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 E04: Waves: Nonlinear Dynamics and Turbulence |
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Chair: Miguel Bustamante, University College Dublin Room: Georgia World Congress Center B206 |
Sunday, November 18, 2018 5:10PM - 5:23PM |
E04.00001: On the Kolmogorov constant for capillary wave turbulence Yulin Pan Recent progress in understanding the theoretical value of Kolmogorov constant for capillary wave turbulence is reported. In addition to reviewing the theoretical derivation, I focus on the clarification and correction of two inconsistent points in the previous derivation, which have resulted in confusions in recent experimental/numerical attempts to verify the theoretical value. The two points include: (i) the definition of wave spectrum in an infinite domain and (ii) an integral involved in the calculation of energy flux by triad resonance. The theoretical formulation after the correction is summarized. |
Sunday, November 18, 2018 5:23PM - 5:36PM |
E04.00002: Simulation-based study of wave coherent structures and mean profiles of wind opposing waves propagation. Tao Cao, Lian Shen We performed a large-eddy simulation (LES) of turbulent wind opposing water waves. Based on the simulation data, detailed analyses of wave coherent structures and mean profiles were conducted. It is found that the wave coherent structure is characterized by large in-phase wave-induced pressure, which is symmetric with respective to the surface wave crest. The in-phase pressure wave fluctuation agrees with the inviscid theory well, indicating a self-similar behavior in the outer region. The out-of-phase wave-induced pressure is relatively small compared to the in-phase pressure fluctuation, yet crucial to the momentum transfer from wind to wave. It is found that the Reynolds shear stress plays a critical role in the generation of out-of-phase pressure, which is the direct cause for the form drag on the surface waves. We also observed a modification on the mean streamwise velocity by the surface waves, which is related to the large favorable pressure gradient on the windward face of the surface waves, and the correspondingly damped intensity of turbulent vorticity. |
Sunday, November 18, 2018 5:36PM - 5:49PM |
E04.00003: On the convergence of the normal form transformation in discrete wave turbulence theory for the Charney-Hasegawa-Mima (CHM) equation Shane Walsh, Miguel D Bustamante A crucial problem in discrete wave turbulence theory concerns extending the validity of the normal form transformation beyond the weakly nonlinear limit. The main difficulty is that even if the transformation converges in a given domain around the origin, there is no assurance that all orbits starting in the domain will remain there at all times. Therefore a situation could arise whereby the original system exhibits behavior that is not captured by the normal form system evolution, regardless of the order of the transformation. We demonstrate this for the CHM equation, Galerkin-truncated to 4 Fourier modes. By calculating the transformation to 7th order (keeping all resonances up to 8-wave), we perform numerical simulations of both the original and mapped equations to find that the problems occur precisely when the initial conditions lead to precession resonance, a finite-amplitude phenomenon characterized by strong energy transfers across Fourier modes [1]. We use the dynamical systems approach to extend this result to complex wave-turbulent regimes in the CHM equation, leading to a working definition of convergence radius for normal transformations in terms of invariant manifolds. [1] Bustamante MD et al. (2014) PRL 113, 084502 |
Sunday, November 18, 2018 5:49PM - 6:02PM |
E04.00004: Energy Dissipation and Boundary Flows in Reflecting Internal Waves Bruce Rodenborn, Anh Nguyen, Charlotte Mabbs, Clayton Bell Theoretical analysis of internal wave reflection from a sloping boundary is typically analyzed using linear or a weakly nonlinear inviscid theory (Dauxois and Young, J. Fluid Mech., 390, 1999; Tabaei et al., J. Fluid Mech. 526, 2005). We previously used kinetic energy density to determine the intensity of the fundamental reflection and harmonic waves. Our experiments and simulation data did not match theory (Rodenborn et al. Phys., Fluids, 23, 2011). However, a later paper by Dettner et al. showed that using integrated kinetic energy density is not a good measure of radiated internal wave power (Phys., Fluids, 25, 2013). We reanalyze the reflection problem using an algorithm by Lee et al., which determines the energy flux of internal waves using experimental velocity field measurements. We compare the energy flow into and out of a surface above the reflection region and find high rates of energy dissipation that peak at the critical angle where the dissipation rate is O(90%) for all conditions studied. The reflecting waves create intense boundary flows but little radiated wave power, which may help explain the eroding of continental slopes to the local angle of tidally generated internal waves (Cacchione et al., Science 296, 2002). |
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