Wave-induced Circulation Research Articles

On the Tropospheric Response to Transient Stratospheric Momentum Torques

Abstract An idealized model is used to examine the tropospheric response to sudden stratospheric warmings (SSWs), by imposing transient stratospheric momentum torques tailored to mimic the wave-forcing impulse associated with spontaneously occurring SSWs. Such an approach enables us to examine both the ∼2–3-week forcing stage of an SSW during which there is anomalous stratospheric wave-activity convergence, as well as the recovery stage during which the wave forcing abates and the stratosphere radiatively recovers over 2–3 months. It is argued that applying a torque is better suited than a heating perturbation for examining the response to SSWs, due to the meridional circulation that is induced to maintain thermal-wind balance (i.e., the “Eliassen adjustment”); an easterly torque yields downwelling at high latitudes and equatorward flow below, similar to the wave-induced circulation that occurs during spontaneously occurring SSWs, whereas a heating perturbation yields qualitatively opposite behavior and thus cannot capture the initial SSW evolution. During the forcing stage, the meridional circulation in response to an impulse comparable to the model’s internal variability is able to penetrate down to the surface and drive easterly-wind anomalies via Coriolis torques acting on the anomalous equatorward flow. During the recovery stage, after which the tropospheric flow has already responded, the meridional circulation associated with the stratosphere’s radiative recovery appears to provide the persistent stratospheric forcing that drives the high-latitude easterly anomalies, whereas planetary waves are found to play a smaller role. This is then augmented by synoptic-wave feedbacks that drive and amplify the annular-mode response.

Some Fundamental Results for Cyclorotor Wave Energy Converters for Optimum Power Capture

Cyclorotor-based wave energy converters (WECs) present a relatively new and innovative paradigm for wave energy harvesting. Their operational principle is based on the generation of lift forces on the rotating hydrofoils due to their interaction with wave-induced circulation of water particles. As a result, relatively little is known about their optimal operation. To date, cyclorotor device performance has been measured by the power of waves radiated by the WEC, while a constant rotational velocity, consistent with the wave frequency, is employed. In this note we show (a) that variation of the cyclorotor velocity within the incoming monochromatic wave period significantly increases the generated mechanical power, while (b) optimising wave cancellation is at odds with the maximisation of shaft power. To optimise shaft power, the letter adopts a multi-harmonic solution for variable cyclorotor rotation rate, inspired by methods developed in other WEC domains.

Assessing Wave Attenuation With Rising Sea Levels for Sustainable Oyster Reef-Based Living Shorelines

In densely populated coastal areas with sea-level rise (SLR), protecting the shorelines against erosion due to the wave impact is crucial. Along with many engineered structures like seawalls and breakwaters, there are also green structures like constructed oyster reefs (CORs) that can not only attenuate the incident waves but also grow and maintain pace with SLR. However, there is a lack of data and understanding of the long-term wave attenuation capacity of the living shoreline structures under SLR. In this study, we used the phase-resolving Boussinesq model, FUNWAVE-TVD, to examine the hydrodynamics including wave height and wave-induced currents around the CORs in the Gandys Beach living shoreline project area in the upper Delaware Bay, United States. Waves were measured at six locations (offshore to onshore, with and without CORs) in the Gandys Beach living shoreline project area for two winter months, during which four nor’easters occurred. We selected three cases that represent prevailing wind, wave, and tide conditions to examine the fine spatial and temporal changes in wave height and current velocity by the construction of the reefs. Wave heights and wave energy spectra generated from FUNWAVE-TVD were then validated with field observations. It is found that FUNWAVE-TVD is capable of simulating waves and associated hydrodynamic processes that interact with CORs. The model results show that wave attenuation rates vary with the incident wave properties and water depth, and wave-induced circulation patterns are affected by the CORs. The wave attenuation capacity of CORs over the next 100 years was simulated with the incorporation of the oyster reef optimal growth zone. Our study found that sustainable wave attenuation capacity can only be achieved when suitable habitat for COR is provided, thus it can vertically grow with SLR. Suitable habitat includes optimal intertidal inundation duration, current velocity for larval transport and settlement, on-reef oyster survival and growth, and other environmental conditions including salinity, temperature, and nutrient availability. Furthermore, the model results suggest that it would take CORs approximately 9 years after construction to reach and maintain the maximum wave attenuation capacity in sustainable living shorelines.

Implementation and comparison of the recent three-dimensional radiation stress theory and vortex-force formalism in an unstructured-grid coastal circulation model

Given the importance of wave–current interaction in estuarine and coastal dynamics, it is crucial to revisit impacts of surface gravity waves on three-dimensional (3D) nearshore circulation. This work investigates wave-induced circulation in three typical coastal systems including an idealized inlet and planar and natural barred beaches, by implementing the recent 3D radiation stress (RS) theory and vortex-force (VF) formalism to an unstructured-grid Finite-Volume Community Ocean Model (FVCOM). In the idealized inlet case, 3D RS generated appreciable currents near barriers and lateral boundaries while VF forced strong flows via breaking and roller-induced accelerations in front of the inlet. Both simulations indicate vertically varying wave-induced circulation that decreases markedly. In the planar beach with obliquely incident waves, both methods successfully produced surface onshore and bottom undertow, as well as the wave breaking and roller-induced longshore currents. Nevertheless, 3D RS generated unrealistic offshore currents close to the shoreline. The coupled models were validated against observations in the natural barred beach, and results indicate that the 3D RS model agrees slightly better with the observed longshore currents while 3D VF captures the vertical shear of the onshore–offshore flows reasonably. Further investigations suggest that both methods produce the wave breaking-induced surface onshore and bottom undertow successfully, yet they are located further offshore resulting from the 3D RS-induced unrealistic offshore currents. Successful implementations of the paired wave–current theories to the unstructured model would be fundamental and beneficial to the coastal ocean modeling community.

Applicability of Multi-layer Wave Model for Prediction of Circulating Current Field Around a Submerged Breakwater

Submerged breakwaters have become an appealing alternative for conventional shore protection structures due to their lower impact on the coastal landscape. These structures however cause more complicated wave-induced circulation currents and, as a result, often fail to meet the expected coastal protective functions. Although previous studies have applied two-dimensional-horizontal (2DH) nearshore current models and quasi-three-dimensional (Q3D) models with different wave-breaking and surface roller models for prediction of the circulation currents around submerged breakwaters, most of these models have failed to reproduce the observed circulation current patterns accurately. The objective of this study is therefore to investigate the applicability of multilayer nonlinear dispersive model to predict circulation current patterns under different incident wave conditions. The recently developed SWASH model was applied to a unique set of laboratory experiments, and the effect of the multilayer model was investigated. According to the experimental observations both near-bottom and near-surface mean current patterns are highly sensitive to the incident wavelength. The two-layer mode was able to reasonably capture the variation in current patterns for different wave periods, while the one-layer mode significantly underestimated the current velocities and failed to represent the dependency of the circulation current patterns on incident wavelengths.

The wave-current interaction in the coastal area

In our investigation of the effect of wind-waves on barotropic mean flow in coastal areas, we compare two methods for calculating wave-induced force. The wave field is simulated by the nearshore spectral wave model SWAN. The wave-induced force (calculated using the radiation stress gradient and dissipation methods) and the Stokes drift are integrated in the COHERENS circulation model in the depth-averaged mode. The coupled set is validated using well-known academic test cases of planar beach and single-barred beach. Finally, in a two-dimensional test case based on Belgian coastal waters we compare simulations of mean flow using the two methods of calculating waveinduced force against field data.<br/> We show clearly that the two methods for calculation of wave-induced force yield very different results even in depth-averaged mode, depending on the angle of incident wave. Simulation of waveinduced circulation using the wave dissipation approach gives better results than using the radiation stress gradient approach. This is clearly visible for strong wave conditions in which the wind is blowing almost parallel to the shore. Under these conditions, the white-capping type of wave breaking is the dominant dissipation mechanism; in the radiation stress gradient, the dissipation signal is not visible, because the energy loss in the spectrum is compensated by wind input.

Decoupling between Precipitation Processes and Mountain Wave Induced Circulations Observed with a Vertically Pointing K-Band Doppler Radar

Recent studies reported that precipitation and mountain waves induced low tropospheric level circulations may be decoupled or masked by greater spatial scale variability despite generally there is a connection between microphysical processes of precipitation and mountain driven air flows. In this paper we analyse two periods of a winter storm in the Eastern Pyrenees mountain range (NE Spain) with different mountain wave induced circulations and low-level turbulence as revealed by Micro Rain Radar (MRR), microwave radiometer and Parsivel disdrometer data during the Cerdanya-2017 field campaign. We find that during the event studied mountain wave wind circulations and low-level turbulence do not affect neither the snow crystal riming or aggregation along the vertical column nor the surface particle size distribution of the snow. This study illustrates that precipitation profiles and mountain induced circulations may be decoupled which can be very relevant for either ground-based or spaceborne remote sensing of precipitation.

DESIGN AND PHYSICAL MODEL STUDIES OF INNOVATIVE LIVING BREAKWATERS

This paper describes two separate but closely related physical models conducted to support the detailed design of the Living Breakwaters project located in Raritan Bay, New York. One study focused on optimizing and verifying the breakwater design elements to ensure they were well adapted to typical and extreme conditions, while the second study focused on verifying the overall performance of multiple living breakwaters in terms of wave attenuation and impacts on nearshore wave-induced circulation. These investigations generated a large quantity of valuable information concerning the design and performance of the breakwaters that will be used to optimize and support the final design and obtain the necessary permits required for construction.

Impacts of wave-induced circulation in the surf zone on wave setup

Wave setup corresponds to the increase in mean water level along the coast associated with the breaking of short-waves and is of key importance for coastal dynamics, as it contributes to storm surges and the generation of undertows. Although overall well explained by the divergence of the momentum flux associated with short waves in the surf zone, several studies reported substantial underestimations along the coastline. This paper investigates the impacts of the wave-induced circulation that takes place in the surf zone on wave setup, based on the analysis of 3D modelling results. A 3D phase-averaged modelling system using a vortex force formalism is applied to hindcast an unpublished field experiment, carried out at a dissipative beach under moderate to very energetic wave conditions (Hm0=6m at breaking and Tp=22s). When using an adaptive wave breaking parameterisation based on the beach slope, model predictions for water levels, short waves and undertows improved by about 30%, with errors reducing to 0.10 m, 0.10 m and 0.09 m/s, respectively. The analysis of model results suggests a very limited impact of the vertical circulation on wave setup at this dissipative beach. When extending this analysis to idealized simulations for different beach slopes ranging from 0.01 to 0.05, it shows that the contribution of the vertical circulation (horizontal and vertical advection and vertical viscosity terms) becomes more and more relevant as the beach slope increases. In contrast, for a given beach slope, the wave height at the breaking point has a limited impact on the relative contribution of the vertical circulation on the wave setup. For a slope of 0.05, the contribution of the terms associated with the vertical circulation accounts for up to 17% (i.e. a 20% increase) of the total setup at the shoreline, which provides a new explanation for the underestimations reported in previously published studies.

Formation of Two-Dimensional Circulation in Response to Unsteady Wave Forcing in the Middle Atmosphere

In previous studies, a steady-state assumption has been frequently used for the analysis of wave-induced meridional circulation. In general, however, the wave forcing is not constant and thus induced circulation can vary in time. Thus, to understand such transient behaviors, time evolutions of a slow variable describing balanced flows and two fast variables describing gravity waves and flows that are slaved to balanced flows are investigated. A Boussinesq equation system is used to examine zonal-mean flow responses to unsteady zonally uniform forcing. Green’s function is used to analytically obtain the evolution of meridional circulation. Responses to zonal wave forcing are mainly examined although responses to a diabatic heating and to wave forcing are discussed in brief. For forcing with a step function shape in time, gravity waves are radiated as a transient response. The time needed to form the circulation depends on the aspect ratio (i.e., latitudinal to vertical lengths) of wave forcing, which determines the group velocity of gravity waves. When the forcing time scale is longer than the inertial period, the response does not include gravity wave radiation and mainly involves a meridional circulation, which is similar to the solution for steady forcing. The two-celled meridional circulation describes the early stage response to the forcing and can be used to examine how the wave forcing is distributed to zonal wind acceleration and Coriolis torque. It is shown that the distribution depends on the aspect ratio of the forcing.

An Integrated Numerical Model for the Design of Coastal Protection Structures

In the present work, an integrated coastal engineering numerical model is presented. The model simulates the linear wave propagation, wave-induced circulation, and sediment transport and bed morphology evolution. It consists of three main modules: WAVE_L, WICIR, and SEDTR. The nearshore wave transformation module WAVE_L (WAVE_Linear) is based on the hyperbolic-type mild slope equation and is valid for a compound linear wave field near coastal structures where the waves are subjected to the combined effects of shoaling, refraction, diffraction, reflection (total and partial), and breaking. Radiation stress components (calculated from WAVE_L) drive the depth averaged circulation module WICIR (Wave Induced CIRculation) for the description of the nearshore wave-induced currents. Sediment transport and bed morphology evolution in the nearshore, surf, and swash zone are simulated by the SEDTR (SEDiment TRansport) module. The model is tested against experimental data to study the effect of representative coastal protection structures and is applied to a real case study of a coastal engineering project in North Greece, producing accurate and consistent results for a versatile range of layouts.

Three-dimensional unstructured modelling of wave-induced circulation over a plane and irregular beach

Nearshore currents have a complicated circulation structure over a beach due to the mutual interaction between waves and currents. To investigate the wave-induced circulation over a beach, a three-dimensional unstructured model accounting for the combined actions of waves and currents is established. The wave distribution over the beach is computed by a wave model and the depth-dependent wave radiation stresses with the surface roller are employed in the hydrodynamic model. The present model takes the mixing coefficients and the bottom shear stress under waves and currents into account. To evaluate the three-dimensional unstructured model, the laboratory experiments over a plane and irregular beach are used to test the performance of the model. The undertow over a plane beach is well reproduced and the vertical variability is captured. The performance of the model over an irregular beach is well displayed in the reproduction of pairs of counter-rotating primary circulations at the embayment troughs. Meanwhile, the secondary circulations are observed in the swash zone. The model captures the circulation systems over a beach and the circulation structures of the wave-induced currents are well exhibited.

Significance of Wave and Tide Induced Circulation in Development of a Fishery Harbour

Waves and tide play important role in the design of a harbour layout. A fishing harbour located at Kerala Coast influenced by tidal currents and wave action due to its shape was studied using 2D mathematical model. The nearshore currents are mainly governed by action of waves. The wave induced currents in the area are mainly in southward direction along the coast. The effect of waves and tidal currents has caused sedimentation inside the harbour. The response of the harbour with respect to variation in tidal heights, currents and wave actions has been studied to optimize the port layout. In this paper, hydrodynamic circulations in the vicinity of the harbour mouth and in the harbour basin resulting due to the combined effect of waves and tides has been studied to assess sedimentation in the region. The layout, which causes minimum circulation in the vicinity of harbour area, is recommended as it is likely to cause lesser sedimentation in the region. A substantial savings in the cost of harbour layout was achieved by reducing the breakwater lengths by 620 m, which provided same effectiveness in restricting sedimentation in the harbour.

Development of a numerical 2-dimensional beach evolution model

This paper presents the description of a 2-dimensional numerical model constructed for the simulation of beach evolution under the action of wind waves only over the arbitrary land and sea topographies around existing coastal structures and formations. The developed beach evolution numerical model is composed of 4 submodels: a nearshore spectral wave transformation model based on an energy balance equation including random wave breaking and diffraction terms to compute the nearshore wave characteristics, a nearshore wave-induced circulation model based on the nonlinear shallow water equations to compute the nearshore depth-averaged wave-induced current velocities and mean water level changes, a sediment transport model to compute the local total sediment transport rates occurring under the action of wind waves, and a bottom evolution model to compute the bed level changes in time based on the gradients of sediment transport rates in cross-shore and longshore directions. The developed models are applied successfully to the SANDYDUCK field experiments and to some conceptual benchmark cases including simulation of rip currents around beach cusps, beach evolution around a single shore perpendicular groin, and a series of offshore breakwaters. The numerical model gave results in agreement with the measurements both qualitatively and quantitatively and reflected the physical concepts well for the selected conceptual cases.

Two-Dimensional Depth-Averaged Beach Evolution Modeling: Case Study of the Kızılırmak River Mouth, Turkey

This study presents an application of a two-dimensional beach evolution model to a shoreline change problem at the Kızılırmak River mouth, which has been facing severe coastal erosion problems for more than 20 years. The shoreline changes at the Kızılırmak River mouth have been thus far investigated by satellite images, physical model tests, and one-dimensional numerical models. The current study uses a two-dimensional depth-averaged numerical beach evolution model, developed based on existing methodologies. This model is mainly composed of four main submodels: a phase-averaged spectral wave transformation model, a two-dimensional depth-averaged numerical wave-induced circulation model, a sediment transport model, and a bottom evolution model. To validate and verify the numerical model, it is applied to several cases of laboratory experiments. Later, the model is applied to a shoreline change problem at the groin field to the east of the Kızılırmak River mouth at the Bafra alluvial plain. The results of the numerical model agree with the existing laboratory and field measurements.

Numerical simulation of wave-induced morphology evolution

This paper presents an integrated coastal engineering numerical model. The model simulates the linear wave propagation, wave-induced circulation, sediment transport and bed morphology evolution. The model consists of three main modules: Wave-LS, Wave-L and Coast. The large-scale module Wave-LS is based on the numerical solution of the directional wave energy balance equation. The near-shore wave transformation module Wave-L is based on the hyperbolic-type mild slope equation and is valid for a compound wave field near coastal structures where the waves are subjected to the combined effects of shoaling, refraction, diffraction, reflection (total and partial) and breaking. Radiation stress components (estimated from the large-scale module as well as from the hyperbolic wave module) drive the depth-averaged circulation module Coast for the description of the near-shore currents and sediment transport in the surf and swash zone. The module Coast is coupled with a three-dimensional bed evolution module to predict coastal bathymetry changes.

Storm-induced readjustment of an embayed beach after modification by protection works

This paper examines storm-induced morphological and hydrodynamic changes after a submerged and a detached breakwater were constructed at La Barceloneta beach (Barcelona, NW Mediterranean) in 2006–2007. The shoreline configurations before and after beach nourishment and the construction of the protective structures were compared using a video dataset comprising 29 storm events spanning the pre- (2001 to 2005, n = 17) and the post-breakwater situation (2006 to 2011, n = 12), and hydrodynamic modelling based on the SMC coastal modelling system. As a result of the protection works, La Barceloneta was subdivided into two beaches separated by an artificial salient. The analysis of shoreline response to storms has been improved by using the shoreline hyperbolic tangent fit to represent the beach planform. Comparing the pre- and post-breakwater situations on the basis of these shoreline fits facilitated the identification of beach rotation processes because interference by smaller-scale morphological features was eliminated (e.g. the formation, changes in shape or migration of mega-cusps). In the current post-breakwater situation, there is evidence for a change in the behaviour of the north-eastern beach triggered by the submerged breakwater built in 2007. Furthermore, a counter-clockwise beach rotation has occurred at the north-eastern beach, whereas the south-western beach has experienced a clockwise beach rotation. This morphodynamic behaviour is caused by a new, complex wave-induced circulation system comprising two dominant alongshore currents flowing in opposite directions. In contrast to the pre-breakwater situation, the alongshore component of the radiation stress does not accomplish beach rotation in the post-breakwater situation.

SPH MODELING OF MEAN VELOCITY CIRCULATION IN A RIP CURRENT SYSTEM

A Lagrangian numerical model called Smoothed Particle Hydrodynamics is used to analyze rip current system generated by a single bar and a rip channel. The pattern of the wave-induced circulation cell over the bar, the oppositely-rotating circulation cell on-shore and a strong seaward-directed current in the rip channel is modeled numerically. The mean horizontal variations of rip current system as well as three-dimensional circulations are studied. The results in three-dimensional space reveal the wave-current interaction and flow patterns in different parts of rip channel, bar, and the trough located near shore. For comparison to experimental data, Eulerian nodes are introduced to the numerical model and SPH interpolation over neighboring Lagrangian particles is implemented to find fluid parameters at those specific nodes. This methodology leads to a better understanding of depth-integrated flows and a more accurate comparison of numerical results with experimental results. Model predictions are compared to laboratory measurements of Drønen et al. (2002) and show good agreement, including mean velocity profiles, mean surface elevation and three-dimensional velocity components.

Mass-Weighted Isentropic Zonal Mean Equatorward Flow in the Northern Hemispheric Winter

In the diagnosis of mass-weighted isentropic zonal mean (MIM), the mean- meridional circulation has a strong extratropical direct (ETD) cell in the northern- hemispheric winter, which turns from downward to equatorward around 45°N and isentropic zonal mean pressure of 850 hPa. The January mean equatorward flow in the extratopical lower troposphere is almost in balance with Eliassen-Palm (E-P) flux divergence for both climatology and interannual variability. This means that the zonal mean equatorward flow in the extratropical lower troposphere is the wave-induced circulation as well as the poleward flow in the stratosphere is.The interannual variation of January mean mass stream functions at (45°N, 850 hPa) positively (negatively) correlates with the zonal mean temperature in the lower troposphere north (south) of about 45°N, respectively. This is consistent with a simple thermodynamic consideration that the strong ETD circulation adiabatically warms up the lower troposphere due to the descending flow in the higher latitudes but cools it down due to the heat advection by the equatorward flow in the middle latitudes (∼35°N).

Three-dimensional simulation of wave-induced circulation: Comparison of three radiation stress formulations

[1] A three-dimensional current-wave modeling system, Curvilinear-grid Hydrodynamics 3D (CH3D)-Simulating Waves Nearshore (SWAN), has been used to simulate wave-induced circulation and compare the performances of three radiation stress (RS) formulations: two depth-dependent formulations (M08 by Mellor (2008) and X04 by Xia et al. (2004)) and one depth-independent formulation (LHS by Longuet-Higgins and Stewart (1964)). While all are based on linear wave theory, LHS uses the vertically integrated equations of motion, and M08 and X04 consider the three-dimensional equations of motion. Results of CH3D-SWAN with three RS formulations are compared with steady state wave setup, observed data in an undertow experiment by Ting and Kirby (1994) (TK94), and observed data in a laboratory fringing reef. All three RS formulations reproduce the analytical solution of wave setup very well. Simulated wave-induced currents and turbulence for TK94 are the best when M08 is used and worst when X04 is used, apparently due to the errors in the X04 formulation. All three RS formulations give good simulation of wave setup in the fringing reef. Wave-induced currents in the fringing reef simulated by the three RS formulations are quite different: M08 produces a single large clockwise gyre in the x-z plane, LHS produces a weaker gyre, and X04 produces a clockwise gyre plus a counterclockwise gyre inside the surf zone. Using the CH3D-Storm Surge Modeling System and M08, storm surge and currents in the Outer Banks and Chesapeake Bay during Hurricane Isabel are simulated. Compared to the earlier simulation obtained with the LHS, M08 produces similar storm surge but slightly improved the wave-induced currents.