In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dyna... more In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dynamics. The numerical model solves the 2DH extended Boussinesq equations proposed by Madsen and Sørensen (1992) where nonlinear and dispersive effects are both relevant whereas it solves NSWE equations where nonlinearity prevails. The shock-capturing features of the finite volume method allow an intrinsic representation of wave breaking and runup; therefore no empirical (calibration) parameters are necessary. Comparison with laboratory measurements demonstrates that the proposed model can accurately predict wave height decay and mean water level setup, for both regular and solitary wave breaking on a sloping beach. The model is also applied to reproduce two-dimensional wave transformation and breaking over a submerged circular shoal, showing good agreement with experimental data.
A Boussinesq-type model is applied herein to study wave propagation and wave breaking over comple... more A Boussinesq-type model is applied herein to study wave propagation and wave breaking over complex bathymetries reproducing common coastal features, namely plane and barred beaches, submerged bars and rip channels. A hybrid finite volume–finite difference numerical scheme solves a set of, in the horizontal plane, two-dimensional extended Boussinesq equations where both nonlinear and dispersive effects are relevant and nonlinear shallow
The motion of shallow-water wave trains is studied in the laboratory in one space dimension and o... more The motion of shallow-water wave trains is studied in the laboratory in one space dimension and one time dimension (1+1). Our focus is on the nonlinear evolution of the wave trains as recorded at five spatially separated probes. Both the linear Fourier transform and the inverse scattering transform (IST}for the periodic Kortewegde Vries (KdV) equation are exploited in the analysis of the daia. IST provides a set of nonlinear basis functions, which are here computed for measured wave data and compared to the sinusoidal basis of the linear Fourier transform. We find that the scattering-transform mode amplitudes are nearly constants of the motion, while the Fourier modes vary substantially in space and time. The results suggest that the KdV equation more nearly describes the nonlinear evolution of the waves than does linear evolution.
This paper describes the application of a new data analysis procedure, which the authors refer to... more This paper describes the application of a new data analysis procedure, which the authors refer to as nonlinear Fourier analysis, to broad-banded surface waves measured in the laboratory. Using this approach a nonlinear surface wave train or wave field may be described as a linear superposition of nonlinearly interacting sine waves, Stokes waves, cnoidal weaves and solitons. The theory is based upon the spectral/scattering transform solution to the Korteweg-de Vries equation with periodic boundary conditions. It is shown how the method can be used to analyse broad-banded surface wave data described by the Pierson-Moskowitz spectrum. Certain nonlinear spectral components are interpreted in terms of radiation stress, a low frequency contribution to the spectrum induced by second order nonlinearities in the wave motion.
This paper deals with the use of submerged detached breakwaters as beach protection, a use that t... more This paper deals with the use of submerged detached breakwaters as beach protection, a use that today has become quite popular. This type of structure has been largely studied both theoretically and through experimental analyses in recent years, however its behaviour has not been completely understood, specially if related to the real irregular wave attacks. In particular some laboratory studies carried out by the authors have pointed out some interesting phenomena associated with the interaction between the nonlinearities of wave transformations in shallow water and submerged breakwaters. Aiming at discerning between the phenomena related to the structure (beach and breakwater) and flume geometry, a new series of laboratory tests have been carried out in a 50 m long wave flume; these tests and the results obtained are described in this work. Besides the study of the behaviour of submerged structures related to the bounded-long-waves, some current velocities have also been measured during this research through directional micro-propeller fluid meters.
In this paper, a shock-capturing numerical model, based on the combined solution of Boussinesq an... more In this paper, a shock-capturing numerical model, based on the combined solution of Boussinesq and nonlinear shallow water equations is validated with respect to the transformation, breaking and runup of irregular waves. Boussinesq equations are applied where dispersive and nonlinear effects are both relevant, assuring an appropriate description of wave propagation from intermediate to shallow waters. Nonlinear shallow water equations are used where dispersion is negligible; their shock-capturing features, exploited by the application of the finite volume method, enable an intrinsic representation of wave breaking and swash zone oscillations. No case by case calibration or tracking algorithms are required. Comparisons with experimental data show that the model is able to simulate wave height variations, mean water level setup, wave runup, and the generation of nearshore currents accurately.
A hybrid scheme composed of ÿnite-volume and ÿnite-di erence methods is introduced for the soluti... more A hybrid scheme composed of ÿnite-volume and ÿnite-di erence methods is introduced for the solution of the Boussinesq equations. While the ÿnite-volume method with a Riemann solver is applied to the conservative part of the equations, the higher-order Boussinesq terms are discretized using the ÿnitedi erence scheme. Fourth-order accuracy in space for the ÿnite-volume solution is achieved using the MUSCL-TVD scheme. Within this, four limiters have been tested, of which van-Leer limiter is found to be the most suitable. The Adams-Basforth third-order predictor and Adams-Moulton fourth-order corrector methods are used to obtain fourth-order accuracy in time. A recently introduced surface gradient technique is employed for the treatment of the bottom slope. A new model 'HYWAVE', based on this hybrid solution, has been applied to a number of wave propagation examples, most of which are taken from previous studies. Examples include sinusoidal waves and bi-chromatic wave propagation in deep water, sinusoidal wave propagation in shallow water and sinusoidal wave propagation from deep to shallow water demonstrating the linear shoaling properties of the model. Finally, sinusoidal wave propagation over a bar is simulated. The results are in good agreement with the theoretical expectations and published experimental results. Copyright ? 2005 John Wiley & Sons, Ltd.
This paper presents a study based on a second-order interpretation of wave ,,energy,, spectra, wh... more This paper presents a study based on a second-order interpretation of wave ,,energy,, spectra, which may explain the build-up of low-and high-frequency peaks for wave spectra measured in shallow water. A comparison between this interpretative model and laboratory data, which were obtained in a bidimensional wave flume, is also given in the paper.
... Marco Petti,1 Paul A. Quinn,2 Gianfranco Liberatore3 k William J. Easson4 ... This allowed th... more ... Marco Petti,1 Paul A. Quinn,2 Gianfranco Liberatore3 k William J. Easson4 ... This allowed the laser sheet in through the side of the flume, below the level of the beach and reflected it off an underwater mirror vertically up through a transparent strip in the beach into the flow. ...
Random wave tests were performed in a flume to investigate wave transformations above a submerged... more Random wave tests were performed in a flume to investigate wave transformations above a submerged bar built on a horizontal bottom. Wave data were analysed in the frequency and time domains. In the time domain, reference was made both to short (/>0.5/") and long waves (with /<0.5/ p). This allowed in particular investigation of transformations of long waves passing over the bar. Experimental results were interpreted using a second-order analytical model, able to separate first-and second-order components from given (measured) variance spectra. The analytical method proved to be conveniently applicable as long as breaking phenomena are not too intense.
Nell'ultimo decennio, lo studio dei fenomeni di mud-debris flow ha assunto un ruolo centrale ... more Nell'ultimo decennio, lo studio dei fenomeni di mud-debris flow ha assunto un ruolo centrale nel campo dell'ingegneria ambientale e questo a seguito di un crescente problema di dissesto idrogeologico che ha interessato numerose zone montane. La necessit\ue0, quindi, di mettere a punto strumenti di indagine che permettano un'analisi della propagazione e dell'arresto di tali fenomeni costituisce uno degli obbiettivi dell'ingegneria. In questo lavoro viene presentato un modello numerico basato sulle equazioni bidimensionali di De Saint Venant rielaborate sostituendo all'originale legame costitutivo newtoniano quello di Herschel-Bulkley. Associato a tali equazioni viene proposto un criterio di arresto, sempre di tipo bidimensionale, ritenuto adeguato alla dimensione del problema. Il metodo di integrazione utilizzato \ue8 ai volumi finiti mentre lo schema, attraverso un'opportuna scelta dei volumi di controllo, risulta di tipo semi implicito con una precisione...
In this paper, a shock-capturing numerical model, based on the combined solution of Boussinesq an... more In this paper, a shock-capturing numerical model, based on the combined solution of Boussinesq and nonlinear shallow water equations is applied to the simulation of wave runup, overtopping and wave train propagation over impermeable, emerged and low-crested, structures. In order to improve the performances of the scheme at wet-dry interfaces, a numerical treatment is introduced to provide well-balancing of advective fluxes and source terms. One-and two-dimensional test cases are presented to validate the performances of the model under both regular and irregular wave conditions.
International Journal of Offshore and Polar Engineering, 2000
This paper describes a study of the hydrodynamics in the swash zone using an impermeable concrete... more This paper describes a study of the hydrodynamics in the swash zone using an impermeable concrete beach in a laboratory flume. Analysis was made of the measurements achieved using level wave gauges and a laser Doppler velocimeter. From these measurements we could derive the mean motion and turbulence characteristics along the main flow direction in 3 vertical sections of the swash zone. Fluid velocity seems almost uniform along the vertical, especially during the up-rush; the behaviour of turbulence dynamics is a mixture of free turbulence generated during wave breaking and convected by the mean motion, and wall turbulence. This work covers analysis in the time and frequency domain, and discusses the turbulent properties of the flow field derived from our measurements.
This work presents a first application of an open source SPH model (DualSPHysics) to study the dy... more This work presents a first application of an open source SPH model (DualSPHysics) to study the dynamics of a debris flow, with reference to the dry debris flow of Alverà, close to Cortina d'Ampezzo (Belluno, Italy). In this part of the Dolomites, debris flows are usually formed by large boulders within the fluid matrix. The adopted Lagrangian approach has allowed to describe the relative motion of a boulder immersed in a fluid mixture. From the numerical results, it has been observed that the boulder travels a greater distance along the channels, when water drives it. On the other hand, without the water thrust, the same boulder would halt much earlier. Furthermore, in all the simulated cases, it has been observed that the boulder stops when a natural narrowing is encountered along the channel bed.
This paper reviews mainly conceptual models and experimental work, in the field and in the labora... more This paper reviews mainly conceptual models and experimental work, in the field and in the laboratory, dedicated during the last decades to studying turbulence of breaking waves and bores moving in very shallow water and in the swash zone. The phenomena associated with vorticity and turbulence structures measured are summarised, including the measurement techniques and the laboratory generation of breaking waves or of flow fields sharing several characteristics with breaking waves. The effect of air entrapment during breaking is discussed. The limits of the present knowledge, especially in modelling a two-or three-phase system, with air and sediment entrapped at high turbulence level, and perspectives of future research are discussed.
In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dyna... more In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dynamics. The numerical model solves the 2DH extended Boussinesq equations proposed by Madsen and Sørensen (1992) where nonlinear and dispersive effects are both relevant whereas it solves NSWE equations where nonlinearity prevails. The shock-capturing features of the finite volume method allow an intrinsic representation of wave breaking and runup; therefore no empirical (calibration) parameters are necessary. Comparison with laboratory measurements demonstrates that the proposed model can accurately predict wave height decay and mean water level setup, for both regular and solitary wave breaking on a sloping beach. The model is also applied to reproduce two-dimensional wave transformation and breaking over a submerged circular shoal, showing good agreement with experimental data.
A Boussinesq-type model is applied herein to study wave propagation and wave breaking over comple... more A Boussinesq-type model is applied herein to study wave propagation and wave breaking over complex bathymetries reproducing common coastal features, namely plane and barred beaches, submerged bars and rip channels. A hybrid finite volume–finite difference numerical scheme solves a set of, in the horizontal plane, two-dimensional extended Boussinesq equations where both nonlinear and dispersive effects are relevant and nonlinear shallow
The motion of shallow-water wave trains is studied in the laboratory in one space dimension and o... more The motion of shallow-water wave trains is studied in the laboratory in one space dimension and one time dimension (1+1). Our focus is on the nonlinear evolution of the wave trains as recorded at five spatially separated probes. Both the linear Fourier transform and the inverse scattering transform (IST}for the periodic Kortewegde Vries (KdV) equation are exploited in the analysis of the daia. IST provides a set of nonlinear basis functions, which are here computed for measured wave data and compared to the sinusoidal basis of the linear Fourier transform. We find that the scattering-transform mode amplitudes are nearly constants of the motion, while the Fourier modes vary substantially in space and time. The results suggest that the KdV equation more nearly describes the nonlinear evolution of the waves than does linear evolution.
This paper describes the application of a new data analysis procedure, which the authors refer to... more This paper describes the application of a new data analysis procedure, which the authors refer to as nonlinear Fourier analysis, to broad-banded surface waves measured in the laboratory. Using this approach a nonlinear surface wave train or wave field may be described as a linear superposition of nonlinearly interacting sine waves, Stokes waves, cnoidal weaves and solitons. The theory is based upon the spectral/scattering transform solution to the Korteweg-de Vries equation with periodic boundary conditions. It is shown how the method can be used to analyse broad-banded surface wave data described by the Pierson-Moskowitz spectrum. Certain nonlinear spectral components are interpreted in terms of radiation stress, a low frequency contribution to the spectrum induced by second order nonlinearities in the wave motion.
This paper deals with the use of submerged detached breakwaters as beach protection, a use that t... more This paper deals with the use of submerged detached breakwaters as beach protection, a use that today has become quite popular. This type of structure has been largely studied both theoretically and through experimental analyses in recent years, however its behaviour has not been completely understood, specially if related to the real irregular wave attacks. In particular some laboratory studies carried out by the authors have pointed out some interesting phenomena associated with the interaction between the nonlinearities of wave transformations in shallow water and submerged breakwaters. Aiming at discerning between the phenomena related to the structure (beach and breakwater) and flume geometry, a new series of laboratory tests have been carried out in a 50 m long wave flume; these tests and the results obtained are described in this work. Besides the study of the behaviour of submerged structures related to the bounded-long-waves, some current velocities have also been measured during this research through directional micro-propeller fluid meters.
In this paper, a shock-capturing numerical model, based on the combined solution of Boussinesq an... more In this paper, a shock-capturing numerical model, based on the combined solution of Boussinesq and nonlinear shallow water equations is validated with respect to the transformation, breaking and runup of irregular waves. Boussinesq equations are applied where dispersive and nonlinear effects are both relevant, assuring an appropriate description of wave propagation from intermediate to shallow waters. Nonlinear shallow water equations are used where dispersion is negligible; their shock-capturing features, exploited by the application of the finite volume method, enable an intrinsic representation of wave breaking and swash zone oscillations. No case by case calibration or tracking algorithms are required. Comparisons with experimental data show that the model is able to simulate wave height variations, mean water level setup, wave runup, and the generation of nearshore currents accurately.
A hybrid scheme composed of ÿnite-volume and ÿnite-di erence methods is introduced for the soluti... more A hybrid scheme composed of ÿnite-volume and ÿnite-di erence methods is introduced for the solution of the Boussinesq equations. While the ÿnite-volume method with a Riemann solver is applied to the conservative part of the equations, the higher-order Boussinesq terms are discretized using the ÿnitedi erence scheme. Fourth-order accuracy in space for the ÿnite-volume solution is achieved using the MUSCL-TVD scheme. Within this, four limiters have been tested, of which van-Leer limiter is found to be the most suitable. The Adams-Basforth third-order predictor and Adams-Moulton fourth-order corrector methods are used to obtain fourth-order accuracy in time. A recently introduced surface gradient technique is employed for the treatment of the bottom slope. A new model 'HYWAVE', based on this hybrid solution, has been applied to a number of wave propagation examples, most of which are taken from previous studies. Examples include sinusoidal waves and bi-chromatic wave propagation in deep water, sinusoidal wave propagation in shallow water and sinusoidal wave propagation from deep to shallow water demonstrating the linear shoaling properties of the model. Finally, sinusoidal wave propagation over a bar is simulated. The results are in good agreement with the theoretical expectations and published experimental results. Copyright ? 2005 John Wiley & Sons, Ltd.
This paper presents a study based on a second-order interpretation of wave ,,energy,, spectra, wh... more This paper presents a study based on a second-order interpretation of wave ,,energy,, spectra, which may explain the build-up of low-and high-frequency peaks for wave spectra measured in shallow water. A comparison between this interpretative model and laboratory data, which were obtained in a bidimensional wave flume, is also given in the paper.
... Marco Petti,1 Paul A. Quinn,2 Gianfranco Liberatore3 k William J. Easson4 ... This allowed th... more ... Marco Petti,1 Paul A. Quinn,2 Gianfranco Liberatore3 k William J. Easson4 ... This allowed the laser sheet in through the side of the flume, below the level of the beach and reflected it off an underwater mirror vertically up through a transparent strip in the beach into the flow. ...
Random wave tests were performed in a flume to investigate wave transformations above a submerged... more Random wave tests were performed in a flume to investigate wave transformations above a submerged bar built on a horizontal bottom. Wave data were analysed in the frequency and time domains. In the time domain, reference was made both to short (/>0.5/") and long waves (with /<0.5/ p). This allowed in particular investigation of transformations of long waves passing over the bar. Experimental results were interpreted using a second-order analytical model, able to separate first-and second-order components from given (measured) variance spectra. The analytical method proved to be conveniently applicable as long as breaking phenomena are not too intense.
Nell'ultimo decennio, lo studio dei fenomeni di mud-debris flow ha assunto un ruolo centrale ... more Nell'ultimo decennio, lo studio dei fenomeni di mud-debris flow ha assunto un ruolo centrale nel campo dell'ingegneria ambientale e questo a seguito di un crescente problema di dissesto idrogeologico che ha interessato numerose zone montane. La necessit\ue0, quindi, di mettere a punto strumenti di indagine che permettano un'analisi della propagazione e dell'arresto di tali fenomeni costituisce uno degli obbiettivi dell'ingegneria. In questo lavoro viene presentato un modello numerico basato sulle equazioni bidimensionali di De Saint Venant rielaborate sostituendo all'originale legame costitutivo newtoniano quello di Herschel-Bulkley. Associato a tali equazioni viene proposto un criterio di arresto, sempre di tipo bidimensionale, ritenuto adeguato alla dimensione del problema. Il metodo di integrazione utilizzato \ue8 ai volumi finiti mentre lo schema, attraverso un'opportuna scelta dei volumi di controllo, risulta di tipo semi implicito con una precisione...
In this paper, a shock-capturing numerical model, based on the combined solution of Boussinesq an... more In this paper, a shock-capturing numerical model, based on the combined solution of Boussinesq and nonlinear shallow water equations is applied to the simulation of wave runup, overtopping and wave train propagation over impermeable, emerged and low-crested, structures. In order to improve the performances of the scheme at wet-dry interfaces, a numerical treatment is introduced to provide well-balancing of advective fluxes and source terms. One-and two-dimensional test cases are presented to validate the performances of the model under both regular and irregular wave conditions.
International Journal of Offshore and Polar Engineering, 2000
This paper describes a study of the hydrodynamics in the swash zone using an impermeable concrete... more This paper describes a study of the hydrodynamics in the swash zone using an impermeable concrete beach in a laboratory flume. Analysis was made of the measurements achieved using level wave gauges and a laser Doppler velocimeter. From these measurements we could derive the mean motion and turbulence characteristics along the main flow direction in 3 vertical sections of the swash zone. Fluid velocity seems almost uniform along the vertical, especially during the up-rush; the behaviour of turbulence dynamics is a mixture of free turbulence generated during wave breaking and convected by the mean motion, and wall turbulence. This work covers analysis in the time and frequency domain, and discusses the turbulent properties of the flow field derived from our measurements.
This work presents a first application of an open source SPH model (DualSPHysics) to study the dy... more This work presents a first application of an open source SPH model (DualSPHysics) to study the dynamics of a debris flow, with reference to the dry debris flow of Alverà, close to Cortina d'Ampezzo (Belluno, Italy). In this part of the Dolomites, debris flows are usually formed by large boulders within the fluid matrix. The adopted Lagrangian approach has allowed to describe the relative motion of a boulder immersed in a fluid mixture. From the numerical results, it has been observed that the boulder travels a greater distance along the channels, when water drives it. On the other hand, without the water thrust, the same boulder would halt much earlier. Furthermore, in all the simulated cases, it has been observed that the boulder stops when a natural narrowing is encountered along the channel bed.
This paper reviews mainly conceptual models and experimental work, in the field and in the labora... more This paper reviews mainly conceptual models and experimental work, in the field and in the laboratory, dedicated during the last decades to studying turbulence of breaking waves and bores moving in very shallow water and in the swash zone. The phenomena associated with vorticity and turbulence structures measured are summarised, including the measurement techniques and the laboratory generation of breaking waves or of flow fields sharing several characteristics with breaking waves. The effect of air entrapment during breaking is discussed. The limits of the present knowledge, especially in modelling a two-or three-phase system, with air and sediment entrapped at high turbulence level, and perspectives of future research are discussed.
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