATERIALS SCIENCE↗

DOE OSTI2024

In situ measurement of three-dimensional intergranular stress localizations and grain yielding under elastoplastic axial-torsional loading

The three-dimensional grain-averaged response of solid bar samples under non-proportional (NP) elastoplastic axial-torsional loading was investigated using in situ high energy diffraction microscopy (HEDM) and companion crystal plasticity finite element (CPFE) modeling. Important stress metrics including applied shear (σ θZ ) and axial (σ ZZ ) stress tensor components, stress and stress deviator tensor invariants (I 1 , J 2 , and J 3 ), von Mises equivalent stress (σ$^{grain}_{VM}$), maximum resolved shear stress (mRSS), stress triaxiality (η), and lode angle parameter ($\barθ$) values were tracked for ~300 grains under two different loading conditions: (1) Torsion-dominated loading (low NP) and (2) Tension-torsion loading (high NP) in equiatomic NiCoCr, a representative multicomponent face-centered cubic (FCC) superalloy. Overall, significant stress localizations existed within both samples as evidenced by the radial dependence of grain-resolved σ θZ , σ$^{grain}_{VM}$, and J 2 ; by comparison, I 1 , J 3 , η, and $\barθ$ metrics did not show discernible trends within the volume. These stress localizations reveal a complex interplay between axial and shear stress components (e.g., stress coupling) resulting in grain yielding near the sample surface largely driven by shear stress, whereas internal grain yielding was largely accommodated by axial stress. Grain-resolved stress localization trends were described well by the CPFE model, although some discrepancies in magnitude occurred, particularly for volumetric stress metrics (I 1 and η) due to initial type II residual stress distributions. The superposition of initial residual stress states onto CPFE grain-resolved data significantly improved model accuracy for η. This suggests that residual stresses more strongly influence the simulation of volumetric rather than deviatoric (yield) stress metrics.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Microstructure and CPO evolution of dynamically recrystallized olivine during complex deformation conditions: a full-field numerical modeling approach

The rheological properties of mantle rocks are strongly dependent on their crystallographic preferred orientation (CPO). Olivine CPO, defined by the orientation of seismically fast [100] axes parallel to flow direction, is also thought to be a dominant contributor to seismic anisotropy in the Earth's upper mantle. However, the amount of deformation needed to overprint a new CPO on a pre-existing fabric and the impact of the inherited CPOs on the transient microstructure evolution, remain unknown. This study employs a full-field numerical approach (VPFFT-ELLE) to explore the dynamic recrystallization and microstructural evolution of olivine polycrystalline aggregates under complex deformation conditions. We test four combinations of successive pure shear and simple shear boundary conditions. Findings indicate that inherited CPOs influence subsequent deformation in a manner dependent on the kinematic relationship between successive stages. In all cases, a minor strain increment (ε ∼0.3–0.6) is sufficient to erase the previous microstructure and CPO. However, when deformation conditions change dramatically (e.g., stretching direction changes orthogonally), the intensity of the new CPO developed is significantly lower and strain distribution are specially altered. During a transient strain stage, pre-existing microstructures undergo extensive reworking, especially when deformation conditions are changed dramatically, such as switching from simple shear to a pure shear condition with a parallel shortening direction relative to the stretching direction. We estimate the significance of these results in interpreting observations of seismic velocity anisotropy, concluding that P-wave seismic anisotropy is significantly and positively correlated with the evolution of olivine CPO with deformation history. This research underscores the transient nature of microstructural rearrangement in olivine aggregates and the necessity for caution in interpreting seismic anisotropy in regions with complex deformation histories, as inherited CPOs can influence current fabric development and induce deviation to the present deformation conditions.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Directional amorphization of covalently-bonded solids: A generalized deformation mechanism in extreme loading

Shock compression subjects materials to a unique regime of high quasi-hydrostatic pressure and coupled shear stresses for durations on the order of 1–10 nanoseconds for laser-driven loading of samples. There is, additionally, an attendant temperature increase due to the shock and the mechanisms of plastic deformation in metals whereby dislocations, twins, and phase transitions nucleate and propagate at velocities near the sound speed. Covalently bonded materials have, by virtue of the directionality of their bonds, great difficulty in responding by conventional plastic deformation to this extreme regime of shock compression. Here, we propose that the shear from shock compression induces amorphization, as observed in Si, Ge, B4C, SiC, and olivine ((Mg, Fe) 2 SO 4 ) and that this is a general deformation mechanism in a broad class of covalently bonded materials. The crystalline structure transforms to amorphous along regions of maximum shear stress, forming nanoscale bands, and thereby relaxing the shear component of the imposed shock stress. This process is usually preceded by the emission and propagation of a critical concentration of dislocations.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Exfoliation of surfactant swollen layered MWW zeolites into two-dimensional zeolite nanosheets using telechelic liquid polybutadiene

We report two-dimensional (2D) zeolites have the potential to enhance mass transport by reducing diffusion lengths and thus find applications in catalysis and separation. High aspect ratio 2D zeolite nanosheets are required for fabrication of thin, high-flux zeolite membranes. Preparation of 2D zeolite nanosheets can be achieved by exfoliation of layered zeolite precursors, which usually requires multiple steps including swelling with cationic surfactants, exfoliation by applying a mechanical force such as shearing or sonication, purification and removal of the surfactants. The exfoliation of surfactant swollen layered zeolite precursors has been studied using molten polystyrene and telechelic liquid polybutadiene, but still requires extensive shearing force. Recently, a novel one-step exfoliation method has been developed for nonswollen MWW zeolite precursors using tetrabutylammonium hydroxide (TBAOH) solution. In this work, we study the exfoliation of surfactant swollen MWW layered precursors (with and without aluminum) in commercially available liquid hydroxyl-terminated polybutadiene (HTPB) with the aim to provide fundamental understanding of the interaction between the liquid polybutadiene and the surfactant swollen layered zeolite precursors. It was found that surfactant swollen ITQ-1, (ITQ-1(S)), a pure silica layered precursor with MWW framework after being swollen with a cationic surfactant, can be exfoliated in liquid HTPB at room temperature without applying any additional shearing force. The aluminum containing surfactant swollen MWW precursors can be also exfoliated in HTPB at room temperature, but require additional shearing forces. The exfoliation process was monitored using rheology experiments and studied by tuning the composition of the zeolite precursors. The interaction between the layered zeolite precursor and the hydroxyl group of the liquid polybutadiene allows the polymer to intercalate the precursor and exfoliate it into nanosheets. The presence of framework aluminum and the nature of the organic structure directing agents (OSDAs) are key parameters affecting the exfoliation process. Framework Al is unfavorable for the exfoliation possibly due to the surface charges introduced by the aluminum. Bulky OSDA, trimethyladamantammonium (TMAda + ), in the interlayer spacing may facilitate the exfoliation.

2D nanosheets↗

DOE OSTI2024

Langmuir turbulence in suspended kelp farms

This study investigates the influence of suspended kelp farms on ocean mixed layer hydrodynamics in the presence of currents and waves. We use the large eddy simulation method, where the wave effect is incorporated by solving the wave-averaged equations. Distinct Langmuir circulation patterns are generated within various suspended farm configurations, including horizontally uniform kelp blocks and spaced kelp rows. Intensified turbulence arises from the farm-generated Langmuir circulation, as opposed to the standard Langmuir turbulence observed without a farm. The creation of Langmuir circulation within the farm is attributed to two primary factors depending on farm configuration: (i) enhanced vertical shear due to kelp frond area density variability, and (ii) enhanced lateral shear due to canopy discontinuity at lateral edges of spaced rows. Both enhanced vertical and lateral shear of streamwise velocity, representing the lateral and vertical vorticity components, respectively, can be tilted into downstream vorticity to create Langmuir circulation. This vorticity tilting is driven by the Craik–Leibovich vortex force associated with the Stokes drift of surface gravity waves. In addition to the farm-generated Langmuir turbulence, canopy shear layer turbulence is created at the farm bottom edge due to drag discontinuity. The intensity of different types of turbulence depends on both kelp frond area density and the geometric configuration of the farm. The farm-generated turbulence has substantial consequences for nutrient supply and kelp growth. These findings also underscore the significance of the presence of obstacle structures in modifying ocean mixed layer characteristics.

Bo, Tong (ORCID:0000000260300561)↗