We study numerically the generation of power laws in the framework of weak turbulence theory for ... more We study numerically the generation of power laws in the framework of weak turbulence theory for surface gravity waves in deep water. Starting from a random wave field, we let the system evolve numerically according to the nonlinear Euler equations for gravity waves in infinitely deep water. In agreement with the theory of Zakharov and Filonenko, we find the formation of a power spectrum characterized by a power law of the form of |k| -2.5 .
We study the formation of extreme events in incoherent systems described by envelope equations, s... more We study the formation of extreme events in incoherent systems described by envelope equations, such as the Nonliner Schrödinger equation. We derive an identity that relates the evolution of the kurtosis (a measure of the relevance of the tails in a probability density function) of the wave amplitude to the rate of change of the width of the Fourier spectrum of the wave field. The result is exact for all dispersive systems characterized by a nonlinear term of the form of the one contained in the Nonlinear Schrödinger equation. Numerical simulations are also performed to confirm our findings. Our work sheds some light on the origin of rogue waves in incoherent dispersive nonlinear media ruled by local cubic nonlinearity.
We investigate experimentally the statistical properties of a wind-generated wave field and the s... more We investigate experimentally the statistical properties of a wind-generated wave field and the spontaneous formation of rogue waves in an annular flume. Unlike many experiments on rogue waves where waves are mechanically generated, here the wave field is forced naturally by wind as it is in the ocean. What is unique about the present experiment is that the annular geometry of the tank makes waves propagating circularly in an unlimited-fetch condition. Within this peculiar framework, we discuss the temporal evolution of the statistical properties of the surface elevation. We show that rogue waves and heavy-tail statistics may develop naturally during the growth of the waves just before the wave height reaches a stationary condition. Our results shed new light on the formation of rogue waves in a natural environment.
We analyse the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase t... more We analyse the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase transition within the Nonlinear Schrödinger model and their interplay with wave turbulence theory. By using numerical experiments we study how the condensate fraction and the first order correlation function behave with respect to the mass, the energy and the size of the system. By relating the free-particle energy to the temperature, we are able to estimate the Berezinskii-Kosterlitz-Thouless transition temperature. Below this transition we observe that for a fixed temperature the superfluid fraction appears to be size-independent, leading to a power-law dependence of the condensate fraction with respect to the system size.
European Journal of Mechanics B-fluids, Mar 1, 2019
We present a technique for measuring the two-dimensional surface water wave elevation both in spa... more We present a technique for measuring the two-dimensional surface water wave elevation both in space and time based on the low-cost Microsoft Kinect sensor. We discuss the capabilities of the system and a method for its calibration. We illustrate the application of the Kinect to an experiment in a small wave tank. A detailed comparison with standard capacitive wave gauges is also performed. Spectral analysis of a random-forced wave field is used to obtain the dispersion relation of water waves, demonstrating the potentialities of the setup for the investigation of the statistical properties of surface waves.
We examine on the static and dynamical properties of quantum knots in a Bose-Einstein condensate.... more We examine on the static and dynamical properties of quantum knots in a Bose-Einstein condensate. In particular, we consider the Gross-Pitaevskii model and revise a technique to construct ab initio the condensate wave-function of a generic torus knot. After analysing its excitation energy, we study its dynamics relating the topological parameter to its translational velocity and characteristic size. We also investigate the breaking mechanisms of non shape-preserving torus knots confirming an evidence of universal decaying behaviour previously observed.
We introduce spatiotemporal optical dark X solitary waves of the (2+1)D hyperbolic nonlinear Schr... more We introduce spatiotemporal optical dark X solitary waves of the (2+1)D hyperbolic nonlinear Schrödinger equation (NLSE), that rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between such NLSE and a well known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary waves may propagate for long distances (tens of nonlinear lengths) before they eventually break up, owing to the modulation instability of the continuous wave background. This finding opens a novel path for the excitation and control of X solitary waves in nonlinear optics.
Classical eduction schemes for turbulent boundary layer bursting processes are based on the assum... more Classical eduction schemes for turbulent boundary layer bursting processes are based on the assumption of empirical threshold constants. The wavelet analysis has been recently considered to be a possible candidate as turbulent structure detection method, overcoming any empirical approach. An application of this mathematical tool to a near wall boundary layer velocity signal is shown. Comparison with classical VITA detection scheme is presented.
Proceedings of 35th International Cosmic Ray Conference — PoS(ICRC2017), 2017
The TurLab facility is a laboratory, equipped with a 5 m diameter and 1 m deep rotating tank, loc... more The TurLab facility is a laboratory, equipped with a 5 m diameter and 1 m deep rotating tank, located in the Physics Department of the University of Turin. Originally built mainly to study problems where system rotation plays a key role in the fluid behaviour such as in atmospheric and oceanic flows at different scales, in the past few years the TurLab facility has been used to perform experiments related to observation of Extreme Energy Cosmic Rays from space using the fluorescence technique, as in the case of the JEM-EUSO mission, where the diffuse night brightness and artificial light sources can vary significantly in time and space inside the Field of View of the telescope. The description of the EUSO@TurLab project and its first results have been presented in the past. During the last two years many upgrades have been performed on the instrumentation mainly related to the read-out electronics: SPACIROC-1 (employed in EUSO-Balloon and EUSO-TA prototypes) and SPACIROC-3 (EUSO-SPB and Mini-EUSO) which allowed to test a fully equipped Elementary Cell of JEM-EUSO. This phase has been named Phase II. Moreover, the Focal Surface of EUSO-Balloon with the level 1 trigger logic implemented in the Photo-Detector Module has been tested at TurLab after the Canada flight. Finally, tests related to the possibility to employ a EUSO-like detector for other type of applications such as wave monitoring and imaging detector have been pursued. The tests and results obtained in EUSO@TurLab Project -Phase II are described.
Thermalization in the nonlinear Klein-Gordon chain that in regimes close to this limit, the predi... more Thermalization in the nonlinear Klein-Gordon chain that in regimes close to this limit, the predictions should apply with some degree of accuracy. In any numerical simulation, the number of modes is always finite, therefore, the resonances in principle may take place only for integer values of wave numbers. However, in nonlinear dispersive wave systems, another effect comes into play, that is the broadening of frequencies [24]: the frequency of the modes becomes stochastic around the value described by the dispersion relation. The implication of this phenomenon is that if N or ϵ are sufficiently large, the resonance conditions, eqs. (10), do not need to be satisfied exactly in the computational grid and quasi-resonances may become important . On the other hand, in the weakly nonlinear regime and when the number of modes is low, we assume that exact resonant interactions in a discrete system may lead on average to an irreversible process just like in the large-box limit, even though a statistical description, i.e., a kinetic equation, with discrete wave numbers has not been developed. This case is considered hereafter.
The temporal and spatial evolutions of nonlinear wave group with an initial Gaussian envelope are... more The temporal and spatial evolutions of nonlinear wave group with an initial Gaussian envelope are theoretically studied under the governing of MNLS equations, demonstrating that the temporal and spatial versions of numerical model are not always consistent in the whole evolution process, particularly in the presence of strong nonlinearity. Moreover, a large set of numerical simulations, performed respectively by these two versions of numerical model, are systematically compared to mechanically generated waves with different initial directional spreading and Benjamin-Feir Index, mainly focusing on the evolution properties of surface elevations such as the coefficients of skewness and kurtosis, the probability density function, and the maximal surface elevation. On the whole, it can be argued that the statistical
We study the five-wave classical scattering matrix for nonlinear and dispersive Hamiltonian equat... more We study the five-wave classical scattering matrix for nonlinear and dispersive Hamiltonian equations with a nonlinearity of the type u ∂u/∂x. Our aim is to find the most general nontrivial form of the dispersion relation ω(k) for which the five-wave interaction scattering matrix is identically zero on the resonance manifold. As could be expected, the matrix in one dimension is zero for the Korteweg-de Vries equation, the Benjamin-Ono equation, and the intermediate long-wave equation. In two dimensions, we find a new equation that satisfies our requirement.
A method for determining envelope solitonlike solutions of a wide class of nonlinear Schrödinger ... more A method for determining envelope solitonlike solutions of a wide class of nonlinear Schrödinger equations, based on a recently-developed correspondence between the generalized Korteweg-de Vries equation and the generalized nonlinear Schrödinger equation (with arbitrary nonlinearity), is presented. A review of the applications of this novel approach for determining, in particular, bright and grey/dark envelope solitonlike solutions of the cubic-quintic nonlinear
For the characterization of developing turbulent flows, which are dominated by the dynamics of vo... more For the characterization of developing turbulent flows, which are dominated by the dynamics of vorticity structures of different scale, it would be very useful to connect the features of the velocity fluctuations detected at a certain point with the evolution of the structures that are present in the nearby regions. To this end, outputs of DNS calculations, which can provide simultaneously both the evolution of the vorticity and the “velocity signals” corresponding to the different regions of the flow field, may be used. Obviously, only low Reynolds number conditions can be analysed, but the influence of basic mechanisms, as roll-up, passage and pairing of vortical structures, can be singled out, both as regards their “signatures” on the velocity time histories, and their effect on different statistical quantities. In particular, indications may be obtained on the processes that contribute to the production of Reynolds stresses, and thus to the average mass transport between two streams at different velocities. This type of analysis might then be considered as a very first step towards the identification of possible procedures for the recognition of the presence and evolution of the dominating vortical structures from velocity signals obtained experimentally at higher Reynolds number.
We report analytical solutions of the vector nonlinear Schrodinger equation that describe rogue w... more We report analytical solutions of the vector nonlinear Schrodinger equation that describe rogue waves in the defocusing regime. The link between modulational instability and rogue waves is displayed.
A great interest has recently been addressed to the study of the statistical properties of homoge... more A great interest has recently been addressed to the study of the statistical properties of homogenous and isotropic turbulence and nowadays most of the experimental results agree on the deviations from the Kolmogorov 1941 laws in the inertial range. To the knowledge of the authors, extensive studies have not been performed for the case of non homogeneous and non isotropic turbulence. In this paper, the statistical properties of the stream-wise velocity fluctuation in a turbulent air channel flow are studied experimentally at various distances from the wall. Strong shear layer events, educed using the classical VITA method (Variable Interval Time Average, [1]) and the LIM method (Local Intermittency Measure, [2]), are considered and related to the deviations from the Kolmogorov theory and from the values obtained by the ESS (Extended Self Similarity, [3]) in homogeneous turbulence.
We study the effect of surface gravity waves on the motion of inertial particles in an incompress... more We study the effect of surface gravity waves on the motion of inertial particles in an incompressible fluid. We perform analytical calculations based on perturbation expansion which allows us to predict the dynamics of inertial particles in deep water regime. We find that the presence of inertia leads to a non-negligible correction to the well-known horizontal Stokes drift velocity. Moreover, we find that the vertical sedimentation velocity is also affected by a drift induced by waves. The latter result may have some relevant consequences on the rate of sedimentation of particles of finite size. We underline that the vertical drift would also be observed in the (hypothetical) absence of the gravitational force. Kinematic numerical simulations are performed and the results are found to be in excellent agreement with the analytical predictions, even for values of parameters beyond the perturbative limit.
We study numerically the generation of power laws in the framework of weak turbulence theory for ... more We study numerically the generation of power laws in the framework of weak turbulence theory for surface gravity waves in deep water. Starting from a random wave field, we let the system evolve numerically according to the nonlinear Euler equations for gravity waves in infinitely deep water. In agreement with the theory of Zakharov and Filonenko, we find the formation of a power spectrum characterized by a power law of the form of |k| -2.5 .
We study the formation of extreme events in incoherent systems described by envelope equations, s... more We study the formation of extreme events in incoherent systems described by envelope equations, such as the Nonliner Schrödinger equation. We derive an identity that relates the evolution of the kurtosis (a measure of the relevance of the tails in a probability density function) of the wave amplitude to the rate of change of the width of the Fourier spectrum of the wave field. The result is exact for all dispersive systems characterized by a nonlinear term of the form of the one contained in the Nonlinear Schrödinger equation. Numerical simulations are also performed to confirm our findings. Our work sheds some light on the origin of rogue waves in incoherent dispersive nonlinear media ruled by local cubic nonlinearity.
We investigate experimentally the statistical properties of a wind-generated wave field and the s... more We investigate experimentally the statistical properties of a wind-generated wave field and the spontaneous formation of rogue waves in an annular flume. Unlike many experiments on rogue waves where waves are mechanically generated, here the wave field is forced naturally by wind as it is in the ocean. What is unique about the present experiment is that the annular geometry of the tank makes waves propagating circularly in an unlimited-fetch condition. Within this peculiar framework, we discuss the temporal evolution of the statistical properties of the surface elevation. We show that rogue waves and heavy-tail statistics may develop naturally during the growth of the waves just before the wave height reaches a stationary condition. Our results shed new light on the formation of rogue waves in a natural environment.
We analyse the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase t... more We analyse the Bose-Einstein condensation process and the Berezinskii-Kosterlitz-Thouless phase transition within the Nonlinear Schrödinger model and their interplay with wave turbulence theory. By using numerical experiments we study how the condensate fraction and the first order correlation function behave with respect to the mass, the energy and the size of the system. By relating the free-particle energy to the temperature, we are able to estimate the Berezinskii-Kosterlitz-Thouless transition temperature. Below this transition we observe that for a fixed temperature the superfluid fraction appears to be size-independent, leading to a power-law dependence of the condensate fraction with respect to the system size.
European Journal of Mechanics B-fluids, Mar 1, 2019
We present a technique for measuring the two-dimensional surface water wave elevation both in spa... more We present a technique for measuring the two-dimensional surface water wave elevation both in space and time based on the low-cost Microsoft Kinect sensor. We discuss the capabilities of the system and a method for its calibration. We illustrate the application of the Kinect to an experiment in a small wave tank. A detailed comparison with standard capacitive wave gauges is also performed. Spectral analysis of a random-forced wave field is used to obtain the dispersion relation of water waves, demonstrating the potentialities of the setup for the investigation of the statistical properties of surface waves.
We examine on the static and dynamical properties of quantum knots in a Bose-Einstein condensate.... more We examine on the static and dynamical properties of quantum knots in a Bose-Einstein condensate. In particular, we consider the Gross-Pitaevskii model and revise a technique to construct ab initio the condensate wave-function of a generic torus knot. After analysing its excitation energy, we study its dynamics relating the topological parameter to its translational velocity and characteristic size. We also investigate the breaking mechanisms of non shape-preserving torus knots confirming an evidence of universal decaying behaviour previously observed.
We introduce spatiotemporal optical dark X solitary waves of the (2+1)D hyperbolic nonlinear Schr... more We introduce spatiotemporal optical dark X solitary waves of the (2+1)D hyperbolic nonlinear Schrödinger equation (NLSE), that rules wave propagation in a self-focusing and normally dispersive medium. These analytical solutions are derived by exploiting the connection between such NLSE and a well known equation of hydrodynamics, namely the type II Kadomtsev-Petviashvili (KP-II) equation. As a result, families of shallow water X soliton solutions of the KP-II equation are mapped into optical dark X solitary wave solutions of the NLSE. Numerical simulations show that optical dark X solitary waves may propagate for long distances (tens of nonlinear lengths) before they eventually break up, owing to the modulation instability of the continuous wave background. This finding opens a novel path for the excitation and control of X solitary waves in nonlinear optics.
Classical eduction schemes for turbulent boundary layer bursting processes are based on the assum... more Classical eduction schemes for turbulent boundary layer bursting processes are based on the assumption of empirical threshold constants. The wavelet analysis has been recently considered to be a possible candidate as turbulent structure detection method, overcoming any empirical approach. An application of this mathematical tool to a near wall boundary layer velocity signal is shown. Comparison with classical VITA detection scheme is presented.
Proceedings of 35th International Cosmic Ray Conference — PoS(ICRC2017), 2017
The TurLab facility is a laboratory, equipped with a 5 m diameter and 1 m deep rotating tank, loc... more The TurLab facility is a laboratory, equipped with a 5 m diameter and 1 m deep rotating tank, located in the Physics Department of the University of Turin. Originally built mainly to study problems where system rotation plays a key role in the fluid behaviour such as in atmospheric and oceanic flows at different scales, in the past few years the TurLab facility has been used to perform experiments related to observation of Extreme Energy Cosmic Rays from space using the fluorescence technique, as in the case of the JEM-EUSO mission, where the diffuse night brightness and artificial light sources can vary significantly in time and space inside the Field of View of the telescope. The description of the EUSO@TurLab project and its first results have been presented in the past. During the last two years many upgrades have been performed on the instrumentation mainly related to the read-out electronics: SPACIROC-1 (employed in EUSO-Balloon and EUSO-TA prototypes) and SPACIROC-3 (EUSO-SPB and Mini-EUSO) which allowed to test a fully equipped Elementary Cell of JEM-EUSO. This phase has been named Phase II. Moreover, the Focal Surface of EUSO-Balloon with the level 1 trigger logic implemented in the Photo-Detector Module has been tested at TurLab after the Canada flight. Finally, tests related to the possibility to employ a EUSO-like detector for other type of applications such as wave monitoring and imaging detector have been pursued. The tests and results obtained in EUSO@TurLab Project -Phase II are described.
Thermalization in the nonlinear Klein-Gordon chain that in regimes close to this limit, the predi... more Thermalization in the nonlinear Klein-Gordon chain that in regimes close to this limit, the predictions should apply with some degree of accuracy. In any numerical simulation, the number of modes is always finite, therefore, the resonances in principle may take place only for integer values of wave numbers. However, in nonlinear dispersive wave systems, another effect comes into play, that is the broadening of frequencies [24]: the frequency of the modes becomes stochastic around the value described by the dispersion relation. The implication of this phenomenon is that if N or ϵ are sufficiently large, the resonance conditions, eqs. (10), do not need to be satisfied exactly in the computational grid and quasi-resonances may become important . On the other hand, in the weakly nonlinear regime and when the number of modes is low, we assume that exact resonant interactions in a discrete system may lead on average to an irreversible process just like in the large-box limit, even though a statistical description, i.e., a kinetic equation, with discrete wave numbers has not been developed. This case is considered hereafter.
The temporal and spatial evolutions of nonlinear wave group with an initial Gaussian envelope are... more The temporal and spatial evolutions of nonlinear wave group with an initial Gaussian envelope are theoretically studied under the governing of MNLS equations, demonstrating that the temporal and spatial versions of numerical model are not always consistent in the whole evolution process, particularly in the presence of strong nonlinearity. Moreover, a large set of numerical simulations, performed respectively by these two versions of numerical model, are systematically compared to mechanically generated waves with different initial directional spreading and Benjamin-Feir Index, mainly focusing on the evolution properties of surface elevations such as the coefficients of skewness and kurtosis, the probability density function, and the maximal surface elevation. On the whole, it can be argued that the statistical
We study the five-wave classical scattering matrix for nonlinear and dispersive Hamiltonian equat... more We study the five-wave classical scattering matrix for nonlinear and dispersive Hamiltonian equations with a nonlinearity of the type u ∂u/∂x. Our aim is to find the most general nontrivial form of the dispersion relation ω(k) for which the five-wave interaction scattering matrix is identically zero on the resonance manifold. As could be expected, the matrix in one dimension is zero for the Korteweg-de Vries equation, the Benjamin-Ono equation, and the intermediate long-wave equation. In two dimensions, we find a new equation that satisfies our requirement.
A method for determining envelope solitonlike solutions of a wide class of nonlinear Schrödinger ... more A method for determining envelope solitonlike solutions of a wide class of nonlinear Schrödinger equations, based on a recently-developed correspondence between the generalized Korteweg-de Vries equation and the generalized nonlinear Schrödinger equation (with arbitrary nonlinearity), is presented. A review of the applications of this novel approach for determining, in particular, bright and grey/dark envelope solitonlike solutions of the cubic-quintic nonlinear
For the characterization of developing turbulent flows, which are dominated by the dynamics of vo... more For the characterization of developing turbulent flows, which are dominated by the dynamics of vorticity structures of different scale, it would be very useful to connect the features of the velocity fluctuations detected at a certain point with the evolution of the structures that are present in the nearby regions. To this end, outputs of DNS calculations, which can provide simultaneously both the evolution of the vorticity and the “velocity signals” corresponding to the different regions of the flow field, may be used. Obviously, only low Reynolds number conditions can be analysed, but the influence of basic mechanisms, as roll-up, passage and pairing of vortical structures, can be singled out, both as regards their “signatures” on the velocity time histories, and their effect on different statistical quantities. In particular, indications may be obtained on the processes that contribute to the production of Reynolds stresses, and thus to the average mass transport between two streams at different velocities. This type of analysis might then be considered as a very first step towards the identification of possible procedures for the recognition of the presence and evolution of the dominating vortical structures from velocity signals obtained experimentally at higher Reynolds number.
We report analytical solutions of the vector nonlinear Schrodinger equation that describe rogue w... more We report analytical solutions of the vector nonlinear Schrodinger equation that describe rogue waves in the defocusing regime. The link between modulational instability and rogue waves is displayed.
A great interest has recently been addressed to the study of the statistical properties of homoge... more A great interest has recently been addressed to the study of the statistical properties of homogenous and isotropic turbulence and nowadays most of the experimental results agree on the deviations from the Kolmogorov 1941 laws in the inertial range. To the knowledge of the authors, extensive studies have not been performed for the case of non homogeneous and non isotropic turbulence. In this paper, the statistical properties of the stream-wise velocity fluctuation in a turbulent air channel flow are studied experimentally at various distances from the wall. Strong shear layer events, educed using the classical VITA method (Variable Interval Time Average, [1]) and the LIM method (Local Intermittency Measure, [2]), are considered and related to the deviations from the Kolmogorov theory and from the values obtained by the ESS (Extended Self Similarity, [3]) in homogeneous turbulence.
We study the effect of surface gravity waves on the motion of inertial particles in an incompress... more We study the effect of surface gravity waves on the motion of inertial particles in an incompressible fluid. We perform analytical calculations based on perturbation expansion which allows us to predict the dynamics of inertial particles in deep water regime. We find that the presence of inertia leads to a non-negligible correction to the well-known horizontal Stokes drift velocity. Moreover, we find that the vertical sedimentation velocity is also affected by a drift induced by waves. The latter result may have some relevant consequences on the rate of sedimentation of particles of finite size. We underline that the vertical drift would also be observed in the (hypothetical) absence of the gravitational force. Kinematic numerical simulations are performed and the results are found to be in excellent agreement with the analytical predictions, even for values of parameters beyond the perturbative limit.
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Papers by Miguel Onorato