Bulletin of the American Physical Society
70th Annual Meeting of the APS Division of Fluid Dynamics
Volume 62, Number 14
Sunday–Tuesday, November 19–21, 2017; Denver, Colorado
Session F19: Internal and Interfacial Waves IInterfacial

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Chair: T.R. Akylas, Massachusetts Institute of Technology Room: 702 
Monday, November 20, 2017 8:00AM  8:13AM 
F19.00001: Harmonic generation by internal waves in a thermohaline staircase with rotation Scott Wunsch Thermohaline staircases, generated by doublediffusive convection, are found in many regions of the ocean. Oceanic internal waves interact with these staircases. Recent results (Sutherland PRF 2016; Ghaemsaidi et al. JFM 2016) show that, in linear theory, internal waves with sufficiently long wavelengths are transmitted through the staircase, while short wavelengths may be reflected. However, nonlinear selfinteraction of internal waves (Diamessis et al. Dyn. Atm. Oceans 2014; Wunsch JFM 2017) with the sharp density jumps within the staircase is expected to generate doublewavenumber harmonics of the incident waves. This effect removes energy from the incident waves, reducing the transmitted energy in some cases. Energy transferred to the harmonic waves may also impact the stability of the staircase. Here, weakly nonlinear theory is used to explore the implications of this nonlinear effect on the dynamics of internal waves in oceanic thermohaline staircases. Rotation is included, and variations with latitude are considered. [Preview Abstract] 
Monday, November 20, 2017 8:13AM  8:26AM 
F19.00002: Energy Dissipation in Reflecting Internal Waves Bruce Rodenborn, Matthew Calvert, Vrinda Desai Internal wave reflection from a uniform sloping boundary is often analyzed using linear or a weakly nonlinear inviscid theory (Dauxois and Young, J. Fluid Mech., {390}, 1999). We previously characterized internal wave intensity in experiments and simulations using the integrated kinetic energy density and found our data did not match theory (Rodenborn et al. Phys., Fluids, 23, 2011). However, an algorithm by Lee et al. (Phys. Fluids, 26, 2014) determines the energy flux of internal waves using just velocity field measurements. We used this method to confirm our earlier results but also analyze the energy dissipation by comparing the energy flux into and out of a surface above the reflection region. We find high rates of energy dissipation that peak at the critical angle where the dissipation rate is $O$(90\%). The high rates of dissipation occur in both the experiments and numerical simulations, even when the numerical wave amplitude is small and the viscosity is reduced by an order of magnitude. This result may help to explain the eroding of continental slopes to the local angle of tidally generated internal waves (Cacchione et al., Science 296, 2002). [Preview Abstract] 
Monday, November 20, 2017 8:26AM  8:39AM 
F19.00003: Internal wave bolus transport dependence on pycnocline thickness Guilherme SalvadorVieira, Michael Allshouse, Harry Swinney Internal waves propagate hundreds to thousands of kilometers, ultimately reaching the continental slope and breaking. These shoaling waves can form boluses, vortices that trap and transport biomatter, sediments and nutrientrich water shoreward. Most previous work on boluses model stratifications composed of two layers of uniform density. Whereas in the oceans density varies continuously with depth, and the thickness of the pycnocline, the layer of rapid density change, varies with location and season. We study the impact of the pycnocline thickness on the dynamics of boluses generated by internal waves breaking on a constant slope topography. Direct numerical simulations provide the complex velocity field, and Lagrangian coherent structure methods are applied to objectively identify fluid trapped and transported with the bolus. Bolus properties are measured as a function of the pycnocline thickness, incoming wave energy, and topographic slope angle. The available potential energy is calculated to give an upper bound for the amount of mixing by the bolus. We find that the bolus dynamics depend significantly on the pycnocline thickness. [Preview Abstract] 
Monday, November 20, 2017 8:39AM  8:52AM 
F19.00004: Internal Solitary Wave Generation by Tidal Flow over Topography Karl Helfrich, Roger Grimshaw Oceanic internal solitary waves are typically generated by barotropic tidal flow over localized topography. Wave generation is characterized by the Froude number $F = U/c_0$, where $U$ is the tidal amplitude and $c_0$ is the long wave phase speed. For steady flow in the resonant regime, $\Delta_m < F  1 < \Delta_M$, forcedKdV (fKdV) theory shows that an upstream propagating undular bore is produced. The response further depends on whether the forcing is an equivalent hole or sill. Here wave generation is studied numerically using a fKdV model with timedependent forcing, $F(t)$, representative of realistic tidal flow. The response depends on $\Delta_{max} = F_{max}1$, where $F_{max}$ is the maximum of $F(t)$. When $\Delta_{max} < \Delta_m$ the flow is always subcritical and solitary waves appear after release of the downstream disturbance. When $\Delta_m < \Delta_{max} < \Delta_M$ the flow reaches criticality at its peak, producing upstream and downstream undular bores that are released as the tide recedes. When $\Delta_{max} > \Delta_M$ the tidal flow goes through the resonant regime twice, producing undular bores with each passage. Solutions representative of Stellwagen Bank and Knight Inlet illustrate the effect of asymmetric topography. [Preview Abstract] 
Monday, November 20, 2017 8:52AM  9:05AM 
F19.00005: An experimental and theoretical investigation of internal wave generation in the presence of a turning depth Allison Lee, Julie Crockett Internal waves generated from the M2 semidiurnal tide flowing over oceanic bathymetry have an important effect on the global energy budget. However, in some regions of the deep ocean the natural frequency ($N)$ falls below this tidal frequency and only rapidly decaying vertical, evanescent, waves are generated. If these evanescent waves reach a depth where $N$ is greater than the tidal frequency, a turning depth, they can become propagating internal waves. To explore the potential influence of this form of internal wave generation on overall ocean energy budgets, we performed experiments to investigate how propagating internal wave kinetic energy from evanescent waves is affected by the local stratification profile, topography shape and distance between the topography and turning depth. An analytical model using linear theory was also developed to estimate the kinetic energy transfer from the evanescent to propagating region. The analysis compares well with experimental results. The results show that the kinetic energy of propagating internal waves increases as the average natural frequency increases and as the distance between the topography and the turning depth decreases. These trends are dependent on topography shape; as the slope of the topography increases, the kinetic energy decreases. [Preview Abstract] 
Monday, November 20, 2017 9:05AM  9:18AM 
F19.00006: Characterization of Interfacial Waves and Pressure Drop in Horizontal OilWater CoreAnnular Flows Amitabh Bhattacharya, Sumit Tripathi, Ramesh Singh, Rico Tabor, K.S. Vinay CoreAnnular Flows (CAF) consist of a highly viscous fluid (e.g. oils, emulsions) being pumped through pipelines while being lubricated by a fluid of a much lower viscosity (e.g. water). In a series of experiments, we study CAF with the core fluid as oil. We find a clear scaling for the energy spectra of the interfacial waves with respect to the shear Reynolds number $Re_c$ of the fluid flow in the annulus. Specifically, we find that, at low values of $Re_c$, the low wavenumber modes of the interface appear to dominate, while, at high values of $Re_c$, the high wavenumber modes of the interface appear to dominate. Linear stability analysis of viscosity stratified flows appears to confirm this trend. The effective friction factor does not appear to change strongly with $Re_c$, suggesting that the interfacial waves do not significantly change the effective shear stress felt by the core fluid. This weak dependence of the friction factor on $Re_c$, along with a model for the holdup ratio, allows us to propose a very straightforward relationship between the pressure gradient and the flow rates of the core and annular fluids, which agrees with the experimental data. [Preview Abstract] 
Monday, November 20, 2017 9:18AM  9:31AM 
F19.00007: Tilting at wave beams: a new perspective on the St Andrew's Cross T R Akylas, T Kataoka, S J Ghaemsaidi, N Holzenberger, T Peacock The generation of internal gravity waves by a vertically oscillating cylinder that is tilted to the horizontal in a stratified fluid of constant buoyancy frequency, is investigated theoretically and experimentally. This forcing arrangement leads to a variant of the classical St Andrew's Cross that has certain unique features: (i) radiation of wave beams is limited due to a lower cutoff frequency set by the cylinder tilt angle to the horizontal; (ii) the response is essentially threedimensional, as end effects eventually come into play when the cutoff frequency is approached, however long a cylinder might be. These results follow from kinematic considerations and are also confirmed by laboratory experiments. The kinematic analysis, moreover, suggests a resonance phenomenon near the cutoff frequency, where viscous and nonlinear effects are likely to play an important part. This scenario is examined by an asymptotic model as well as experimentally. [Preview Abstract] 
Monday, November 20, 2017 9:31AM  9:44AM 
F19.00008: Propagation of 3D internal gravity wave beams in a slowly varying stratification Boyu Fan, T. R. Akylas The timemean flows induced by internal gravity wave beams (IGWB) with 3D variations have been shown to have dramatic implications for longterm IGWB dynamics. While uniform stratifications are convenient both theoretically and in the laboratory, stratifications in the ocean can vary by more than an order of magnitude over the ocean depth. Here, in view of this fact, we study the propagation of a 3D IGWB in a slowly varying stratification. We assume that the stratification varies slowly relative to the local variations in the wave profile. In the 2D case, the IGWB bends in response to the changing stratification, but nonlinear effects are minor even in the finite amplitude regime. For a 3D IGWB, in addition to bending, we find that nonlinearity results in the transfer of energy from waves to a largescale timemean flow associated with the mean potential vorticity, similar to IGWB behavior in a uniform stratification. In a weakly nonlinear setting, we derive coupled evolution equations that govern this process. We also use these equations to determine the stability properties of 2D IGWB to 3D perturbations. These findings indicate that 3D effects may be relevant and possibly fundamental to IGWB dynamics in nature. [Preview Abstract] 
Monday, November 20, 2017 9:44AM  9:57AM 
F19.00009: On resonant coupling of acoustic waves and gravity waves Christophe Millet Acoustic propagation in the atmosphere is often modeled using modes that are confined within waveguides causing the sound to propagate through multiple paths to the receiver. On the other hand, direct observations in the lower stratosphere show that the gravity wave field is intermittent, and is often dominated by rather well defined largeamplitude wave packets. In the present work, we use normal modes to describe both the gravity wave field and the acoustic field. The gravity wave spectrum is obtained by launching few monochromatic waves whose properties are chosen stochastically to mimic the intermittency. Owing to the disparity of the gravity and acoustic length scales, the interactions between the gravity wave field and each of the acoustic modes can be described using a multiplescale analysis. The appropriate amplitude evolution equation for the acoustic field involves certain random terms that can be directly related to the gravity wave sources. We will show that the cumulative effect of gravity wave breakings makes the sensitivity of groundbased acoustic signals large, in that small changes in the gravity wave parameterization can create or destroy specific acoustic features. [Preview Abstract] 
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