At the water surface, the wind-drift current is mainly induced by the viscous drag, and the wave ... more At the water surface, the wind-drift current is mainly induced by the viscous drag, and the wave height amplification is mainly induced by the form drag. The partition of the total drag into viscous drag and form drag was studied in [1]. Fig. 4 and 5 show examples of variahal-00856102,
[1] The flux, etat de la mer, et teledetection en conditions de fetch variable (FETCH) was aimed ... more [1] The flux, etat de la mer, et teledetection en conditions de fetch variable (FETCH) was aimed at studying the physical processes associated with air-sea exchanges and mesoscale oceanic circulation in a coastal region dominated by frequent strong offshore winds. The experiment took place in March-April 1998 in the northwestern Mediterranean Sea (Gulf of Lion). Observations were collected with the R/V L'Atalante, with an air-sea interaction spar (ASIS) buoy, with waverider buoys, and with research aircraft equipped for in situ and remote sensing measurements. The present paper is an introduction to the following special section, which groups 12 papers (including this one) presenting results on turbulent flux measurements at the ocean surface, on the behavior of the marine atmospheric boundary layer, on the ocean waves characteristics, on the ocean circulation, and on remote sensing of surface parameters. This overview presents the background and objectives of FETCH, the experimental setup and operations, and the dominant atmospheric and oceanic conditions and introduces the different papers of the special section.
Dans le cadre du contrat Region PACA AEROPITCH et du projet SpinFloat porte par EOLFI, nous avons... more Dans le cadre du contrat Region PACA AEROPITCH et du projet SpinFloat porte par EOLFI, nous avons etudie les effets que pourraient apporter le controle-commande du calage des pales (pitch) pour une eolienne a axe de rotation verticale, a trois pales, destinee a terme a etre posee en mer sur un support flottant. Nous avons construit une maquette a l’echelle que nous avons testeedans la grande soufflerie air-mer de l’Institut Pytheas sur Luminy a Marseille. Nous avons concu un systeme de servomoteurs permettant de tourner de facon independante les trois pales de l’eolienne pour ajuster au mieux l’angle d’attaque des pales par rapport au vent incident a chaque instant de la rotation. Nous avons mesure les efforts, les vitesses de rotation, et l’ecoulement d’air autour des pales par un systeme d’imagerie de particules (PIV) avec un large systeme d’ensemencement de particules. Nous avons optimise des lois de pitch pour atteindre des vitesses de rotation maximales en utilisant une boucle ...
We theoretically and experimentally examine the effect of forcing and damping on systems that can... more We theoretically and experimentally examine the effect of forcing and damping on systems that can be described by the nonlinear Schrödinger equation (NLSE), by making use of the phase-space predictions of the three-wave truncation. In the latter, the spectrum is truncated to only the fundamental frequency and the upper and lower sidebands. Our experiments are performed on deep water waves, which are better described by the higher-order NLSE, the Dysthe equation. We therefore extend our analysis to this system. However, our conclusions are general for NLSE systems. By means of experimentally obtained phase-space trajectories, we demonstrate that forcing and damping cause a separatrix crossing during the evolution. When the system is damped, it is pulled outside the separatrix, which in the real space corresponds to a phase-shift of the envelope and therefore doubles the period of the Fermi–Pasta–Ulam–Tsingou recurrence cycle. When the system is forced by the wind, it is pulled inside...
La modelisation du depot sec des aerosols submicroniques au-dessus d’une surface d’eau en mouveme... more La modelisation du depot sec des aerosols submicroniques au-dessus d’une surface d’eau en mouvement est un sujet d’actualite. Par exemple, en cas d’incident sur des centrales nucleaires, les aerosols submicroniques contamines, peuvent se propager dans l’atmosphere sur des tres grandes distances, puis progressivement se deposer sur le sol, sur la mer, les lacs et les rivieres. De plus, les aerosols atmospheriques sont des elements qui jouent un role dans le developpement planctonique [1]. Des progres restent a faire pour prevoir ces depots par la modelisation, notamment au-dessus de surfaces liquides en mouvement. Nous presentons ici une analyse des resultats de modelisation compares aux donnees experimentales obtenues dans la soufflerie de simulations des echanges ocean-atmosphere de IRPHE. Des mesures de depot dans l’eau d’aerosols d’uranine, injectes dans l’air, ont ete effectuees pour differentes conditions de vitesse de vent et de vitesse de courant marin. Nous proposons une mod...
Remote-controlled trimaran Ocarina (Ocean couple a l'atmosphere : recherche instrumentee sur ... more Remote-controlled trimaran Ocarina (Ocean couple a l'atmosphere : recherche instrumentee sur navire annexe / Ocean coupled to the atmosphere: instrumented research on an auxiliary ship). The OCARINA platform (Ocean Coupled to the Atmosphere, Research on the Interface on the Annex Ship) is a surface naval drone specifically developed to measure turbulent and radiative exchanges at the ocean/atmosphere interface. Designed and produced at LATMOS in 2009, the initial version of OCARINA has evolved through campaigns and collaborations with DT-INSU, Ifremer, LOCEAN, and IRPHE. The onboard instruments are an inertial unit, a GPS, a sonic anemometer, a probe for measuring rising and falling radiative flows in the infrared and in visible wavelengths, a submerged probe of the CT type, and a meteorological station. The level 2 data provided are: the location, speed, heading and route followed the height and significant period of waves longer than two meters the water temperature (SST) at a...
The science guiding the EUREC$^4$A campaign and its measurements is presented. EUREC$^4$A compris... more The science guiding the EUREC$^4$A campaign and its measurements is presented. EUREC$^4$A comprised roughly 5 weeks of measurements in the downstream winter trades of the North Atlantic – eastward and southeastward of Barbados. Through its ability to characterize processes operating across a wide range of scales, EUREC$^4$A marked a turning point in our ability to observationally study factors influencing clouds in the trades, how they will respond to warming, and their link to other components of the earth system, such as upper-ocean processes or the life cycle of particulate matter. This characterization was made possible by thousands (2500) of sondes distributed to measure circulations on meso- (200 km) and larger (500 km) scales, roughly 400 h of flight time by four heavily instrumented research aircraft; four global-class research vessels; an advanced groundbased cloud observatory; scores of autonomous observing platforms operating in the upper ocean (nearly 10 000 profiles), l...
The Inertial-Dissipation method (IDM) and the Eddy Correlation Method (ECM) are usually used in l... more The Inertial-Dissipation method (IDM) and the Eddy Correlation Method (ECM) are usually used in laboratory or open field experiments to estimate the momentum fluxes at the air-sea interface. Effects of surface waves on the kinetic energy balance equation and its consequence on the estimation of momentum fluxes have been pointed on by different authors (Donelan et al (1997), Janssen (1999), Drennan et al (1999)). The analytical model of Janssen is based on the concept of potential wave induced motions and suggests that, in the presence of surface growing waves, the IDM can underestimate the momentum flux. In situ experiments show that IDM and ECM do not agree in presence of swell or close to the surface for pure wind waves. We present here the results of a series of experiments conducted in the large windwave tank at IRPHE (Marseille). A complete experimental set-up was used in order to measure the downstream and the vertical velocities in air flow, the air-flow pressure fluctuations and the instantaneous deflections of the air-water interface. Momentum fluxes and kinetic transport terms were determined for different wind and wave conditions. The results show that close to the surface in presence of waves, the two methods do not agree i.e. the IDM underestimates the momentum flux. This is due to the non-zero value of the kinetic transport term. Above the Wavy Boundary Layer the two methods collapse. Moreover, in absence of waves (experimental run with a floating coat located at the interface) the IDM and the ECM agree because the transport term is equal to zero. Effects of background waves on fluxes are quantified.
ABSTRACT OCARINA (Ocean Coupled with Atmosphere : Recherche Instrumentale sur Navire Annexe) is a... more ABSTRACT OCARINA (Ocean Coupled with Atmosphere : Recherche Instrumentale sur Navire Annexe) is a small moving platform deployed from a research vessel. Turbulent fluxes, radiation fluxes, and wave state can all be derived from the instruments embedded on OCARINA, which include a sonic anemometer, an inertial platform, a CT probe, and other sensors. OCARINA was recently deployed during the FROMVAR experiment in Mer d'Iroise. It was successfully operated in winds up to 12 m/s and waves up to 4 m. The platform and datasets will be presented. Turbulent fluxes estimated with OCARINA data will be compared to data collected on the host vessel.
ABSTRACT The possible influence of accelerated winds on air-water momentum fluxes is being studie... more ABSTRACT The possible influence of accelerated winds on air-water momentum fluxes is being studied through detailed laboratory measurements in a large wind-wave flume. Wind stress over the water surface, waves and surface drift are measured in the 40m long wind-wave tank at IRPHE, Marseille. While momentum fluxes are estimated directly through the eddy correlation method in a station about the middle of the tank, they provide information corresponding to rather short non-dimensional fetch not previously reported. Wave evolution along the tank is determined through a series of wave gauges, and the wind-induced surface drift is obtained at one of the first measuring stations at the beginning of the tank. At each experimental run very low wind was on (about 1m/s) for a certain period and suddenly it was constantly accelerated to reach about 13 m/s (as well as 8 and 5 m/s during different runs) in about 15 sec to as long as 600 sec. The wind was kept constant at that high speed for 2 to 10 min, and then suddenly and constantly decelerate to 0. Data from the constant high winds provided us with reference equilibrium conditions for at least 3 different wind speed. We, nevertheless, focus in the recordings while wind was being constantly accelerated expecting some contribution to the understanding of gustiness, the implied wind wave growth and the onset of surface drift. Wind-wave growth is observed to lag behind the wind stress signal, and furthermore, a two regime wind stress is noticed, apparently well correlated with a) the incipient growth and appearance of the first waves and b) the arrival of waves from the up-wind section of the tank. Results of non-dimensional wave energy as a function of non-dimensional fetch represent an extension of at least 2 decades shorter non-dimensional fetch to the wave growth curves typically found in the literature. The linear tendency of wave growth compares very well only when wind is reaching its maximum, while during the accelerated wind period a lower non-dimensional wave energy is found. Details on the onset of wind-induced surface drift at the beginning of the tank will be addressed within the context of accelerated wind conditions. This work represents a RugDiSMar Project (CONACYT 155793) contribution. The support from ANUIES-ECOS M09-U01 project, CONACYT-187112 Estancia Sabática, and Institute Carnot, is greatly acknowledged.
IEEE International Geoscience and Remote Sensing Symposium
Simultaneous backscattering measurements with radar and sonar in the large wind wave facility in ... more Simultaneous backscattering measurements with radar and sonar in the large wind wave facility in Marseilles, France shows that bound and free waves coexist on the water surface. By observing the surface from above and below, we were able to show definitively that the bound waves ride on the front face of the dominant wave in the tank. Because of the large width of the tank, we were able to vary the azimuth angle of both the radar and sonar, which viewed a common surface area, and observe the dependence of both free and bound waves on azimuth angle.
The nonlinear Schrodinger equation, who is one of the most significant equations in physics, may ... more The nonlinear Schrodinger equation, who is one of the most significant equations in physics, may model accurately the propagation of nonlinear waves. Some nonlinear waves are known to be unstable to side-band perturbation. This instability, known as the Benjamin-Feir [1] instability or Modulation Instability (MI) in a broader context, can be described by exact pulsating solutions, also referred to as Akhmediev Breathers (ABs). These solutions are of significant importance, since they describe the exact and complete growth and decay cycles of the modulation instability, leading to the Fermi Pasta Ulam [2] (FPU) recurrence. We report here different theoretical, numerical and experimental evidence on AB dynamics, MI, and FPU recurrence, relative to water waves. We will show some similarities with the propagation of non-linear optic waves leading to breathers, dark and gray solitons and rogue waves. The experiments were conducted in different wave tanks and air-sea interaction facilitie...
The effect of wind forcing on monochromatic modulated water waves was investigated both numerical... more The effect of wind forcing on monochromatic modulated water waves was investigated both numerically and experimentally in the context of the Modified Non-Linear Schrodinger (MNLS) equation framework. While wind is usually associated with a frequency downshift of the dominant spectral peak, we show that it may induce an upshift of the spectral mean due to an asymmetric amplification of the spectrum. Here the weighted average spectral mean is equal to the ratio of the momentum of the envelope to its norm and it detects any asymmetries in the spectrum (Segur et al. 2005). Wind can however indirectly induce frequency downshifts, by promoting dissipative effects like wave breaking. We highlight that the definition of the up-and downshift in terms of peak frequency or average frequency is critical for a relevant discussion. In our model, the wind input consists of a leading order forcing term that amplifies all frequencies equally and induces a broadening of the spectrum, and a higher ord...
At the water surface, the wind-drift current is mainly induced by the viscous drag, and the wave ... more At the water surface, the wind-drift current is mainly induced by the viscous drag, and the wave height amplification is mainly induced by the form drag. The partition of the total drag into viscous drag and form drag was studied in [1]. Fig. 4 and 5 show examples of variahal-00856102,
[1] The flux, etat de la mer, et teledetection en conditions de fetch variable (FETCH) was aimed ... more [1] The flux, etat de la mer, et teledetection en conditions de fetch variable (FETCH) was aimed at studying the physical processes associated with air-sea exchanges and mesoscale oceanic circulation in a coastal region dominated by frequent strong offshore winds. The experiment took place in March-April 1998 in the northwestern Mediterranean Sea (Gulf of Lion). Observations were collected with the R/V L'Atalante, with an air-sea interaction spar (ASIS) buoy, with waverider buoys, and with research aircraft equipped for in situ and remote sensing measurements. The present paper is an introduction to the following special section, which groups 12 papers (including this one) presenting results on turbulent flux measurements at the ocean surface, on the behavior of the marine atmospheric boundary layer, on the ocean waves characteristics, on the ocean circulation, and on remote sensing of surface parameters. This overview presents the background and objectives of FETCH, the experimental setup and operations, and the dominant atmospheric and oceanic conditions and introduces the different papers of the special section.
Dans le cadre du contrat Region PACA AEROPITCH et du projet SpinFloat porte par EOLFI, nous avons... more Dans le cadre du contrat Region PACA AEROPITCH et du projet SpinFloat porte par EOLFI, nous avons etudie les effets que pourraient apporter le controle-commande du calage des pales (pitch) pour une eolienne a axe de rotation verticale, a trois pales, destinee a terme a etre posee en mer sur un support flottant. Nous avons construit une maquette a l’echelle que nous avons testeedans la grande soufflerie air-mer de l’Institut Pytheas sur Luminy a Marseille. Nous avons concu un systeme de servomoteurs permettant de tourner de facon independante les trois pales de l’eolienne pour ajuster au mieux l’angle d’attaque des pales par rapport au vent incident a chaque instant de la rotation. Nous avons mesure les efforts, les vitesses de rotation, et l’ecoulement d’air autour des pales par un systeme d’imagerie de particules (PIV) avec un large systeme d’ensemencement de particules. Nous avons optimise des lois de pitch pour atteindre des vitesses de rotation maximales en utilisant une boucle ...
We theoretically and experimentally examine the effect of forcing and damping on systems that can... more We theoretically and experimentally examine the effect of forcing and damping on systems that can be described by the nonlinear Schrödinger equation (NLSE), by making use of the phase-space predictions of the three-wave truncation. In the latter, the spectrum is truncated to only the fundamental frequency and the upper and lower sidebands. Our experiments are performed on deep water waves, which are better described by the higher-order NLSE, the Dysthe equation. We therefore extend our analysis to this system. However, our conclusions are general for NLSE systems. By means of experimentally obtained phase-space trajectories, we demonstrate that forcing and damping cause a separatrix crossing during the evolution. When the system is damped, it is pulled outside the separatrix, which in the real space corresponds to a phase-shift of the envelope and therefore doubles the period of the Fermi–Pasta–Ulam–Tsingou recurrence cycle. When the system is forced by the wind, it is pulled inside...
La modelisation du depot sec des aerosols submicroniques au-dessus d’une surface d’eau en mouveme... more La modelisation du depot sec des aerosols submicroniques au-dessus d’une surface d’eau en mouvement est un sujet d’actualite. Par exemple, en cas d’incident sur des centrales nucleaires, les aerosols submicroniques contamines, peuvent se propager dans l’atmosphere sur des tres grandes distances, puis progressivement se deposer sur le sol, sur la mer, les lacs et les rivieres. De plus, les aerosols atmospheriques sont des elements qui jouent un role dans le developpement planctonique [1]. Des progres restent a faire pour prevoir ces depots par la modelisation, notamment au-dessus de surfaces liquides en mouvement. Nous presentons ici une analyse des resultats de modelisation compares aux donnees experimentales obtenues dans la soufflerie de simulations des echanges ocean-atmosphere de IRPHE. Des mesures de depot dans l’eau d’aerosols d’uranine, injectes dans l’air, ont ete effectuees pour differentes conditions de vitesse de vent et de vitesse de courant marin. Nous proposons une mod...
Remote-controlled trimaran Ocarina (Ocean couple a l'atmosphere : recherche instrumentee sur ... more Remote-controlled trimaran Ocarina (Ocean couple a l'atmosphere : recherche instrumentee sur navire annexe / Ocean coupled to the atmosphere: instrumented research on an auxiliary ship). The OCARINA platform (Ocean Coupled to the Atmosphere, Research on the Interface on the Annex Ship) is a surface naval drone specifically developed to measure turbulent and radiative exchanges at the ocean/atmosphere interface. Designed and produced at LATMOS in 2009, the initial version of OCARINA has evolved through campaigns and collaborations with DT-INSU, Ifremer, LOCEAN, and IRPHE. The onboard instruments are an inertial unit, a GPS, a sonic anemometer, a probe for measuring rising and falling radiative flows in the infrared and in visible wavelengths, a submerged probe of the CT type, and a meteorological station. The level 2 data provided are: the location, speed, heading and route followed the height and significant period of waves longer than two meters the water temperature (SST) at a...
The science guiding the EUREC$^4$A campaign and its measurements is presented. EUREC$^4$A compris... more The science guiding the EUREC$^4$A campaign and its measurements is presented. EUREC$^4$A comprised roughly 5 weeks of measurements in the downstream winter trades of the North Atlantic – eastward and southeastward of Barbados. Through its ability to characterize processes operating across a wide range of scales, EUREC$^4$A marked a turning point in our ability to observationally study factors influencing clouds in the trades, how they will respond to warming, and their link to other components of the earth system, such as upper-ocean processes or the life cycle of particulate matter. This characterization was made possible by thousands (2500) of sondes distributed to measure circulations on meso- (200 km) and larger (500 km) scales, roughly 400 h of flight time by four heavily instrumented research aircraft; four global-class research vessels; an advanced groundbased cloud observatory; scores of autonomous observing platforms operating in the upper ocean (nearly 10 000 profiles), l...
The Inertial-Dissipation method (IDM) and the Eddy Correlation Method (ECM) are usually used in l... more The Inertial-Dissipation method (IDM) and the Eddy Correlation Method (ECM) are usually used in laboratory or open field experiments to estimate the momentum fluxes at the air-sea interface. Effects of surface waves on the kinetic energy balance equation and its consequence on the estimation of momentum fluxes have been pointed on by different authors (Donelan et al (1997), Janssen (1999), Drennan et al (1999)). The analytical model of Janssen is based on the concept of potential wave induced motions and suggests that, in the presence of surface growing waves, the IDM can underestimate the momentum flux. In situ experiments show that IDM and ECM do not agree in presence of swell or close to the surface for pure wind waves. We present here the results of a series of experiments conducted in the large windwave tank at IRPHE (Marseille). A complete experimental set-up was used in order to measure the downstream and the vertical velocities in air flow, the air-flow pressure fluctuations and the instantaneous deflections of the air-water interface. Momentum fluxes and kinetic transport terms were determined for different wind and wave conditions. The results show that close to the surface in presence of waves, the two methods do not agree i.e. the IDM underestimates the momentum flux. This is due to the non-zero value of the kinetic transport term. Above the Wavy Boundary Layer the two methods collapse. Moreover, in absence of waves (experimental run with a floating coat located at the interface) the IDM and the ECM agree because the transport term is equal to zero. Effects of background waves on fluxes are quantified.
ABSTRACT OCARINA (Ocean Coupled with Atmosphere : Recherche Instrumentale sur Navire Annexe) is a... more ABSTRACT OCARINA (Ocean Coupled with Atmosphere : Recherche Instrumentale sur Navire Annexe) is a small moving platform deployed from a research vessel. Turbulent fluxes, radiation fluxes, and wave state can all be derived from the instruments embedded on OCARINA, which include a sonic anemometer, an inertial platform, a CT probe, and other sensors. OCARINA was recently deployed during the FROMVAR experiment in Mer d'Iroise. It was successfully operated in winds up to 12 m/s and waves up to 4 m. The platform and datasets will be presented. Turbulent fluxes estimated with OCARINA data will be compared to data collected on the host vessel.
ABSTRACT The possible influence of accelerated winds on air-water momentum fluxes is being studie... more ABSTRACT The possible influence of accelerated winds on air-water momentum fluxes is being studied through detailed laboratory measurements in a large wind-wave flume. Wind stress over the water surface, waves and surface drift are measured in the 40m long wind-wave tank at IRPHE, Marseille. While momentum fluxes are estimated directly through the eddy correlation method in a station about the middle of the tank, they provide information corresponding to rather short non-dimensional fetch not previously reported. Wave evolution along the tank is determined through a series of wave gauges, and the wind-induced surface drift is obtained at one of the first measuring stations at the beginning of the tank. At each experimental run very low wind was on (about 1m/s) for a certain period and suddenly it was constantly accelerated to reach about 13 m/s (as well as 8 and 5 m/s during different runs) in about 15 sec to as long as 600 sec. The wind was kept constant at that high speed for 2 to 10 min, and then suddenly and constantly decelerate to 0. Data from the constant high winds provided us with reference equilibrium conditions for at least 3 different wind speed. We, nevertheless, focus in the recordings while wind was being constantly accelerated expecting some contribution to the understanding of gustiness, the implied wind wave growth and the onset of surface drift. Wind-wave growth is observed to lag behind the wind stress signal, and furthermore, a two regime wind stress is noticed, apparently well correlated with a) the incipient growth and appearance of the first waves and b) the arrival of waves from the up-wind section of the tank. Results of non-dimensional wave energy as a function of non-dimensional fetch represent an extension of at least 2 decades shorter non-dimensional fetch to the wave growth curves typically found in the literature. The linear tendency of wave growth compares very well only when wind is reaching its maximum, while during the accelerated wind period a lower non-dimensional wave energy is found. Details on the onset of wind-induced surface drift at the beginning of the tank will be addressed within the context of accelerated wind conditions. This work represents a RugDiSMar Project (CONACYT 155793) contribution. The support from ANUIES-ECOS M09-U01 project, CONACYT-187112 Estancia Sabática, and Institute Carnot, is greatly acknowledged.
IEEE International Geoscience and Remote Sensing Symposium
Simultaneous backscattering measurements with radar and sonar in the large wind wave facility in ... more Simultaneous backscattering measurements with radar and sonar in the large wind wave facility in Marseilles, France shows that bound and free waves coexist on the water surface. By observing the surface from above and below, we were able to show definitively that the bound waves ride on the front face of the dominant wave in the tank. Because of the large width of the tank, we were able to vary the azimuth angle of both the radar and sonar, which viewed a common surface area, and observe the dependence of both free and bound waves on azimuth angle.
The nonlinear Schrodinger equation, who is one of the most significant equations in physics, may ... more The nonlinear Schrodinger equation, who is one of the most significant equations in physics, may model accurately the propagation of nonlinear waves. Some nonlinear waves are known to be unstable to side-band perturbation. This instability, known as the Benjamin-Feir [1] instability or Modulation Instability (MI) in a broader context, can be described by exact pulsating solutions, also referred to as Akhmediev Breathers (ABs). These solutions are of significant importance, since they describe the exact and complete growth and decay cycles of the modulation instability, leading to the Fermi Pasta Ulam [2] (FPU) recurrence. We report here different theoretical, numerical and experimental evidence on AB dynamics, MI, and FPU recurrence, relative to water waves. We will show some similarities with the propagation of non-linear optic waves leading to breathers, dark and gray solitons and rogue waves. The experiments were conducted in different wave tanks and air-sea interaction facilitie...
The effect of wind forcing on monochromatic modulated water waves was investigated both numerical... more The effect of wind forcing on monochromatic modulated water waves was investigated both numerically and experimentally in the context of the Modified Non-Linear Schrodinger (MNLS) equation framework. While wind is usually associated with a frequency downshift of the dominant spectral peak, we show that it may induce an upshift of the spectral mean due to an asymmetric amplification of the spectrum. Here the weighted average spectral mean is equal to the ratio of the momentum of the envelope to its norm and it detects any asymmetries in the spectrum (Segur et al. 2005). Wind can however indirectly induce frequency downshifts, by promoting dissipative effects like wave breaking. We highlight that the definition of the up-and downshift in terms of peak frequency or average frequency is critical for a relevant discussion. In our model, the wind input consists of a leading order forcing term that amplifies all frequencies equally and induces a broadening of the spectrum, and a higher ord...
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