Bulletin of the American Physical Society
71st Annual Meeting of the APS Division of Fluid Dynamics
Volume 63, Number 13
Sunday–Tuesday, November 18–20, 2018; Atlanta, Georgia
Session Q04: Internal and Interfacial Waves |
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Chair: Akylas Triantaphyllos, Massachusetts Institute of Technology Room: Georgia World Congress Center B206 |
Tuesday, November 20, 2018 12:50PM - 1:03PM |
Q04.00001: Spontaneous instability in internal solitary-like waves Chengzhu Xu, Marek Stastna, David Deepwell We study the onset of shear instability in internal solitary-like waves propagating in a quasi two-layer stratification, using high-resolution, two-dimensional direct numerical simulations with a spectral collocation method. We focus on large-amplitude, broadening limited waves whose minimum Richardson numbers are approximately 0.08. We demonstrate that, depending on the length of the high shear region (in which the local Richardson number is less than 0.25) relative to the width of the wave, instability can occur spontaneously along the wave's flat crest. We also show that, at least on the laboratory scale, the growth rate of the instability is Reynolds number dependent, such that for certain waves the onset of instability is possible only if the Reynolds number is sufficiently large. We further show that, for waves in which spontaneous instability does not occur, the onset of instability can still be triggered by small, but finite amplitude noise, and that the spatial structure and growth rate of the instability depends on the amplitude of the initial perturbation. |
Tuesday, November 20, 2018 1:03PM - 1:16PM |
Q04.00002: Exploring the convective instability in a shoaling internal solitary wave of depression over gentle slopes Gustavo A Rivera-Rosario, Peter Diamessis The shoaling internal solitary wave (ISW) of depression is explored through a high resolution deformed spectral multidomain penalty method flow solver. The ISW becomes convectively unstable while maintaining its symmetric shape and an unstable region develops in the wave interior, characterized by the entrapment of heavier-over-light fluid, in the form of a recirculating core. The convective instability is attributed to the stretching of the near-surface vorticity layer of the baroclinic background current. According to field observations in the South China Sea, this region may drive turbulent-induced mixing, estimated to be up to four times larger than that in the open ocean. Motivated by such observations and recent 2D simulations by the authors, emphasis is placed on the convective breaking that leads to a subsurface core, using 3D simulations, where the ISW propagates in the normal-to-isobath direction and a transitional structure develops in the transverse. As the wave enters the breaking regime, the growth of the gravest lateral instability is compared with the rate of development of convective overturn associated with the core. As such, a preliminary understanding of the formation of recirculating cores in ISWs is obtained. |
Tuesday, November 20, 2018 1:16PM - 1:29PM |
Q04.00003: Numerical study of surface-internal wave interaction based on a two-layer fluid model Xuanting Hao, Lian Shen The interaction between surface waves and internal waves is an important physical process in oceans. It is challenging to simultaneously resolve the surface waves and internal waves from the first principles of hydrodynamics because of the large difference in their length scales. In this study, we conduct numerical simulations based on a two-layer fluid model with the assumption of potential flow, and the dynamics of surface waves and internal waves are captured in phase-resolved simulation. The initial condition is a linear superposition of the eigenfunctions of the model, including the surface wave modes adapted from the JONSWAP spectrum and the internal wave modes reconstructed from the solutions of a KdV-type equation. In our results, we observe a distinct roughness change in the surface wave field, with a smooth region adjacent to a rough region. We have quantified this roughness change using the local steepness and wavenumber spectrum. Further analysis in the wavenumber-frequency space shows that short surface waves are reflected by the internal wave-induced motion. Our result suggests that the internal wave-induced motion plays a key role in the formation of surface signatures. |
Tuesday, November 20, 2018 1:29PM - 1:42PM |
Q04.00004: Role of background mean flow in the PSI of internal wave beams Boyu Fan, Triantaphyllos Akylas Parametric subharmonic instability (PSI) is believed to play a major role in the long-term fate of internal waves in stratified fluids such as the oceans and atmosphere. As PSI involves a transfer of energy from large to small scales, it is hypothesized to be a major contributor to wave dissipation and mixing. While the idealized PSI of three interacting plane waves is well understood, its applicability to realistic oceanic scenarios remains unclear and discrepancies between predictions and observations of dissipation rates remain unresolved. In particular, large-scale currents are ubiquitous in the natural environment and their effects on the dynamics of PSI are not yet well understood. To this end, we consider an internal wave beam of finite width propagating in a background mean flow and theoretically investigate its stability to fine-scale subharmonic perturbations. In a weakly nonlinear setting, we derive evolution equations for the perturbations and we find that the presence of a weak background mean flow can either weaken or enhance PSI, suggesting that the oceanic scenario may be more complex than previously thought. |
Tuesday, November 20, 2018 1:42PM - 1:55PM |
Q04.00005: Effect of stratification profile on internal wave energy generated by flow over realistic topographies Allison Lee, Kyle Hakes, Yuxuan Liu, Julie Crockett, Michael Allshouse Previous research has shown that evanescent waves, which are formed in weakly stratified regions and decay rapidly, can pass into regions of stronger stratification and become propagating internal waves. To better understand the potential impact of these uniquely formed internal waves on the ocean energy budget, experiments were performed with four different topographies and with four types of realistic stratifications profiles. Specifically, two Gaussian topographies, a sinusoidal topography with two peaks, and a complex topography were used to represent a local seamount, multiple hills, and a complex variation of topography. Experiments indicate that the kinetic energy content of the internal waves is highly dependent upon the topography shape and the stratification profile in both the evanescent and propagating regions. The experimental analysis of kinetic energy is compared to both an analytical model and numerical simulations with good agreement. |
Tuesday, November 20, 2018 1:55PM - 2:08PM |
Q04.00006: Can Triadic Resonance Instability be ignited by the interaction between an internal wave field and a vortex ring? Katherine Grayson, Stuart Dalziel, Andrew Lawrie The role played by Triadic Resonance Instability (TRI) in transferring energy across the wavenumber and frequency spectra for internal waves is becoming increasingly recognised. However, much of the experimental work to date has considered the development of this crucial mechanism in the idealised conditions of monochromatic plane waves or wave beams. Here we present novel experimental results exploring whether TRI can be ignited in a pre-existing wave beam by the passage of a vortex ring. In this study, the internal wave field is generated from the motion of a flexible horizontal boundary condition, driven by an array of independently controlled actuators. This allows for varying amplitude, frequency and wavelength in both the spatial and temporal domain. We therefore examine the effect of varying the wave input parameters on the generation of this instability and determine if, under certain conditions, the presence of the vortex ring can ignite the TRI. |
Tuesday, November 20, 2018 2:08PM - 2:21PM |
Q04.00007: Mean flow generation due to oblique reflection of internal waves at a slope Triantaphyllos Akylas, Takeshi Kataoka A theoretical study is made of the mean flow induced by the reflection of a weakly nonlinear internal gravity wave beam at a uniform rigid slope, in the general case where the beam meets the slope at an arbitrary direction, not necessarily parallel to the isobaths, and the flow cannot be taken as 2D. In the vertical direction, the Eulerian mean flow due to such an oblique reflection is equal and opposite to the Stokes drift, so the Lagrangian mean flow vanishes, as in a 2D reflection. The horizontal mean flow, however, is controlled by the mean potential vorticity (PV), which in contrast to 2D does not vanish, and the horizontal Lagrangian mean flow is generally non-zero. Furthermore, for oblique reflection, viscous dissipation can lead to resonant generation of horizontal mean flow owing to irreversible production of mean PV, a phenomenon known as streaming. |
Tuesday, November 20, 2018 2:21PM - 2:34PM |
Q04.00008: Measuring energy dissipation of reflecting internal waves using experiments and simulations Anh Quoc Nguyen, Charlotte E Mabbs, Clayton Bell, Bruce E Rodenborn Lee et al. found a new method to measure internal wave energy using only the experimentally determined velocity field (Lee et al., Phys. Fluids, 26, 2014). However, this method has never been used to study the reflection of internal waves from sloping boundaries. Our previous study (Rodenborn et al. Phys., Fluids, 23, 2011) used integrated kinetic energy density as a proxy measure of the radiated wave power. Dettner et al. subsequently showed that kinetic energy density is not a good measure of the radiated wave power (Phys., Fluids, 25, 2013). They also showed that radiated wave power is weak when strong boundary flows are excited by tidal motion over model topography. We use the method of Lee et al. to analyze our experimental particle image velocimetry measurements and compare them with simulations where the energy flux is determined using the pressure and velocity fields. We find good agreement between our experimental and numerical simulation data for reflecting internal waves. We also find that there is a high rate of energy dissipation during the reflection process when the boundary flows are strongest, which occurs at the critical angle. |
Tuesday, November 20, 2018 2:34PM - 2:47PM |
Q04.00009: Experimental investigation of nonlinear internal waves in deep water with miscible fluids Roberto Camassa, Matthew Hurley, Richard M McLaughlin, Pierre-Yves Passaggia, Colin Thomson We report the first experimental evidence of nonlinear Internal Solitary Waves in deep water and for miscible fluids. The results consisting of amplitude, speed, and wavelength are validated against experiments and direct numerical simulations where the effect of the diffused interface is taken into account. The waves are generated by means of a dam break and their evolution is recorded with Laser Induced Fluorescence and Particle Image Velocimetry. In particular, data collected in a frame moving with the waves are presented here for the first time. Our results are representative of geophysical applications in the deep ocean where weakly nonlinear theories fail to capture the characteristics of large amplitude ISWs from field observations. |
Tuesday, November 20, 2018 2:47PM - 3:00PM |
Q04.00010: Lagrangian Transport by Vertically Bounded Internal Gravity Wavepackets Bruce Sutherland, Ton van den Bremer Horizontally propagating, vertically bounded internal wave modes induce both a horizontal Eulerian flow (EF) and a Stokes drift (SD) which, combined, result in the Lagrangian transport of fluid. Through theory, confirmed by numerical simulations, we predict the EF and SD are found for modes in arbitrary stratification. In the case of mode-1 waves in uniform stratification, we recover the mode-2 structures of the EF and SD originally predicted by McIntyre (J. Fluid Mech. 1973) including a singularity that results from a resonance occurring when the EF has phase speed equal to the group speed of the wavepacket. In top-hat stratification, the EF is not in itself a single mode. Consequently this singularity disappears and a new sequence of resonances are manifest as the induced flow resonates with higher order vertical modes. Generally, the vertically integrated EF and SD are each zero if the background density varies continuously. However, in the limit of a two-layer fluid, an interfacial wave induces an EF and SD whose vertical integrals are each non-zero but which together sum to zero. This singular behaviour occurs because a two-layer fluid does not permit higher order vertical modes. |
Tuesday, November 20, 2018 3:00PM - 3:13PM |
Q04.00011: Measuring interfacial tension using waves Yuk Man Lau, Willem van de Water, Jerry Westerweel Interfacial tension measurement using parametrically excited interfacial waves is investigated. The method is assessed for applicability of acquiring low interfacial tension values between liquid-liquid layers. In the present experiments, an oil-water system is used. Low interfacial waves are generated by adding surfactant to the two-phase system to decrease the interfacial tension. Wavenumber of the excited system is obtained from shadowgraphs. To determine the interfacial tension value, a linear stability model is adapted. On basis of this model, it is concluded that there is a lower limit of interfacial tension value which can be measured using mechanically excited waves. |
Tuesday, November 20, 2018 3:13PM - 3:26PM |
Q04.00012: Gravity wave breaking in Jovian atmospheres Jhett Bordwell, Benjamin Brown, Jeffrey S Oishi The atmospheres of Jovian planets are composed of a lower convective region with an overlying radiative region, where waves are driven due to the convective motion at the boundary. The release of energy and mixing due to the breaking of these gravity waves in planetary atmospheres may make significant contributions to the atmospheric dynamics and chemistry of Jovian atmospheres. We perform a study of the effects of radiative, viscous, and dissipative damping upon these waves, and find wave breaking heights using steepening and static stability criteria for the three main classes of Jovian planets. Using linear stability and weakly nonlinear analysis, we solve for the amplitudes of the fastest growing unstable modes, and explore their effects upon the energetics and mixing properties of the atmosphere. |
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