A 3D unstructured grid nearshore hydrodynamic model based on the vortex force formalism

Acknowledgments This work was partly supported by joint Engineering and Physical Science Research Council (EPSRC) UK and Technology Foundation STW Netherlands funded SINBAD (EP/J005541/1) project. P. Zheng was supported by the China Scholarship Council during his four-year PhD study at the University of Liverpool. We would like to thank Prof. C.S. Chen of the University of Massachusetts-Dartmouth for providing the source code of FVCOM and also the SWAN developers for developing and providing this open source code. We would also like to thank the staff and personnel involved in collecting and maintaining the DUCK’94 experiment dataset and the anonymous reviewers for their constructive comments and suggestions. Computational support was provided by the Chadwick High Performance Computer at University of Liverpool and also the facilities of N8 HPC Centre of Excellence, provided and funded by the N8 consortium and EPSRC (EP/K000225/1).Peer reviewedPublisher PD

The spatio-temporal spectrum of turbulent flows

Identification and extraction of vortical structures and of waves in a disorganised flow is a mayor challenge in the study of turbulence. We present a study of the spatio-temporal behavior of turbulent flows in the presence of different restitutive forces. We show how to compute and analyse the spatio-temporal spectrum from data stemming from numerical simulations and from laboratory experiments. Four cases are considered: homogeneous and isotropic turbulence, rotating turbulence, stratified turbulence, and water wave turbulence. For homogeneous and isotropic turbulence, the spectrum allows identification of sweeping by the large scale flow. For rotating and for stratified turbulence, the spectrum allows identification of the waves, precise quantification of the energy in the waves and in the turbulent eddies, and identification of physical mechanisms such as Doppler shift and wave absorption in critical layers. Finally, in water wave turbulence the spectrum shows a transition from gravity-capillary waves to bound waves as the amplitude of the forcing is increased.Comment: Added new references and analysi

Cumulant expansions for atmospheric flows

The equations governing atmospheric flows are nonlinear. Consequently, the hierarchy of cumulant equations is not closed. But because atmospheric flows are inhomogeneous and anisotropic, the nonlinearity may manifest itself only weakly through interactions of mean fields with disturbances such as thermals or eddies. In such situations, truncations of the hierarchy of cumulant equations hold promise as a closure strategy. We review how truncations at second order can be used to model and elucidate the dynamics of atmospheric flows. Two examples are considered. First, we study the growth of a dry convective boundary layer, which is heated from below, leading to turbulent upward energy transport and growth of the boundary layer. We demonstrate that a quasilinear truncation of the equations of motion, in which interactions of disturbances among each other are neglected but interactions with mean fields are taken into account, can capture the growth of the convective boundary layer even if it does not capture important turbulent transport terms. Second, we study the evolution of two-dimensional large-scale waves representing waves in Earth's upper atmosphere. We demonstrate that a cumulant expansion truncated at second order (CE2) can capture the evolution of such waves and their nonlinear interaction with the mean flow in some circumstances, for example, when the wave amplitude is small enough or the planetary rotation rate is large enough. However, CE2 fails to capture the flow evolution when nonlinear eddy--eddy interactions in surf zones become important. Higher-order closures can capture these missing interactions. The results point to new ways in which the dynamics of turbulent boundary layers may be represented in climate models, and they illustrate different classes of nonlinear processes that can control wave dissipation and momentum fluxes in the troposphere.Comment: 43 pages, 10 figures, accepted for publication in the New Journal of Physic

Resonant Interactions in Rotating Homogeneous Three-dimensional Turbulence

Direct numerical simulations of three-dimensional (3D) homogeneous turbulence under rapid rigid rotation are conducted to examine the predictions of resonant wave theory for both small Rossby number and large Reynolds number. The simulation results reveal that there is a clear inverse energy cascade to the large scales, as predicted by 2D Navier-Stokes equations for resonant interactions of slow modes. As the rotation rate increases, the vertically-averaged horizontal velocity field from 3D Navier-Stokes converges to the velocity field from 2D Navier-Stokes, as measured by the energy in their difference field. Likewise, the vertically-averaged vertical velocity from 3D Navier-Stokes converges to a solution of the 2D passive scalar equation. The energy flux directly into small wave numbers in the $k_z=0$ plane from non-resonant interactions decreases, while fast-mode energy concentrates closer to that plane. The simulations are consistent with an increasingly dominant role of resonant triads for more rapid rotation

Towards the numerical simulation of 5 Floating Point Absorber Wave Energy Converters installed in a line array using OpenFOAM

In this paper we use the CFD toolbox OpenFOAM to perform numerical simulations of multiple floating point absorber Wave Energy Converters (WECs) in a numerical wave basin. The two-phase Navier-Stokes fluid solver is coupled with a motion solver to simulate the wave-induced rigid body heave motion. The purpose of this paper is twofold. The first objective is to extend numerical simulations of a single WEC unit to multiple WECs and to tackle the issues of modelling individual floating objects close to each other in an array layout. The second objective aims to include all the physical processes (e.g. friction forces) observed during experimental model tests in the numerical simulations. The achievements are verified by validating the numerical model with laboratory experiments for free decay and regular wave tests using a line array of two and five WECs. For all the simulations presented, a good agreement is found between the numerical and experimental results for the WECs’ heave motions, the surge forces on the WECs and the perturbed wave field. As a result, our coupled CFD–motion solver proves to be a suitable and accurate toolbox for the study of wave-structure interaction problems of WEC arrays.location: Cork, Irelandstatus: publishe

Nonlinear resonances of water waves

In the last fifteen years, a great progress has been made in the understanding of the nonlinear resonance dynamics of water waves. Notions of scale- and angle-resonances have been introduced, new type of energy cascade due to nonlinear resonances in the gravity water waves have been discovered, conception of a resonance cluster has been much and successful employed, a novel model of laminated wave turbulence has been developed, etc. etc. Two milestones in this area of research have to be mentioned: a) development of the $q$-class method which is effective for computing integer points on the resonance manifolds, and b) construction of the marked planar graphs, instead of classical resonance curves, representing simultaneously all resonance clusters in a finite spectral domain, together with their dynamical systems. Among them, new integrable dynamical systems have been found that can be used for explaining numerical and laboratory results. The aim of this paper is to give a brief overview of our current knowledge about nonlinear resonances among water waves, and formulate three most important open problems at the end.Comment: 14 pages, 3 figures, to appear in DCDS, final version (small changes in the text, type errors corrected, some additional bibliographic items added