Nonlinear interaction of shear flow with a free surface

1994 ◽  
Vol 260 ◽  
pp. 211-246 ◽  
Author(s):  
Athanassios A. Dimas ◽  
George S. Triantafyllou
Keyword(s):  
Free Surface ◽  
Velocity Field ◽  
Shear Flow ◽  
Nonlinear Evolution ◽  
Ocean Surface ◽  
Computer Code ◽  
Linear Instability ◽  
Free Surface Elevation ◽  
Instability Waves ◽  
Induced Velocity

In this paper the nonlinear evolution of two-dimensional shear-flow instabilities near the ocean surface is studied. The approach is numerical, through direct simulation of the incompressible Euler equations subject to the dynamic and kinematic boundary conditions at the free surface. The problem is formulated using boundary-fitted coordinates, and for the numerical simulation a spectral spatial discretization method is used involving Fourier modes in the streamwise direction and Chebyshev polynomials along the depth. An explicit integration is performed in time using a splitting scheme. The initial state of the flow is assumed to be a known parallel shear flow with a flat free surface. A perturbation having the form of the fastest growing linear instability mode of the shear flow is then introduced, and its subsequent evolution is followed numerically. According to linear theory, a shear flow with a free surface has two linear instability modes, corresponding to different branches of the dispersion relation: Branch I, at low wavenumbers; and Branch II, at high wavenumbers for low Froude numbers, and low wavenumbers for high Froude numbers. Our simulations show that the two branches have a distinctly different nonlinear evolution.Branch I: At low Froude numbers, Branch I instability waves develop strong oval-shaped vortices immediately below the ocean surface. The induced velocity field presents a very sharp shear near the crest of the free-surface elevation in the horizontal direction. As a result, the free-surface wave acquires steep slopes, while its amplitude remains very small, and eventually the computer code crashes suggesting that the wave will break.Branch II: At low Froude numbers, Branch II instability waves develop weak vortices with dimensions considerably smaller than their distance from the ocean surface. The induced velocity field at the ocean surface varies smoothly in space, and the free-surface elevation takes the form of a propagating wave. At high Froude numbers, however, the growing rates of the Branch II instability waves increase, resulting in the formation of strong vortices. The free surface reaches a large amplitude, and strong vertical velocity shear develops at the free surface. The computer code eventually crashes suggesting that the wave will break. This behaviour of the ocean surface persists even in the infinite-Froude-number limit.It is concluded that the free-surface manifestation of shear-flow instabilities acquires the form of a propagating water wave only if the induced velocity field at the ocean surface varies smoothly along the direction of propagation.

scholarly journals Simulación numérica del sloshing

2019 ◽  
pp. 68-75
Keyword(s):  
Free Surface ◽  
Rio De Janeiro ◽  
Computer Code ◽  
Numerical Code ◽  
Offshore Platforms ◽  
Initial Condition ◽  
Free Surface Elevation ◽  
Variation Diminishing ◽  
Computational Mesh ◽  
The Finite Difference Method

Simulación numérica del sloshing Numerical simulation of sloshing Miguel A. Celis Carbajal, Juan B.V.Wanderley, Marcelo A.S. Neves Universidad Federal de Rio de Janeiro/COPPE, Rio de Janeiro, RJ, Brasil DOI: https://doi.org/10.33017/RevECIPeru2011.0012/ RESUMEN El sloshing es de gran importancia en la dinámica de los buques y plataformas offshore. Es uno de los factores que pueden causar cargas indeseables e incluso la zozobra de los cuerpos flotantes. Esto sucede cuando el buque está en condiciones no deseadas, tales como la inundación progresiva en condiciones de avería. El objetivo es representar numéricamente el efecto del sloshing, el modelo numérico está basado en el método de diferencias finitas, en el cual representaremos el fluido incompresible y sin efectos viscosos a través de la ecuación de Euler este se resuelven mediante el esquema upwind TVD (Disminución de la Variación Total), esta fue formulado por Roe (1984) [1] y Sweby (1984) [2]. El código computacional representa el efecto del sloshing en un compartimento cerrado en 2D y 3D. Para representar adecuadamente el compartimento se utiliza una malla computacional estructurada. Las condiciones iniciales son impuestas por un plano inclinado de la superficie libre. Otro intento de probar la versatilidad del código informático es mediante la simulación de la caída de una esfera de agua sobre la superficie libre del tanque con agua. Descriptores: CFD, Sloshing TVD. ABSTRACT In this paper, we study the effect of sloshing in a compartment of a naval artifact. The sloshing is of great importance in the dynamics of ships and offshore platforms, it is one of the factors that may cause the capsizing. This happens when the ship is under undesirable conditions, such as progressive flooding or fault conditions. The goal is to represent numerically the effect of sloshing. The numerical code is validated through comparisons with numerical and experimental data obtained in the literature. The numerical model is based on the finite difference method, where the Euler equations are solved using the upwind scheme and TVD (Total Variation Diminishing) Roe (1984) and Sweby (1984). The computer code for 2D represents the effect of sloshing in a closed vessel. To adequately represent the reservoir of the naval artifact, we used a structured computational mesh, where the fluid is forced to move by the excitation applied to the tank, this type of excitation is harmonic in sway. For the 3D computer code, a sloped free surface elevation is used as initial condition. Another attempt to realize the versatility of the computer code was the fall of a sphere of water on the free surface of the tank. Keywords: CFD, Sloshing TVD.

A nonlinear Schrödinger equation for gravity waves slowly modulated by linear shear flow

2020 ◽  
Author(s):  
Shaofeng Li ◽  
Juan Chen ◽  
Anzhou Cao ◽  
Jinbao Song
Keyword(s):  
Free Surface ◽  
Shear Flow ◽  
Gravity Waves ◽  
Surface Elevation ◽  
Necessary Condition ◽  
Free Surface Elevation ◽  
Dinger Equation ◽  
Freak Waves ◽  
Positive Vorticity ◽  
Linear Shear

<p>Assume that a fluid is inviscid, incompressible, and irrotational. A nonlinear Schrödinger equation (NLSE) describing the evolution of gravity waves in finite water depth is derived using the multiple scale analysis method. The gravity waves are influenced by a linear shear flow, which is composed of a uniform flow and a shear flow with constant vorticity. The modulational instability (MI) of the NLSE was analyzed in this paper, and the region of MI for gravity waves (the necessary condition for the existence of freak waves) was identified. In this paper, the uniform background flows along or against wave propagation are referred to as down-flow and up-flow, respectively. Uniform up-flow enhances the MI, whereas uniform down-flow reduces it. Positive vorticity enhances the MI, while negative vorticity reduces it. Hence, the influence of positive (negative) vorticity on MI can be balanced out by that of uniform down- (up-)flow. Furthermore, the Peregrine breather (PB) solution of the NLSE is applied to freak waves. Uniform up-flow increases the steepness of free surface elevation, while uniform down-flow decreases it. Positive vorticity increases the steepness of free surface elevation, whereas negative vorticity decreases it.</p>

A Numerical Investigation on 2D and 3D Sloshing Effects

2011 ◽  
Author(s):  
Miguel A. Celis C. ◽  
Juan B. V. Wanderley ◽  
Marcelo A. S. Neves
Keyword(s):  
Free Surface ◽  
Computer Code ◽  
Numerical Code ◽  
Offshore Platforms ◽  
Initial Condition ◽  
Free Surface Elevation ◽  
Variation Diminishing ◽  
Computational Mesh ◽  
The Finite Difference Method ◽  
2D And 3D

In this paper, we study the effect of sloshing in a compartment of a naval artifact. The sloshing is of great importance in the dynamics of ships and offshore platforms, it is one of the factors that may cause the capsizing. This happens when the ship is under undesirable conditions, such as progressive flooding or fault conditions. The goal is to represent numerically the effect of sloshing. The numerical code is validated through comparisons with numerical and experimental data obtained in the literature. The numerical model is based on the finite difference method, where the Euler equations are solved using the upwind scheme and TVD (Total Variation Diminishing) Roe (1984) and Sweby (1984). The computer code for 2D represents the effect of sloshing in a closed vessel. To adequately represent the reservoir of the naval artifact, we used a structured computational mesh, where the fluid is forced to move by the excitation applied to the tank, this type of excitation is harmonic in sway. For the 3D computer code, a sloped free surface elevation is used as initial condition. Another attempt to realize the versatility of the computer code was the fall of a sphere of water on the free surface of the tank.

A note on the instabilities of a horizontal shear flow with a free surface

2000 ◽  
Vol 406 ◽  
pp. 337-346 ◽  
Author(s):  
L. ENGEVIK
Keyword(s):  
Surface Tension ◽  
Free Surface ◽  
Shear Flow ◽  
Velocity Profile ◽  
Froude Number ◽  
The Other ◽  
Algebraic Equations ◽  
Horizontal Shear ◽  
Analytical Treatment ◽  
Unstable Region

The instabilities of a free surface shear flow are considered, with special emphasis on the shear flow with the velocity profile U* = U*0sech2 (by*). This velocity profile, which is found to model very well the shear flow in the wake of a hydrofoil, has been focused on in previous studies, for instance by Dimas & Triantyfallou who made a purely numerical investigation of this problem, and by Longuet-Higgins who simplified the problem by approximating the velocity profile with a piecewise-linear profile to make it amenable to an analytical treatment. However, none has so far recognized that this problem in fact has a very simple solution which can be found analytically; that is, the stability boundaries, i.e. the boundaries between the stable and the unstable regions in the wavenumber (k)–Froude number (F)-plane, are given by simple algebraic equations in k and F. This applies also when surface tension is included. With no surface tension present there exist two distinct regimes of unstable waves for all values of the Froude number F > 0. If 0 < F [Lt ] 1, then one of the regimes is given by 0 < k < (1 − F2/6), the other by F−2 < k < 9F−2, which is a very extended region on the k-axis. When F [Gt ] 1 there is one small unstable region close to k = 0, i.e. 0 < k < 9/(4F2), the other unstable region being (3/2)1/2F−1 < k < 2 + 27/(8F2). When surface tension is included there may be one, two or even three distinct regimes of unstable modes depending on the value of the Froude number. For small F there is only one instability region, for intermediate values of F there are two regimes of unstable modes, and when F is large enough there are three distinct instability regions.

scholarly journals An evaluation of linear instability waves as sources of sound in a supersonic turbulent jet

2002 ◽  
Vol 14 (10) ◽  
pp. 3593-3600 ◽  
Author(s):  
Kamran Mohseni ◽  
Tim Colonius ◽  
Jonathan B. Freund
Keyword(s):  
Linear Instability ◽  
Turbulent Jet ◽  
Instability Waves

Numerical Investigation of Focused Waves and Their Interaction With a Vertical Cylinder Using REEF3D

2017 ◽  
Vol 139 (4) ◽  
Author(s):  
Hans Bihs ◽  
Mayilvahanan Alagan Chella ◽  
Arun Kamath ◽  
Øivind Asgeir Arntsen
Keyword(s):  
Free Surface ◽  
Stokes Equations ◽  
Free Surface Flows ◽  
Surface Elevation ◽  
Numerical Wave Tank ◽  
Free Surface Elevation ◽  
Wave Tank ◽  
Numerical Wave ◽  
Focused Wave ◽  
The Impact

For the stability of offshore structures, such as offshore wind foundations, extreme wave conditions need to be taken into account. Waves from extreme events are critical from the design perspective. In a numerical wave tank, extreme waves can be modeled using focused waves. Here, linear waves are generated from a wave spectrum. The wave crests of the generated waves coincide at a preselected location and time. Focused wave generation is implemented in the numerical wave tank module of REEF3D, which has been extensively and successfully tested for various wave hydrodynamics and wave–structure interaction problems in particular and for free surface flows in general. The open-source computational fluid dynamics (CFD) code REEF3D solves the three-dimensional Navier–Stokes equations on a staggered Cartesian grid. Higher order numerical schemes are used for time and spatial discretization. For the interface capturing, the level set method is selected. In order to test the generated waves, the time series of the free surface elevation are compared with experimental benchmark cases. The numerically simulated free surface elevation shows good agreement with experimental data. In further computations, the impact of the focused waves on a vertical circular cylinder is investigated. A breaking focused wave is simulated and the associated kinematics is investigated. Free surface flow features during the interaction of nonbreaking focused waves with a cylinder and during the breaking process of a focused wave are also investigated along with the numerically captured free surface.

Nonlinear Wave Crest Distribution on a Vertical Breakwater

2018 ◽  
Author(s):  
Valentina Laface ◽  
Giovanni Malara ◽  
Felice Arena ◽  
Ioannis A. Kougioumtzoglou ◽  
Alessandra Romolo
Keyword(s):  
Experimental Data ◽  
Free Surface ◽  
Vertical Wall ◽  
Surface Elevation ◽  
Wave Crest ◽  
Height Distribution ◽  
Free Surface Elevation ◽  
Pressure Transducers ◽  
Pressure Time ◽  
Time Histories

The paper addresses the problem of deriving the nonlinear, up to the second order, crest wave height probability distribution in front of a vertical wall under the assumption of finite spectral bandwidth, finite water depth and long-crested waves. The distribution is derived by relying on the Quasi-Deterministic representation of the free surface elevation in front of the vertical wall. The theoretical results are compared against experimental data obtained by utilizing a compressive sensing algorithm for reconstructing the free surface elevation in front of the wall. The reconstruction is pursued by starting from recorded wave pressure time histories obtained by utilizing a row of pressure transducers located at various levels. The comparison shows that there is an excellent agreement between the proposed distribution and the experimental data and confirm the deviation of the crest height distribution from the Rayleigh one.

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