Dynamics of Unstable Stokes Waves: A Numerical and Experimental Study

2014 ◽  
Author(s):  
Amin Chabchoub ◽  
Robinson Perić ◽  
Norbert P. Hoffmann
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Rogue Waves ◽  
Surface Flow ◽  
Navier Stokes ◽  
Ocean Engineering ◽  
Navier Stokes Equations ◽  
Stokes Waves ◽  
Finite Volume Approach ◽  
Short Term Prediction

Being an appropriate prototype to describe oceanic rogue waves, the Peregrine breather solution of the nonlinear Schrödinger equation is investigated numerically and experimentally to analyze the dynamics of modulationally unstable Stokes waves. The evolution of the water surface elevation is studied numerically by solving the Navier-Stokes equations using a finite-volume approach and a volume of fluid method. The comparison of the numerical results with wave tank experiments show a very good agreement. The results confirm the ability of the chosen method to model the modulation instability of Stokes waves, in particular, breather dynamics in water waves with high accuracy even up to the onset of breaking. We also investigate the sub-surface flow fields, which may be of significance for the short-term prediction of extreme wave focusing in narrow-banded sea state conditions and therefore, for ocean engineering applications.

scholarly journals Recent Results from Analysis of Flow Structures and Energy Modes Induced by Viscous Wave around a Surface-Piercing Cylinder

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Giancarlo Alfonsi ◽  
Agostino Lauria ◽  
Leonardo Primavera
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wave Flow ◽  
Ocean Engineering ◽  
Navier Stokes Equations ◽  
Pressure Formulation ◽  
The Subject ◽  
Run Up ◽  
Velocity Pressure

Due to its relevance in ocean engineering, the subject of the flow field generated by water waves around a vertical circular cylinder piercing the free surface has recently started to be considered by several research groups. In particular, we studied this problem starting from the velocity-potential framework, then the implementation of the numerical solution of the Euler equations in their velocity-pressure formulation, and finally the performance of the integration of the Navier-Stokes equations in primitive variables. We also developed and applied methods of extraction of the flow coherent structures and most energetic modes. In this work, we present some new results of our research directed, in particular, toward the clarification of the main nonintuitive character of the phenomenon of interaction between a wave and a surface-piercing cylinder, namely, the fact that the wave exerts its maximum force and exhibits its maximum run-up on the cylindrical obstacle at different instants. The understanding of this phenomenon becomes of crucial importance in the perspective of governing the entity of the wave run-up on the obstacle by means of wave-flow-control techniques.

scholarly journals Evidence of Landau Damping in a Fluid Coupled with an Anharmonic Lattice

2018 ◽  
Author(s):  
Andrei Ludu ◽  
Eric Padilla ◽  
M. A. Qaayum Mazumder
Keyword(s):  
Drag Force ◽  
Water Waves ◽  
Stokes Equations ◽  
Collisionless Plasma ◽  
Rogue Waves ◽  
Landau Damping ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Anharmonic Lattice ◽  
Specific Frequency

The Landau damping effect was observed in collisionless plasma, as a microscopic resonant mechanism between electromagnetic radiation and the collective modes. In this paper we demonstrate the occurrence of the Landau damping at macroscopic scale in the interaction between water waves and anharmonic lattice of magnetic buoys. By coupling the Navier-Stokes equations for incompressible fluid with the nonlinear dynamics of an anharmonic magnetic lattice we obtain a resonant transfer of momentum and energy between the two systems. The velocity of the flow is obtained in the Stokes approximation with Basset type of drag force. The dynamics of the buoys is calculated in the surfactant approximation for a specific frequency, then we use Fourier analysis to obtain the general time variable interaction. After involving an integral Dirichlet transform we obtain the time dependent expression of the drag force, the interaction waves-lattice with a new term in the form of a Caputo fractional derivative. We compare the results of the model with experiments performed in a wave tank with free floating magnetic buoys under the action of small amplitude gravitational waves. This configuration can be applied in studies for the attenuation with resonant damping of rogue waves, storms or tsunamis.

Double diffusive effects on pressure-driven miscible displacement flows in a channel

2012 ◽  
Vol 712 ◽  
pp. 579-597 ◽  
Author(s):  
Manoranjan Mishra ◽  
A. De Wit ◽  
Kirti Chandra Sahu
Keyword(s):  
Stokes Equations ◽  
Miscible Displacement ◽  
Interfacial Instability ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Finite Volume Approach ◽  
Diffusive Effects ◽  
The Moment ◽  
Double Diffusive ◽  
Pressure Driven

AbstractThe pressure-driven miscible displacement of a less viscous fluid by a more viscous one in a horizontal channel is studied. This is a classically stable system if the more viscous solution is the displacing one. However, we show by numerical simulations based on the finite-volume approach that, in this system, double diffusive effects can be destabilizing. Such effects can appear if the fluid consists of a solvent containing two solutes both influencing the viscosity of the solution and diffusing at different rates. The continuity and Navier–Stokes equations coupled to two convection–diffusion equations for the evolution of the solute concentrations are solved. The viscosity is assumed to depend on the concentrations of both solutes, while density contrast is neglected. The results demonstrate the development of various instability patterns of the miscible ‘interface’ separating the fluids provided the two solutes diffuse at different rates. The intensity of the instability increases when increasing the diffusivity ratio between the faster-diffusing and the slower-diffusing solutes. This brings about fluid mixing and accelerates the displacement of the fluid originally filling the channel. The effects of varying dimensionless parameters, such as the Reynolds number and Schmidt number, on the development of the ‘interfacial’ instability pattern are also studied. The double diffusive instability appears after the moment when the invading fluid penetrates inside the channel. This is attributed to the presence of inertia in the problem.

scholarly journals COMPARISON OF DIFFERENT METHODS FOR GENERATION AND ABSORPTION OF WATER WAVES

2019 ◽  
Vol 18 (1) ◽  
pp. 71 ◽  
Author(s):  
J. M. P. Conde
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Numerical Models ◽  
Experimental Studies ◽  
Wave Generation ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Wave Absorption ◽  
Water Level Rise

The knowledge of water wave characteristics (generation, propagation, transformation and breaking) is fundamental for hydrodynamic studies and the design of ocean, coastal and port structures. In addition to the small-scale experimental studies, the use of numerical models is also a very important tool in hydrodynamic studies. To have reliable numerical results a proper validation is required. The main objective of this paper is to compare different methods of wave generation and wave absorption in a numerical flume, and to find what is the most suited to simulate non-breaking regular wave propagation in a two-dimensional flume in deep water condition. The numerical simulations were made using the OpenFOAM® software package. Two solvers, waves2Foam and IHFoam/OlaFlow, the utility GroovyBC and a mesh stretching technique are compared. These numerical codes solve the transient Navier-Stokes equations and use a VoF (Volume of Fluid) method to identify the free surface. A solution dependence study with the methods of wave generation and wave absorption is presented. The results are also compared with the theoretical wave and experimental data. The results show that the different methods of generation produce waves similar to the theoretical and the experimental ones, only slightly differences were visible. The three method of wave dissipation considered produce very different results: IHFoam/OlaFlow is not able to dissipate the wave tested; the mesh stretching technique is able to dissipate the waves but produces a water level rise; the waves2Foam solver is able to dissipate properly the wave tested.

scholarly journals Simulations of oil spread on a water surface

2000 ◽  
Vol 214 (6) ◽  
pp. 889-900
Author(s):  
Y Liu ◽  
H Liu ◽  
H Zhang ◽  
G Miao
Keyword(s):  
Water Waves ◽  
Wave Reflection ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Advection Equation ◽  
Navier Stokes Equations ◽  
Oil Slick ◽  
Smooth Plane ◽  
Wavy Surfaces ◽  
Set Up

Numerical simulation of an oil slick spreading on still and wavy surfaces is described in this paper. The so-called σ transformation is used to transform the time-varying physical domain into a fixed calculation domain for the water wave motions and, at the same time, the continuity equation is changed into an advection equation of wave elevation. This evolution equation is discretized by the forward time and central space scheme, and the momentum equations by the projection method. A damping zone is set up in front of the outlet boundary coupled with a Sommerfeld-Orlanski condition at that boundary to minimize the wave reflection. The equations for the oil slick are depth-averaged and coupled with the water motions when solving numerically. As examples, sinusoidal and solitary water waves, the oil spread on a smooth plane and on still and wavy water surfaces are calculated to examine the accuracy of simulating water waves by Navier-Stokes equations, the effect of damping zone on wave reflection and the precise structures of oil spread on waves.

Free Surface Flow Past Ships in Shallow Water

2002 ◽  
Author(s):  
A. Ganguly ◽  
V. Shigunov ◽  
O. Turan
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Near Field ◽  
Free Surface Flow ◽  
Steady State Solution ◽  
Surface Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Medium Speed ◽  
Measured Resistance

A finite volume method with a multiphase type free surface description is employed to calculate the flow around ships in shallow and restricted channels. The flows at critical and supercritical depth Froude numbers (Fnd = 1.0 and Fnd = 1.18) are calculated for Series–60 monohull and a medium speed catamaran. A steady state solution for Reynolds-averaged Navier-Stokes equations with a k-ε turbulence model is obtained by time marching. Computed wave profiles are in good agreement with model tests in the near field of the ship. The computed and measured resistance agree fairly well.

A Three Dimensional Non-Hydrostatic Numerical Model for Free Surface Flow and Mass Transportation

2013 ◽  
Vol 353-356 ◽  
pp. 2496-2501
Author(s):  
Biao Lv
Keyword(s):  
Numerical Model ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Navier Stokes ◽  
Mass Transportation ◽  
Governing Equations ◽  
Navier Stokes Equations ◽  
Good Agreement

A three dimensional non-hydrostatic numerical model is presented based on the incompressible Navier-Stokes equations and mass transport equations. An unstructured finite-volume technique is used to discretized the governing equations with good adaptable to complicated boundary. A conservative scalar transport algorithm is also applied in this model. An integral method of the top- layer pressure is applied to reduce the number of vertical layers. Three classical examples including periodic waves propagating over a submerged bar and non-hydrostatic lock exchange are used to demonstrate the capability and efficiency of the model. The simulation results are in good agreement with the analytical solution and experimental data.

scholarly journals Stokes’s Fundamental Contributions to Fluid Dynamics

2019 ◽  
pp. 115-128
Author(s):  
Peter Lynch
Keyword(s):  
Fluid Dynamics ◽  
Water Waves ◽  
Stokes Equations ◽  
Weather Prediction ◽  
Finite Amplitude ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Basic Equations ◽  
Primary Focus

George Gabriel Stokes made fundamental mathematical contributions to fluid dynamics that had profound practical consequences. The basic equations formulated by him play a central role in numerical weather prediction, in the simulation of blood flow in the body and in countless other important applications. In this chapter the primary focus is on the two most important areas of Stokes’s work on fluid dynamics, the derivation of the Navier–Stokes equations and the theory of finite amplitude oscillatory water waves.

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