Bulletin of the American Physical Society
76th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2023; Washington, DC
Session L44: Waves: Nonlinear Dynamics and Turbulence 
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Chair: Alexander Hrabski, University of Michigan Room: 208AB 
Monday, November 20, 2023 8:00AM  8:13AM 
L44.00001: Fullydeveloped Wave Turbulence in the Numerical Kinetic Limit Alexander A Hrabski, Yulin Pan Wave Turbulence (WT) describes an outofequilibrium process in nonlinear wave systems, characterized by interscale energy cascades and powerlaw spectra. Under a few statistical assumptions and in the limits of an infinite domain and small wave amplitude (together, the kinetic limit), a turbulence closure for the evolution of wave action spectrum naturally arises. This closure forms the basis of the widelyadopted weak WT theory. Almost all realistic systems exist outside of the kinetic limit, however, and a quantitative understanding of the WT closure realized in this setting is for the most part lacking. 
Monday, November 20, 2023 8:13AM  8:26AM 
L44.00002: Role of threewave interactions in surface gravity wave turbulence Zhou Zhang, Yulin Pan Standard derivation of the Hasselmann kinetic equation for surface gravity waves assumes the dominance of quartet resonant interactions. As a result, the triadresonance terms are removed from the dynamical equations using a Lee transformation. While such transformation is supposed to be only valid for infinitesimal nonlinearity level, the derived kinetic equation is widely used in wave modeling for finiteamplitude waves. In this work, we numerically study the effect of triad interactions (in particular, the quasiresonance of three waves) in surface gravity wave turbulence. Our method decomposes the energy transfer into contributions from triad and quartet interactions, thus the role of each type of interaction can be elucidated. We apply this method for both evolving and stationary spectra, and find that the triad interactions play a significant role at low nonlinearity level. The results imply modification of the kinetic equation to better account for the triad interactions in certain cases. 
Monday, November 20, 2023 8:26AM  8:39AM 
L44.00003: Energy cascade due to nonlinear interactions of internal gravity waves Yue Cynthia WU, Yulin Pan The kinetic energy spectra of oceanic internal gravity waves (IGWs) from recent field measurements exhibit large variability, deviating from the standard GarrettMunk (GM) models. However, the current finescale parameterization of turbulent dissipation is based on the GM76 model, which does not consider general spectral shapes. Thus an improved estimate of turbulent dissipation for different spectra is needed for better parameterization of ocean mixing for global circulation and climate models. The rate of turbulent dissipation occurring at small scales can be inferred from knowledge of energy transfer due to nonlinear wavewave interactions at intermediate scales. In this work, we conduct direct calculation of energy transfer based on the wave kinetic equation in the wave turbulence theory and compare the energy flux across a critical vertical wavenumber that provides energy available for dissipation with the estimate from finescale parameterization. Three representative spectra, i.e., the GM75 and GM76 models as well as a spectrum fitted from observation, are analyzed. Key mechanisms, i.e., local and three nonlocal interactions (parametric subharmonic instability, elastic scattering and induced diffusion) are identified with their contribution to the energy transfer quantified. This will shed light on a new formulation of finescale parameterization incorporating varying spectral forms of IGWs and a realistic ocean environment. 
Monday, November 20, 2023 8:39AM  8:52AM 
L44.00004: Transition from weak turbulence to collapse turbulence regimes in the MMT model Ashleigh P Simonis, Yulin Pan Understanding the role of coherent structures emerging from a field of random waves is a topic of great interest in the nonlinear wave community. While there has been extensive research on the topic of strongly nonlinear localized coherent structures (e.g., solitons and breathers) in integrable systems, the behavior of such structures in nonintegrable systems is not yet as well understood. We study the forceddissipated focusing onedimensional (1D) MajdaMcLaughlinTabak (MMT) with localized wave collapses as a result of soliton instability. Our results show that when the forcing perturbation strength is weak, there are few wave collapses in the field and there is good agreement with weak wave turbulence (WTT) predictions. As the forcing perturbation strength increases, we see an increase in high amplitude collapses, intermittency, and the departure from a powerlaw spectrum to an exponentially decaying spectrum resembling that of a twospecies gas (comprised of waves and collapses). This is a novel discovery in the context of the MMT model and can be thought of as an analogy to a soliton gas in integrable turbulence. The transition from a weak turbulence regime to a strongly nonlinear “collapse” turbulence regime is also a new feature identified for the MMT model. 
Monday, November 20, 2023 8:52AM  9:05AM 
L44.00005: Threewave resonant interactions between two dispersion branches Filip Novkoski, Eric Falcon, ChiTuong Pham We report the experimental observation of nonlinear threewave resonant interactions between two different branches of the dispersion relation of hydrodynamic waves, namely the gravitycapillary and sloshing modes [1]. These atypical interactions are investigated within a torus of fluid for which the sloshing mode can be easily excited. A triadic resonance instability is then observed due to this threewave twobranch interaction mechanism, with a mother wave on the sloshing branch generating two gravitycapillary daughter waves. The waves are shown to be phaselocked and the efficiency of this interaction is found to be maximal when the gravitycapillary phase velocity matches the group velocity of the sloshing mode. For a stronger forcing, additional waves are generated by a cascade of threewave interactions populating the wave spectrum, both at large and small scales. Such a threewave twobranch interaction mechanism is probably not restricted to hydrodynamics and could be of interest in other systems involving several propagation modes 
Monday, November 20, 2023 9:05AM  9:18AM Author not Attending 
L44.00006: Abstract Withdrawn

Monday, November 20, 2023 9:18AM  9:31AM 
L44.00007: Experimental evidence of the dispersion relation of Kelvin waves along a freesurface vortex Jason Barckicke, Christophe Gissinger, Eric Falcon Kelvin waves are waves that propagate along vortices in turbulent flows or in quantum turbulence. Although ubiquitous in nature, they are challenging to access experimentally. Here, we investigate a freesurface vortex, like a bathtub vortex, that forms at the interface between water and air, within a container with a hole at its bottom, in response to injectors arranged circularly around the outlet. In this outofequilibrium stationary state, the vortex extends vertically over 50 cm with a diameter of the order of the millimeter. When excited using a wavemaker, we experimentally evidence Kelvin waves propagating along such a vortex and report their full dispersion relation for the first time. The latter exhibits a rich spectral structure with several branches, as helical bending modes. Our findings pave the way for the experimental investigation of Kelvin wave turbulence predicted theoretically. 
Monday, November 20, 2023 9:31AM  9:44AM 
L44.00008: Experimental evidence of intermittency in a random shockwave regime Guillaume Ricard, Eric Falcon We report the experimental observation of the dynamical and statistical properties of a wave field dominated by random shock waves on the surface of a fluid. By using a magnetic fluid (ferrofluid) within a high external magnetic field, we successfully achieved an experimentally nearly nondispersive surfacewave field [1]. Conversely to theoretical Burgers shock waves, the shockwave fronts are not fully vertical, but drive the dynamics [1]. We also experimentally evidence, for the first time, that this field dominated by random shock waves generates intense smallscale intermittency [2]. The statistical properties of this intermittency are then found to be in good agreement with a Burgerslike intermittency model, modified to take account of the finite steepness of the experimental shock waves [2]. 
Monday, November 20, 2023 9:44AM  9:57AM 
L44.00009: FastSlow Wave Transitions Induced by a Random Mean Flow Samuel Boury, Oliver Bühler, Jalal Shatah Motivated by recent asymptotic results in atmosphereocean fluid dynamics, we present an idealized numerical and theoretical study of twodimensional dispersive waves propagating through a smallamplitude random mean flow. The objective is to delineate clearly the conditions under which the cumulative Dopplershifting and refraction by the mean flow can change the group velocity of the waves not only in direction, but also in magnitude. The latter effect enables a possible transition from fast to slow waves, which behave very differently. Within our model we find the conditions on the dispersion relation and the mean flow amplitude that allow or rule out such fast–slow transitions. For steady mean flows we determine a novel finite mean flow amplitude threshold below which such transitions can be ruled out indefinitely. For unsteady mean flows a sufficiently rapid rate of change means that this threshold goes to zero, i.e., in this scenario all waves eventually undergo a fast–slow transition regardless of mean flow amplitude, with corresponding implications for the longterm fate of these waves. 
Monday, November 20, 2023 9:57AM  10:10AM 
L44.00010: Amplification of Maximum Ice Bending Strain and Reduction of Wave Energy Transmission due to SumFrequency Triad Wave Interactions in a FiniteLength Sea Ice Sheet Max Pierce, Yuming Liu, Dick K Yue Floating sea ice acts as a lowpass filter of incident wave energy from open water, allowing only long waves to penetrate far past the ice boundary. However, nonlinear sumfrequency interactions among longer waves propagating through an ice sheet transfer energy to high frequency waves which are only minimally transmitted past the leading ice edge from open water. We consider leadingorder triad interactions in an ice sheet of finite length through direct numerical simulations using a modified highorder spectral (HOS) method. We demonstrate that generated higher frequency waves result in more than twice the maximum bending strain predicted by linear theory, affecting the occurrence of ice breakup, as well as an appreciable decrease in transmitted wave energy flux, modifying the understanding of wave attenuation through an aggregate ice field. The extent of these nonlinear effects is shown to depend on a parameter in terms of ice length, wavelength and steepness. 
Monday, November 20, 2023 10:10AM  10:23AM 
L44.00011: Application of Surfriding and Broaching mode based on IMO SecondGeneration Intact Stability Criteria for the ships Dongmin Shin, Byungyoung Moon IMO (International Maritime Organization) have recently discussed the technical problems related to the secondgeneration intact stability criteria of ships. The secondgeneration intact stability criteria refer to five modes of vulnerability when the ship sailing in the ocean. In this study, we described a method to verify the criteria of the surfriding/broaching. In case that Lv1 (Level 1) vulnerability criteria is not satisfied based on the relatively simple calculation using the Froude number (Fn), we presented the calculation procedure for the Lv2 (Level 2) criteria considering the hydrodynamics in waves. The results were reviewed based on the data for given previous ships. In absence of shipspecific data, a similar Lv2 result was confirmed by comparing the result obtained by calculating the added mass with the case where the added mass was 10% of the ship mass. This result will contribute to basic ship design process according to the IMO draft regulation. 
Monday, November 20, 2023 10:23AM  10:36AM Author not Attending 
L44.00012: Cauchy problem for a loaded integrodifferential equation Umida Baltaeva PDEs and integrodifferential equations of the convolution type arise in mathematical models of physical, biological, and technical systems and in other areas where it is necessary to take into account the history of processes. Constitutive relations in a linear processes of inhomogeneous diffusion and propagation of waves with memory contain a time and spacedependent memory kernel. Problems of memory kernels identification in parabolic and hyperbolic integrodifferential equations have been intensively studied. 
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