Vortex Force Research Articles

Hydrodynamics of linear acceleration in bluegill sunfish, Lepomis macrochirus.

In their natural habitat, fish rarely swim steadily. Instead they frequently accelerate and decelerate. Relatively little is known about how fish produce extra force for acceleration in routine swimming behavior. In this study, we examined the flow around bluegill sunfish Lepomis macrochirus during steady swimming and during forward acceleration, starting at a range of initial swimming speeds. We found that bluegill produce vortices with higher circulation during acceleration, indicating a higher force per tail beat, but they do not substantially redirect the force. We quantified the flow patterns using high speed video and particle image velocimetry and measured acceleration with small inertial measurement units attached to each fish. Even in steady tail beats, the fish accelerates slightly during each tail beat, and the magnitude of the acceleration varies. In steady tail beats, however, a high acceleration is followed by a lower acceleration or a deceleration, so that the swimming speed is maintained; in unsteady tail beats, the fish maintains the acceleration over several tail beats, so that the swimming speed increases. We can thus compare the wake and kinematics during single steady and unsteady tail beats that have the same peak acceleration. During unsteady tail beats when the fish accelerates forward for several tail beats, the wake vortex forces are much higher than those at the same acceleration during single tail beats in steady swimming. The fish also undulates its body at higher amplitude and frequency during unsteady tail beats. These kinematic changes likely increase the fluid dynamic added mass of the body, increasing the forces required to sustain acceleration over several tail beats. The high amplitude and high frequency movements are also likely required to generate the higher forces needed for acceleration. Thus, it appears that bluegill sunfish face a trade-off during acceleration: the body movements required for acceleration also make it harder to accelerate.

Vortex-induced vibration of a rotating sphere

Vortex-induced vibration (VIV) of a sphere represents one of the most generic fundamental fluid–structure interaction problems. Since vortex-induced vibration can lead to structural failure, numerous studies have focused on understanding the underlying principles of VIV and its suppression. This paper reports on an experimental investigation of the effect of imposed axial rotation on the dynamics of vortex-induced vibration of a sphere that is free to oscillate in the cross-flow direction, by employing simultaneous displacement and force measurements. The VIV response was investigated over a wide range of reduced velocities (i.e. velocity normalised by the natural frequency of the system): $3\leqslant U^{\ast }\leqslant 18$, corresponding to a Reynolds number range of $5000<Re<30\,000$, while the rotation ratio, defined as the ratio between the sphere surface and inflow speeds, $\unicode[STIX]{x1D6FC}=|\unicode[STIX]{x1D714}|D/(2U)$, was varied in increments over the range of $0\leqslant \unicode[STIX]{x1D6FC}\leqslant 7.5$. It is found that the vibration amplitude exhibits a typical inverted bell-shaped variation with reduced velocity, similar to the classic VIV response for a non-rotating sphere but without the higher reduced velocity response tail. The vibration amplitude decreases monotonically and gradually as the imposed transverse rotation rate is increased up to $\unicode[STIX]{x1D6FC}=6$, beyond which the body vibration is significantly reduced. The synchronisation regime, defined as the reduced velocity range where large vibrations close to the natural frequency are observed, also becomes narrower as $\unicode[STIX]{x1D6FC}$ is increased, with the peak saturation amplitude observed at progressively lower reduced velocities. In addition, for small rotation rates, the peak amplitude decreases almost linearly with $\unicode[STIX]{x1D6FC}$. The imposed rotation not only reduces vibration amplitudes, but also makes the body vibrations less periodic. The frequency spectra revealed the occurrence of a broadband spectrum with an increase in the imposed rotation rate. Recurrence analysis of the structural vibration response demonstrated a transition from periodic to chaotic in a modified recurrence map complementing the appearance of broadband spectra at the onset of bifurcation. Despite considerable changes in flow structure, the vortex phase ($\unicode[STIX]{x1D719}_{vortex}$), defined as the phase between the vortex force and the body displacement, follows the same pattern as for the non-rotating case, with the $\unicode[STIX]{x1D719}_{vortex}$ increasing gradually from low values in Mode I of the sphere vibration to almost $180^{\circ }$ as the system undergoes a continuous transition to Mode II of the sphere vibration at higher reduced velocity. The total phase ($\unicode[STIX]{x1D719}_{total}$), defined as the phase between the transverse lift force and the body displacement, only increases from low values after the peak amplitude response in Mode II has been reached. It reaches its maximum value (${\sim}165^{\circ }$) close to the transition from the Mode II upper plateau to the lower plateau, reminiscent of the behaviour seen for the upper to lower branch transition for cylinder VIV. Hydrogen-bubble visualisations and particle image velocimetry (PIV) performed in the equatorial plane provided further insights into the flow dynamics near the sphere surface. The mean wake is found to be deflected towards the advancing side of the sphere, associated with an increase in the Magnus force. For higher rotation ratios, the near-wake rear recirculation zone is absent and the flow is highly vectored from the retreating side to the advancing side, giving rise to large-scale shedding. For a very high rotation ratio of $\unicode[STIX]{x1D6FC}=6$, for which vibrations are found to be suppressed, a one-sided large-scale shedding pattern is observed, similar to the shear-layer instability one-sided shedding observed previously for a rigidly mounted rotating sphere.

Vortex force map method for viscous flows of general airfoils

In a previous paper, an inviscid vortex force map approach was developed for the normal force of a flat plate at arbitrarily high angle of attack and leading/trailing edge force-producing critical regions were identified. In this paper, this vortex force map approach is extended to viscous flows and general airfoils, for both lift and drag forces due to vortices. The vortex force factors for the vortex force map are obtained here by using Howe’s integral force formula. A decomposed form of the force formula, ensuring vortices far away from the body have negligible effect on the force, is also derived. Using Joukowsky and NACA0012 airfoils for illustration, it is found that the vortex force map for general airfoils is similar to that of a flat plate, meaning that force-producing critical regions similar to those of a flat plate also exist for more general airfoils and for viscous flow. The vortex force approach is validated against NACA0012 at several angles of attack and Reynolds numbers, by using computational fluid dynamics.

Vortex force of an impulsively started plate at high angle of attack

PurposeA quantitative study that can identify the primary aerodynamic forces and relate them to individual vortical structures is lacking. The paper aims to clarify the quantitative relationships between the aerodynamic forces and vortical structures.Design/methodology/approachThe various contributions to the aerodynamic forces on the two-dimensional impulsively started plate are investigated from the perspective of the vorticity moment theorem. The angles of attacks are set to 45°, 58.5° and 72°, while the Reynolds number is 10,000 based on the chord length. Compared with the traditional pressure force analysis, this theorem not only tells us the total aerodynamic force during the motion, but also enables us to quantify the forces contributed from the fluid elements with non-zero vorticity.FindingsIt is found that the time-dependent force behaviors are dominated by the formations and evolutions of these vortical structures. The analysis of the time-averaged forces demonstrates that the lift contributed from the leading edge vortex (LEV) is nearly four times larger than the total lift and the drag contributed from the starting vortex (SV) is almost equal to the total drag when the angle of attack (AoA) increases to 72°, which means the LEV is “lift structure” whereas the SV is “drag structure”.Practical implicationsThe present method provides a better perspective for flow control and drag reduction by relating the forces directly to the individual vorticity structures.Originality/valueIn this paper, the Vorticity Moment Theory is first used to study the quantitative relationships between the aerodynamic forces and the vortices.

Persistent Shoreline Shape Induced From Offshore Geologic Framework: Effects of Shoreface Connected Ridges

AbstractMechanisms relating offshore geologic framework to shoreline evolution are determined through geologic investigations, oceanographic deployments, and numerical modeling. Analysis of shoreline positions from the past 50 years along Fire Island, New York, a 50 km long barrier island, demonstrates a persistent undulating shape along the western half of the island. The shelf offshore of these persistent undulations is characterized with shoreface‐connected sand ridges (SFCR) of a similar alongshore length scale, leading to a hypothesis that the ridges control the shoreline shape through the modification of flow. To evaluate this, a hydrodynamic model was configured to start with the US East Coast and scale down to resolve the Fire Island nearshore. The model was validated using observations along western Fire Island and buoy data, and used to compute waves, currents and sediment fluxes. To isolate the influence of the SFCR on the generation of the persistent shoreline shape, simulations were performed with a linearized nearshore bathymetry to remove alongshore transport gradients associated with shoreline shape. The model accurately predicts the scale and variation of the alongshore transport that would generate the persistent shoreline undulations. In one location, however, the ridge crest connects to the nearshore and leads to an offshore‐directed transport that produces a difference in the shoreline shape. This qualitatively supports the hypothesized effect of cross‐shore fluxes on coastal evolution. Alongshore flows in the nearshore during a representative storm are driven by wave breaking, vortex force, advection and pressure gradient, all of which are affected by the SFCR.

Numerical simulation of vortex-induced vibration of a circular cylinder with different surface roughnesses

The effects of surface roughness on the vortex-induced vibration (VIV) performances of a circular cylinder were studied numerically. The VIV response amplitude, response frequency, vortex force, vortex phase and vortex shedding flow pattern with different degrees of surface roughness were compared. The numerical results show that the VIV response amplitude decreases with increased surface roughness. For a smooth cylinder and a cylinder with small surface roughness, the VIV response could be divided into three branches: initial branch, upper branch and lower branch. In the initial and upper branches, the vortex shedding flow pattern displays a 2S mode. However, the VIV response produces a 2P mode vortex shedding pattern in the lower branch. For a cylinder with large surface roughness, the VIV response can be divided into only two branches: an initial branch and a lower branch. In the initial branch, the vortex shedding flow pattern displays a 2S mode, but in the lower branch, the pattern changes to the 2P mode. The transition of 2S mode to 2P mode is caused by the abrupt change of the vortex phase between the vortex force and the VIV response.

Assessing the performance of formulations for nonlinear feedback of surface gravity waves on ocean currents over coastal waters

This study presents applications of a two-way coupled wave-circulation modelling system over coastal waters, with a special emphasis of performance assessments of two different methods for nonlinear feedback of ocean surface gravity waves on three-dimensional (3D) ocean currents. These two methods are the vortex force (VF) formulation suggested by Bennis et al. (2011) and the latest version of radiation stress (RS) formulation suggested by Mellor (2015). The coupled modelling system is first applied to two idealized test cases of surf-zone scales to validate implementations of these two methods in the coupled wave-circulation system. Model results show that the latest version of RS has difficulties in producing the undertow over the surf zone. The coupled system is then applied to Lunenburg Bay (LB) of Nova Scotia during Hurricane Juan in 2003. The coupled system using both the VF and RS formulations generates much stronger and more realistic 3D circulation in the Bay during Hurricane Juan than the circulation-only model, demonstrating the importance of surface wave forces to the 3D ocean circulation over coastal waters. However, the RS formulation generates some weak unphysical currents outside the wave breaking zone due to a less reasonable representation for the vertical distribution of the RS gradients over a slopping bottom. These weak unphysical currents are significantly magnified in a two-way coupled system when interacting with large surface waves, degrading the model performance in simulating currents at one observation site. Our results demonstrate that the VF formulation with an appropriate parameterization of wave breaking effects is able to produce reasonable results for applications over coastal waters during extreme weather events. The RS formulation requires a complex wave theory rather than the linear wave theory for the approximation of a vertical RS term to improve its performance under both breaking and non-breaking wave conditions.

Three‐dimensional transient rip currents: Bathymetric excitation of low‐frequency intrinsic variability

AbstractThe ROMS‐WEC model [Uchiyama et al., 2010] based on an Eulerian wave‐averaged vortex‐force asymptotic theory of McWilliams et al. (2004) is applied to analyze 3‐D transient wave‐driven rip currents and associated intrinsic very low‐frequency (VLF) variability in the surf zone on a surveyed bathymetry under spatiotemporally uniform offshore incident waves. The 3‐D rip currents are substantially depth‐dependent due to the vertical recirculation, composed of pairs of counter‐rotating longitudinal overturning roll cells that promote surface convergence. The vortex force plays an important role in vorticity budget, preconditioning overall vorticity reduction. These rip currents are intrinsically unstable and contribute about 70% to kinetic energy (KE) as eddy kinetic energy (EKE), consistent with observations. The dominant fluctuation period fits the VLF band, at about 18 min. The current effect on waves (CEW) alters not only the mean rip structure, but also the associated turbulence as the modified cross‐shore EKE profile with considerable accentuation in the inner surf zone. Increased alongshore bathymetric variability proportionally intensifies KE and intrinsic EKE, whereas it reduces the VLF period. With a guide of a pseudo 2D model, we reveal that vortex tilting effect due to the horizontal vorticity inherent in the 3‐D rip currents promotes collapse of the 3‐D eddies through an enhanced forward kinetic energy cascade, leading to short‐lived, laterally‐stretched 3‐D eddies resulting in elongated filaments that decay more quickly than coherent, long‐lived, circular 2‐D eddies.

Influence of Stokes Drift Decay Scale on Langmuir Turbulence

AbstractAccurately scaling Langmuir turbulence (LT) in the ocean surface boundary layer (OSBL) is critical for improving ocean, weather, and climate models. The physical processes by which the structure of LT depends on surface waves’ Stokes drift decay length scale are examined. An idealized model for OSBL turbulent kinetic energy (TKE) provides a conceptual framework with three physical processes: TKE transport, dissipation, and production by the Craik–Leibovich (CL) vortex force (VF) associated with the Stokes drift shear. TKE profiles depend on OSBL depth h, surface roughness length z0, and wavenumber k through the nondimensional parameters kh and kz0. These parameters determine the rate and length scale for the dissipation of TKE produced by the CL-VF. For kz0 ≫ 1, TKE input by the CL-VF is governed by a surface flux with TKE rapidly decaying with depth. Only for kz0 < 1 can TKE penetrate deeper into the OSBL, with the TKE penetration depth controlled by kh. Turbulence-resolving large-eddy simulation results support this conceptual framework and indicate that the dominant Langmuir cell size scales with (kh)−1. Within the depth of dominant Langmuir cells, TKE dissipation is approximately balanced by CL-VF production. Shorter waves contribute less to deeper vertical velocity variance 〈w2〉 because the CL-VF is less effective in generating larger-scale LT. Depth-averaged 〈w2〉 scales with a modified Langmuir number Laϕ = (u*/usϕ)1/2, where u* denotes the water-side surface friction velocity and usϕ is a depth-integrated weighted Stokes drift shear or, equivalently, a spectrally filtered surface Stokes drift.

A 3D unstructured grid nearshore hydrodynamic model based on the vortex force formalism

A new three-dimensional nearshore hydrodynamic model system is developed based on the unstructured-grid version of the third generation spectral wave model SWAN (Un-SWAN) coupled with the three-dimensional ocean circulation model FVCOM to enable the full representation of the wave-current interaction in the nearshore region. A new wave–current coupling scheme is developed by adopting the vortex-force (VF) scheme to represent the wave–current interaction. The GLS turbulence model is also modified to better reproduce wave-breaking enhanced turbulence, together with a roller transport model to account for the effect of surface wave roller. This new model system is validated first against a theoretical case of obliquely incident waves on a planar beach, and then applied to three test cases: a laboratory scale experiment of normal waves on a beach with a fixed breaker bar, a field experiment of oblique incident waves on a natural, sandy barred beach (Duck’94 experiment), and a laboratory study of normal-incident waves propagating around a shore-parallel breakwater. Overall, the model predictions agree well with the available measurements in these tests, illustrating the robustness and efficiency of the present model for very different spatial scales and hydrodynamic conditions. Sensitivity tests indicate the importance of roller effects and wave energy dissipation on the mean flow (undertow) profile over the depth. These tests further suggest to adopt a spatially varying value for roller effects across the beach. In addition, the parameter values in the GLS turbulence model should be spatially inhomogeneous, which leads to better prediction of the turbulent kinetic energy and an improved prediction of the undertow velocity profile.

Rip currents and alongshore flows in single channels dredged in the surf zone

AbstractTo investigate the dynamics of flows near nonuniform bathymetry, single channels (on average 30 m wide and 1.5 m deep) were dredged across the surf zone at five different times, and the subsequent evolution of currents and morphology was observed for a range of wave and tidal conditions. In addition, circulation was simulated with the numerical modeling system COAWST, initialized with the observed incident waves and channel bathymetry, and with an extended set of wave conditions and channel geometries. The simulated flows are consistent with alongshore flows and rip‐current circulation patterns observed in the surf zone. Near the offshore‐directed flows that develop in the channel, the dominant terms in modeled momentum balances are wave‐breaking accelerations, pressure gradients, advection, and the vortex force. The balances vary spatially, and are sensitive to wave conditions and the channel geometry. The observed and modeled maximum offshore‐directed flow speeds are correlated with a parameter based on the alongshore gradient in breaking‐wave‐driven‐setup across the nonuniform bathymetry (a function of wave height and angle, water depths in the channel and on the sandbar, and a breaking threshold) and the breaking‐wave‐driven alongshore flow speed. The offshore‐directed flow speed increases with dissipation on the bar and reaches a maximum (when the surf zone is saturated) set by the vertical scale of the bathymetric variability.

Vortex Induced Vibration of Subsea Umbilicals: A Case Study of Deep Offshore Nigeria

This study involved using typical Joint North Sea Wave Project (JONSWAP) based Umbilical design of lengths 3044m, 3215m, 4481m and 2873m clamped to Floating Production Storage and Offloading (FPSO) unit in Deep Offshore Nigeria at water depth of 2000m. Relevant metOcean data was used to simulate the environmental conditions. The process was simulated using different wave spectra on OrcaFlex software. JONSWAP spectra results for Umbilical-1 to Umbilical-4 at near-surface current (End A: 850m) showed a Transverse Vortex Force (TVF) range of 0.0115 – 0.018kN/m; 0.009 – 0.0149kN/m; 0.006-0.014kN/m; 0.0048 -0.009kN/m, respectively. For Ochi-Hubble spectra, the corresponding TVF range obtained include: 0.004 - 0.0305kN/m; 0.004 - 0.028kN/m; 0.003 - 0.027kN/m; 0.003 - 0.0232kN/m, respectively. JONSWAP spectra showed maxima (t, TVF) values of (0.013, 0.018); (0.012, 0.0149); (0.008, 0.014); (0.0074, 0.009) from Umbilical-1 to Umbilical-4, respectively. With the Ochi-Hubble spectra, maxima (t, TVF) values were (0.018, 0.0305); (0.016, 0.028); (0.013, 0.027); (0.0141, 0.0232) for Umbilical-1 to Umbilical-4, respectively. Hence, maxima (t, TVF) values were greater for Ochi-Hubble than JONSWAP. Simulation plots indicate that adjusting the peakedness parameter (γ) of the JONSWAP spectra does not give the required accuracy for this region. Therefore, using a JONSWAP based Umbilical design in Ochi-Hubble environment like Offshore Nigeria shows higher vortex induced vibration (VIV) at near surfaces leading to higher TVF, and higher fatigue damage tendency.

An aerodynamic model for insect flapping wings in forward flight

This paper proposes a semi-empirical quasi-steady aerodynamic model of a flapping wing in forward flight. A total of 147 individual cases, which consisted of advance ratios J of 0 (hovering), 0.125, 0.25, 0.5, 0.75, 1 and ∞, and angles of attack α of −5 to 95° at intervals of 5°, were examined to extract the aerodynamic coefficients. The Polhamus leading-edge suction analogy and power functions were then employed to establish the aerodynamic model. In order to preserve the existing level of simplicity, KP and KV, the correction factors of the potential and vortex force models, were rebuilt as functions of J and α. The estimations were nearly identical to direct force/moment measurements which were obtained from both artificial and practical wingbeat motions of a hawkmoth. The model effectively compensated for the influences of J, particularly showing outstanding moment estimation capabilities. With this model, we found that using a lower value of α during the downstroke would be an effective strategy for generating adequate lift in forward flight. The rotational force and moment components had noticeable portions generating both thrust and counteract pitching moment during pronation. In the upstroke phase, the added mass component played a major role in generating thrust in forward flight. The proposed model would be useful for a better understanding of flight stability, control, and the dynamic characteristics of flapping wing flyers, and for designing flapping-wing micro air vehicles.

Fatigue Damage of Vertical Rigid Risers due to In-Line Vortex Induced Vibration in Nigeria Shallow Waters

In-line and Transverse Vortex Induced Vibrations (VIV) pose potential Fatigue damage threat to Vertical Rigid Risers (VRR) even in the less volatile Nigeria Shallow Waters. In this paper, a typical VRR of 31.031m length clamped to a fixed jacket platform in 18.29m water depth was used while relevant metOcean data were used to simulate the environmental conditions. The process was statically and dynamically simulated using different wave spectra on Orcaflex platform. The results from JONSWAP spectra showed a fatigue damage value of 102.5 x 10-5 due to in-line VIV which is greater than 29.1 x 10-5 due to transverse VIV. The results from the Ochi-Hubble spectra indicate a fatigue damage value of 96.2 x 10-5 due to in-line VIV which is greater than 7.03 x 10-5 due to transverse VIV. Also, the in-line vortex force (VF) analysis on the VRR for the JONSWAP spectra showed VF range, beginning from the touchdown point (TDP) to the unstraked region (UR), of 0.16 - 0.34kN/m; 0.01 - 0.53kN/m; and 0 - 0.85kN/m at End A (0m); 8.74m and 21.00m, respectively. Whereas, for the Ochi-Hubble spectra, VF range, from TDP to the UR, of 0.16 - 0.302kN/m; 0.018 - 0.56kN/m; 0 - 1.42kN/m at End A (0m); 8.74m and 21.00m, respectively, were obtained. The results for both spectra showed zero in-line VF on the VRR at 23.69m, 26.21m and End B (31.031m). Hence, fatigue damage and VF due to in-line VIV is important from the TDP to most parts of the UR on the VRR irrespective of the wave spectra and requires proper analysis in riser designs.

Asymptotically solvable model for a solitonic vortex in a compressible superfluid

Vortex motion is a complex problem due to the interplay between the short-range physics at the vortex core level and the long-range hydrodynamical effects. Here we show that the hydrodynamic equations of vortex motion in a compressible superfluid can be solved asymptotically in a model ‘slab’ geometry. Starting from an exact solution for an incompressible fluid, the hydrodynamic equations are solved with a series expansion in a small tunable parameter provided by the ratio of the healing length, characterising the vortex cores, to the slab width. The key dynamical properties of the vortex, the inertial and physical masses, are well defined and renormalizable. They are calculated at leading order beyond the logarithmic accuracy that has limited previous approaches. Subtracting the asymptotic solutions of the universal hydrodynamic problem from experimental observations of vortex motion exposes the physics of the vortex core and provides a window into interesting many-body phenomena that are currently poorly understood including the role of quantum pressure. Our results provide a solid framework for further detailed study of the vortex mass and vortex forces in strongly correlated and exotic superfluids.

Effect of bed vicinity on vortex shedding and force coefficients of fluid flow on an offshore pipeline

The effect of rigid bed proximity on flow parameters and hydrodynamic loads in offshore pipelines exposed to turbulent flow is investigated numerically. The Galerkin finite volume method is employed to solve the unsteady incompressible 2D Navier–Stokes equations. The large eddy simulation turbulence model is solved using the artificial compressibility method and dual time-stepping approach. The proposed algorithm is developed for a wide range of turbulent flows with Reynolds numbers of 9500 to 1.5×104. Evaluation of the developed numerical model shows that the proposed technique is capable of properly predicting hydrodynamic forces and simulating the flow pattern. The obtained results show that the lift and drag coefficients are strongly affected by the gap ratio. The mean drag coefficient slightly increases as the gap ratio increases, although the mean lift coefficient rapidly decreases. The vortex shedding suppression happen at the gap ratio of less than 0.2.

A coupled wave-hydrodynamic model of an atoll with high friction: Mechanisms for flow, connectivity, and ecological implications

We present a hydrodynamic analysis of an atoll system from modeling simulations using a coupled wave and three-dimensional hydrodynamic model (COAWST) applied to Palmyra Atoll in the Central Pacific. This is the first time the vortex force formalism has been applied in a highly frictional reef environment. The model results agree well with field observations considering the model complexity in terms of bathymetry, bottom roughness, and forcing (waves, wind, metrological, tides, regional boundary conditions), and open boundary conditions. At the atoll scale, strong regional flows create flow separation and a well-defined wake, similar to 2D flow past a cylinder. Circulation within the atoll is typically forced by waves and tides, with strong waves from the north driving flow from north to south across the atoll, and from east to west through the lagoon system. Bottom stress is significant for depths less than about 60m, and in addition to the model bathymetry, is important for correct representation of flow in the model. Connectivity within the atoll system shows that the general trends follow the mean flow paths. However, some connectivity exists between all regions of the atoll system due to nonlinear processes such as eddies and tidal phasing. Moderate wave stress, short travel time (days since entering the reef system), and low temperature appear to be the most ideal conditions for high coral cover at this site.

Observations and 3D hydrodynamics-based modeling of decadal-scale shoreline change along the Outer Banks, North Carolina

Long-term decadal-scale shoreline change is an important parameter for quantifying the stability of coastal systems. The decadal-scale coastal change is controlled by processes that occur on short time scales (such as storms) and long-term processes (such as prevailing waves). The ability to predict decadal-scale shoreline change is not well established and the fundamental physical processes controlling this change are not well understood. Here we investigate the processes that create large-scale long-term shoreline change along the Outer Banks of North Carolina, an uninterrupted 60km stretch of coastline, using both observations and a numerical modeling approach. Shoreline positions for a 24-yr period were derived from aerial photographs of the Outer Banks. Analysis of the shoreline position data showed that, although variable, the shoreline eroded an average of 1.5m/yr throughout this period. The modeling approach uses a three-dimensional hydrodynamics-based numerical model coupled to a spectral wave model and simulates the full 24-yr time period on a spatial grid running on a short (second scale) time-step to compute the sediment transport patterns. The observations and the model results show similar magnitudes (O(105m3/yr)) and patterns of alongshore sediment fluxes. Both the observed and the modeled alongshore sediment transport rates have more rapid changes at the north of our section due to continuously curving coastline, and possible effects of alongshore variations in shelf bathymetry. The southern section with a relatively uniform orientation, on the other hand, has less rapid transport rate changes. Alongshore gradients of the modeled sediment fluxes are translated into shoreline change rates that have agreement in some locations but vary in others. Differences between observations and model results are potentially influenced by geologic framework processes not included in the model. Both the observations and the model results show higher rates of erosion (∼−1m/yr) averaged over the northern half of the section as compared to the southern half where the observed and modeled averaged net shoreline changes are smaller (<0.1m/yr). The model indicates accretion in some shallow embayments, whereas observations indicate erosion in these locations. Further analysis identifies that the magnitude of net alongshore sediment transport is strongly dominated by events associated with high wave energy. However, both big- and small- wave events cause shoreline change of the same order of magnitude because it is the gradients in transport, not the magnitude, that are controlling shoreline change. Results also indicate that alongshore momentum is not a simple balance between wave breaking and bottom stress, but also includes processes of horizontal vortex force, horizontal advection and pressure gradient that contribute to long-term alongshore sediment transport. As a comparison to a more simple approach, an empirical formulation for alongshore sediment transport is used. The empirical estimates capture the effect of the breaking term in the hydrodynamics-based model, however, other processes that are accounted for in the hydrodynamics-based model improve the agreement with the observed alongshore sediment transport.

A vortex force study for a flat plate at high angle of attack

The vortex force is studied for a flat plate at arbitrarily large angle of attack. A suitable vortex force approach, adapted from a previous work, is used to study the vortex force and to build a vortex force line map to identify the force effect of any potential vortex. This map can be used exactly for a potential point vortex and approximately for a concentrated leading-edge vortex (LEV) or trailing-edge vortex (TEV); the latter are shown to have a non-potential vortex core. By means of this map, we identify a force-producing critical region, due to pressure suction, above the front and rear parts of the plate for an LEV and a TEV, respectively. The impulsively started flow problem is used as an application, with validation by computational fluid dynamics. The force variation in time is decomposed into four repeatable stages (force release, force enhancement, stall and force recovery) in close relation to the individual and combined effect by an LEV and a TEV. A pressure distribution analysis shows that force enhancement is due to pressure suction by an LEV, while stall and force recovery are respectively due to the upwash effect (which reduces the pressure below the plate) of a new TEV right off the plate and the pressure suction of this TEV having now moved above the plate. A viscous effect causes a small-amplitude oscillation on the force curves by promoting multiple small-scale LEVs.

On theories dealing with the interaction of surface waves and ocean circulation

ABSTRACTThe classic theory for the interaction of surface gravity waves and the general ocean circulation entails the so‐called wave radiation stress terms in the phase‐averaged momentum equation. The equations of motion are for the combined Eulerian current and Stokes drift. On the other hand, a more recent approach includes the so‐called vortex force term in the momentum equation wherein the only wave property is Stokes drift. The equations of motion are for the Eulerian current. The idea has gained traction in the ocean science community, a fact that motivates this paper. A question is: can both theories be correct? This paper answers the question in the negative and presents arguments in favor of the wave radiation theory. The vortex force approach stems from an interesting mathematical construct, but it does stand up to physical or mathematical scrutiny as described in this paper. Although not the primary focus of the paper, some discussion of Langmuir circulation is included since the vortex force was first introduced as the basis of this oceanic cellular phenomenon. Finaly the paper explains the difference in the derivation of the radiation stress theory and the vortex force theory: the later theory entails errors related to its use of curl and reverse‐curl [or uncurl] processes.