Enhancing Signal-to-Noise Ratios of High-Frequency Rayleigh Waves Extracted from Ambient Seismic Noises in Topographic Region

2020 ◽  
Vol 110 (2) ◽  
pp. 793-802
Author(s):  
Ping Ping ◽  
Risheng Chu ◽  
Yu Zhang ◽  
Jun Xie
Keyword(s):  
Free Surface ◽  
Correlation Functions ◽  
High Frequency ◽  
Rayleigh Waves ◽  
Vertical Component ◽  
Noise Correlation ◽  
Surface Boundary ◽  
Elastic Wedge ◽  
Signal To Noise ◽  
Surface Boundary Conditions

ABSTRACT High-frequency Rayleigh waves can be extracted from ambient seismic noises through noise correlation functions (NCFs), which provides a useful tool to image shallow structures in topographic regions, for example, landslides. Topography may affect signal-to-noise ratios (SNRs) of extracted Rayleigh waves. It is necessary to investigate the propagation features of Rayleigh waves passing a 3D topography. Based on the incident and scattered waves satisfying the free surface boundary conditions, we first derive the displacement responses of Rayleigh waves across a 3D elastic wedge. The results show that the particle motions of Rayleigh waves are an ellipse whose longer axis is always perpendicular to the topographic free surface. Therefore, the Qg component, perpendicular to the topographic free surface, is a better choice to extract high-frequency Rayleigh waves than the conventional vertical component. To verify the choice, we carry out numerical simulations to extract high-frequency NCFs for a typical 3D massif model. Finally, we apply this approach to extract high-frequency Rayleigh-wave NCFs on the Xishancun landslide in southwestern China. The NCFs obtained using the Qg component have more coherent waveforms and higher SNRs than those using the vertical component. We conclude that the Qg component has advantages in extracting high-frequency Rayleigh waves over the conventional vertical component.

Novel free surface boundary conditions for spilling breaking waves

2020 ◽  
Vol 159 ◽  
pp. 103717
Author(s):  
Nikta Iravani ◽  
Peyman Badiei ◽  
Maurizio Brocchini
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Breaking Waves ◽  
Surface Boundary ◽  
Surface Boundary Conditions

scholarly journals Linear pulse structure and signalling in a film flow on an inclined plane

1999 ◽  
Vol 396 ◽  
pp. 37-71 ◽  
Author(s):  
LEONID BREVDO ◽  
PATRICE LAURE ◽  
FREDERIC DIAS ◽  
THOMAS J. BRIDGES
Keyword(s):  
Free Surface ◽  
Saddle Point ◽  
Convective Instability ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Numerical Results ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

The film flow down an inclined plane has several features that make it an interesting prototype for studying transition in a shear flow: the basic parallel state is an exact explicit solution of the Navier–Stokes equations; the experimentally observed transition of this flow shows many properties in common with boundary-layer transition; and it has a free surface, leading to more than one class of modes. In this paper, unstable wavepackets – associated with the full Navier–Stokes equations with viscous free-surface boundary conditions – are analysed by using the formalism of absolute and convective instabilities based on the exact Briggs collision criterion for multiple k-roots of D(k, ω) = 0; where k is a wavenumber, ω is a frequency and D(k, ω) is the dispersion relation function.The main results of this paper are threefold. First, we work with the full Navier–Stokes equations with viscous free-surface boundary conditions, rather than a model partial differential equation, and, guided by experiments, explore a large region of the parameter space to see if absolute instability – as predicted by some model equations – is possible. Secondly, our numerical results find only convective instability, in complete agreement with experiments. Thirdly, we find a curious saddle-point bifurcation which affects dramatically the interpretation of the convective instability. This is the first finding of this type of bifurcation in a fluids problem and it may have implications for the analysis of wavepackets in other flows, in particular for three-dimensional instabilities. The numerical results of the wavepacket analysis compare well with the available experimental data, confirming the importance of convective instability for this problem.The numerical results on the position of a dominant saddle point obtained by using the exact collision criterion are also compared to the results based on a steepest-descent method coupled with a continuation procedure for tracking convective instability that until now was considered as reliable. While for two-dimensional instabilities a numerical implementation of the collision criterion is readily available, the only existing numerical procedure for studying three-dimensional wavepackets is based on the tracking technique. For the present flow, the comparison shows a failure of the tracking treatment to recover a subinterval of the interval of unstable ray velocities V whose length constitutes 29% of the length of the entire unstable interval of V. The failure occurs due to a bifurcation of the saddle point, where V is a bifurcation parameter. We argue that this bifurcation of unstable ray velocities should be observable in experiments because of the abrupt increase by a factor of about 5.3 of the wavelength across the wavepacket associated with the appearance of the bifurcating branch. Further implications for experiments including the effect on spatial amplification rate are also discussed.

REEF3D::FNPF—A Flexible Fully Nonlinear Potential Flow Solver

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Hans Bihs ◽  
Weizhi Wang ◽  
Csaba Pakozdi ◽  
Arun Kamath
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Wave Model ◽  
Surface Boundary ◽  
Wave Fields ◽  
Flow Solver ◽  
Surface Boundary Conditions ◽  
Nonlinear Potential ◽  
Numerical Wave ◽  
Computational Resources

Abstract In situations where the calculation of ocean wave propagation and impact on structures are required, fast numerical solvers are desired in order to find relevant wave events. Computational fluid dynamics (CFD)-based numerical wave tanks (NWTs) emphasize on the hydrodynamic details such as fluid–structure interaction, which make them less ideal for the event identification due to the large computational resources involved. Therefore, a computationally efficient numerical wave model is needed to identify the events both for offshore deep-water wave fields and coastal wave fields where the bathymetry and coastline variations have strong impact on wave propagation. In the current paper, a new numerical wave model is represented that solves the Laplace equation for the flow potential and the nonlinear kinematic and dynamics free surface boundary conditions. This approach requires reduced computational resources compared to CFD-based NWTs. The resulting fully nonlinear potential flow solver REEF3D::FNPF uses a σ-coordinate grid for the computations. This allows the grid to follow the irregular bottom variation with great flexibility. The free surface boundary conditions are discretized using fifth-order weighted essentially non-oscillatory (WENO) finite difference methods and the third-order total variation diminishing (TVD) Runge–Kutta scheme for time stepping. The Laplace equation for the potential is solved with Hypre’s stabilized bi-conjugated gradient solver preconditioned with geometric multi-grid. REEF3D::FNPF is fully parallelized following the domain decomposition strategy and the message passing interface (MPI) communication protocol. The numerical results agree well with the experimental measurements in all tested cases and the model proves to be efficient and accurate for both offshore and coastal conditions.

Three-Dimensional Large Amplitude Body Motions in Waves

2007 ◽  
Author(s):  
Xinshu Zhang ◽  
Robert F. Beck
Keyword(s):  
Free Surface ◽  
Three Dimensional ◽  
Surface Boundary ◽  
Forward Speed ◽  
Time Step ◽  
Surface Boundary Conditions ◽  
Submerged Body ◽  
Calm Water ◽  
Wigley Hull ◽  
Constant Strength

Three-dimensional, time-domain, wave-body interactions are studied in this paper for cases with and without forward speed. In the present approach, an exact body boundary condition and linearized free surface boundary conditions are used. By distributing desingularized sources above the calm water surface and using constant-strength panels on the exact submerged body surface, the boundary integral equations are solved numerically at each time step. Once the fluid velocities on the free surface are computed, the free surface elevation and potential are updated by integrating the free surface boundary conditions. After each time step, the body surface and free surface are regrided due to the instantaneous changing submerged body geometry. The desingularized method applied on the free surface produces non-singular kernels in the integral equations by moving the fundamental singularities a small distance outside of the fluid domain. Constant strength panels are used for bodies with any arbitrary shape. Extensive results are presented to validate the efficiency of the present method. These results include the added mass and damping computations for a hemisphere. The calm water wave resistance for a submerged spheroid and a Wigley hull are also presented. All the computations with forward speed are started from rest and proceed until a steady state is reached. Finally, the time-domain forced motion results for a modified Wigley hull with forward speed are shown and compared with the experiments for both linear computations and body-exact computations.

REEF3D::FNPF: A Flexible Fully Nonlinear Potential Flow Solver

2019 ◽  
Author(s):  
Hans Bihs ◽  
Weizhi Wang ◽  
Tobias Martin ◽  
Arun Kamath
Keyword(s):  
Wave Propagation ◽  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Surface Boundary ◽  
Flow Solver ◽  
Surface Boundary Conditions ◽  
Nonlinear Potential ◽  
Numerical Wave ◽  
Computational Resources

Abstract In situations where the calculation of ocean wave propagation and impact on offshore structures is required, fast numerical solvers are desired in order to find relevant wave events in a first step. After the identification of the relevant events, Computational Fluid Dynamics (CFD) based Numerical Wave Tanks (NWT) with an interface capturing two-phase flow approach can be used to resolve the complex wave structure interaction, including breaking wave kinematics. CFD models emphasize detail of the hydrodynamic physics, which makes them not the ideal candidate for the event identification due to the large computational resources involved. In the current paper a new numerical wave model is represented that solves the Laplace equation for the flow potential and the nonlinear kinematic and dynamics free surface boundary conditions. This approach requires reduced computational resources compared to CFD based NWTs. In contrast to existing approaches, the resulting fully nonlinear potential flow solver REEF3D::FNPF uses a σ-coordinate grid for the computations. Solid boundaries are incorporated through a ghost cell immersed boundary method. The free surface boundary conditions are discretized using fifth-order WENO finite difference methods and the third-order TVD Runge-Kutta scheme for time stepping. The Laplace equation for the potential is solved with Hypres stabilized bi-conjugated gradient solver preconditioned with geometric multi-grid. REEF3D::FNPF is fully parallelized following the domain decomposition strategy and the MPI communication protocol. The model is successfully tested for wave propagation benchmark cases for shallow water conditions with variable bottom as well as deep water.

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