scholarly journals STEEP UNSTEADY WATER WAVES: AN EFFICIENT COMPUTATIONAL SCHEME

1984 ◽  
Vol 1 (19) ◽  
pp. 65 ◽  
Author(s):  
J.W. Dold ◽  
D.H. Peregrine
Keyword(s):  
Water Waves ◽  
Water Surface ◽  
Unsteady Motion ◽  
Boundary Integral ◽  
Computational Scheme ◽  
Multiple Time ◽  
Numerical Implementation ◽  
Surface Motion ◽  
Cauchy Theorem ◽  
Derivatives Of

A new method for computing the unsteady motion of a water surface, including the overturning of water waves as they break, has been developed. It is based on a Cauchy theorem boundary integral for the evaluation of multiple time derivatives of the surface motion. The numerical implementation of the method is efficient, accurate and stable.

Surface Gravity Waves

2017 ◽  
Author(s):  
John A. Adam
Keyword(s):  
Gravity Waves ◽  
Water Waves ◽  
Water Surface ◽  
Wave Pattern ◽  
The Body ◽  
Surface Gravity ◽  
Shallow Water Waves ◽  
Ship Waves ◽  
Surface Gravity Waves ◽  
Basic Fluid

This chapter deals with the underlying mathematics of surface gravity waves, defined as gravity waves observed on an air–sea interface of the ocean. Surface gravity waves, or surface waves, differ from internal waves, gravity waves that occur within the body of the water (such as between parts of different densities). Examples of gravity waves are wind-generated waves on the water surface, as well tsunamis and ocean tides. Wind-generated gravity waves on the free surface of the Earth's seas, oceans, ponds, and lakes have a period of between 0.3 and 30 seconds. The chapter first describes the basic fluid equations before discussing the dispersion relations, with a particular focus on deep water waves, shallow water waves, and wavepackets. It also considers ship waves and how dispersion affects the wave pattern produced by a moving object, along with long and short waves.

Numerical Calculation of the Wave Integrals in the Linearized Theory of Water Waves

1977 ◽  
Vol 21 (01) ◽  
pp. 1-10 ◽  
Author(s):  
Hung-Tao Shen ◽  
Cesar Farell
Keyword(s):  
Water Waves ◽  
Velocity Potential ◽  
Three Dimensional ◽  
Three Dimensional Flow ◽  
Integral Term ◽  
Linearized Theory ◽  
Single Integral ◽  
Numerical Computing ◽  
Complex Exponential ◽  
Derivatives Of

A method for the numerical evaluation of the derivatives of the linearized velocity potential for three-dimensional flow past a unit source submerged in a uniform stream is presented together with a discussion of existing techniques. It is shown in particular that calculation of the double integral term in these functions can be efficiently accomplished in terms of a single integral with the integrand expressed in terms of the complex exponential integral, for which numerical computing techniques are available.

Wave-Induced Effect on the Airside Velocity Field Above the Wind-Generated Water Waves

2008 ◽  
Author(s):  
Nasiruddin Shaikh ◽  
Kamran Siddiqui
Keyword(s):  
Velocity Field ◽  
Water Waves ◽  
Water Surface ◽  
Flow Behavior ◽  
Wave Crest ◽  
Reynolds Stresses ◽  
Momentum Exchange ◽  
Significant Wave ◽  
Wind Speeds ◽  
Wave Induced

An experimental study was conducted to investigate the influence of surface waves on the airside flow behavior over the water surface. Two-dimensional velocity field in a plane perpendicular to the surface was measured using particle image velocimetry (PIV) at wind speeds of 3.7 and 4.4 m s−1. The results show that the wave induced velocities are significant immediately adjacent to the water surface and their magnitudes decreases with height and become negligible at a height three times the significant wave height. The structure of the wave induced vorticity indicates two different type of flow pattern on the windward and leeward sides of the wave crest. Positive and negative magnitudes of the turbulent and wave induced Reynolds stress respectively, indicates upward and down transfer of momentum flux across air water interface. The results also indicate that the flow dynamics in the region two to three times significant wave heights are significantly different than that at greater heights. Higher magnitudes of the turbulent and wave induced Reynolds stresses were observed in this region which could not be predicted from the measurements at greater heights. Thus, it is concluded the understanding of the wave effects to the airflow field especially within the crest-trough region is vital to improve our knowledge about the air-water heat, mass and momentum exchange.

Nonlinear Water Waves in the Presence of Submerged Elliptic Cylinder

2004 ◽  
Author(s):  
Nikolai I. Makarenko
Keyword(s):  
Free Surface ◽  
Water Waves ◽  
Boundary Integral Equations ◽  
Fluid Velocity ◽  
Elliptic Cylinder ◽  
Small Time ◽  
Boundary Integral ◽  
Nonlinear Water Waves ◽  
Wave Elevation ◽  
Boundary Equations

The fully nonlinear problem on unsteady two-dimensional water waves generated by elliptic cylinder, that is horizontally submerged beneath a free surface, is considered. An analytical boundary integral equations method using a version of Milne-Thomson transformation is developed. Boundary equations (the BEq system) determine immediately exact wave elevation and fluid velocity at free surface. Small-time solution expansion is obtained in the case of accelerated cylinder starting from rest.

Hydrodynamic Interactions of the Truncated Porous Vertical Circular Cylinder With Water Waves

2018 ◽  
Author(s):  
Charaf Ouled Housseine ◽  
Sime Malenica ◽  
Guillaume De Hauteclocque ◽  
Xiao-Bo Chen
Keyword(s):  
Circular Cylinder ◽  
Porous Body ◽  
Wave Diffraction ◽  
Water Waves ◽  
Expansion Method ◽  
Integral Equation Method ◽  
Boundary Integral ◽  
Diffraction Radiation ◽  
Linear Potential ◽  
Eigenfunction Expansion Method

Wave diffraction-radiation by a porous body is investigated here. Linear potential flow theory is used and the associated Boundary Value Problem (BVP) is formulated in frequency domain within a linear porosity condition. First, a semi-analytical solution for a truncated porous circular cylinder is developed using the dedicated eigenfunction expansion method. Then the general case of wave diffraction-radiation by a porous body with an arbitrary shape is discussed and solved through Boundary Integral Equation Method (BIEM). The main goal of these developments is to adapt the existing diffraction-radiation code (HYDROSTAR) for that type of applications. Thus the present study of the porous cylinder consists a validation work of (BIEM) numerical implementation. Excellent agreement between analytical and numerical results is observed. Porosity influence on wave exciting forces, added mass and damping is also investigated.

scholarly journals KINEMATICS AND RETURN FLOW IN A CLOSED WAVE FLUME

1988 ◽  
Vol 1 (21) ◽  
pp. 31 ◽  
Author(s):  
Jerald D. Ramsden ◽  
John H. Nath
Keyword(s):  
Water Waves ◽  
Water Surface ◽  
Large Scale ◽  
Wave Motion ◽  
Finite Amplitude ◽  
Return Flow ◽  
Order Stream ◽  
Wave Flume ◽  
Seventh Order ◽  
Surface Measurements

Stokes (1847) showed that finite amplitude progressing waves cause a net drift of fluid, in the direction of wave motion, which occurs in the upper portion of the water column. In a closed wave flume this drift must be accompanied by a return flow toward the wave generator to satisfy the conservation of mass. This study presents Eulerian velocity and water surface measurements soon after the onset of wave motion from 12 locations in a large scale flume. Waves with .67 < kh < 2.29 and .09 < H/h < .39 were produced in a water depth of 3.5 meters. Superimposing the return flow theory of Kim (1984) with seventh order stream function theory is shown to improve the velocity predictions. The measured return flows are a function of time and depth and agree with Kim's theory as a first approximation. The mean water surface set-down agrees with the theory of Brevik (1979) except for the nearly deep water waves.

scholarly journals Statistical Parameters of the Air Turbulent Boundary Layer over Steep Water Waves Measured by the PIV Technique

2011 ◽  
Vol 41 (8) ◽  
pp. 1421-1454 ◽  
Author(s):  
Yu. Troitskaya ◽  
D. Sergeev ◽  
O. Ermakova ◽  
G. Balandina
Keyword(s):  
Boundary Layer ◽  
Turbulent Boundary Layer ◽  
Interaction Parameter ◽  
Water Waves ◽  
Water Surface ◽  
Wind Wave ◽  
Wave Interaction ◽  
Statistical Parameters ◽  
Piv Technique ◽  
Wave Induced

Abstract A turbulent airflow with a centerline velocity of 4 m s−1 above 2.5-Hz mechanically generated gravity waves of different amplitudes has been studied in experiments using the particle image velocimetry (PIV) technique. Direct measurements of the instantaneous flow velocity fields above a curvilinear interface demonstrating flow separation are presented. Because the airflow above the wavy water surface is turbulent and nonstationary, the individual vector fields are conditionally averaged sampled on the phase of the water elevation. The flow patterns of the phase-averaged fields are relatively smooth. Because the averaged flow does not show any strongly nonlinear effects, the quasi-linear approximation can be used. The parameters obtained by the flow averaging are compared with the theoretical results obtained within the theoretical quasi-linear model of a turbulent boundary layer above the wavy water surface. The wave-induced pressure disturbances in the airflow are calculated using the retrieved statistical ensemble of wind flow velocities. The energy flux from the wind to waves and the wind–wave interaction parameter are estimated using the obtained wave-induced pressure disturbances. The estimated values of the wind–wave interaction parameter are in a good agreement with the theory.

scholarly journals Controlled impact of a disk on a water surface: cavity dynamics

2009 ◽  
Vol 633 ◽  
pp. 381-409 ◽  
Author(s):  
RAYMOND BERGMANN ◽  
DEVARAJ VAN DER MEER ◽  
STEPHAN GEKLE ◽  
ARJAN VAN DER BOS ◽  
DETLEF LOHSE
Keyword(s):  
Particle Image Velocimetry ◽  
Water Surface ◽  
High Speed ◽  
Particle Image ◽  
Boundary Integral ◽  
Infinite Cylinder ◽  
High Speed Imaging ◽  
Image Velocimetry ◽  
Minimal Radius ◽  
Surface Cavity

In this paper we study the transient surface cavity which is created by the controlled impact of a disk of radius h0 on a water surface at Froude numbers below 200. The dynamics of the transient free surface is recorded by high-speed imaging and compared to boundary integral simulations giving excellent agreement. The flow surrounding the cavity is measured with high-speed particle image velocimetry and is found to also agree perfectly with the flow field obtained from the simulations.We present a simple model for the radial dynamics of the cavity based on the collapse of an infinite cylinder. This model accounts for the observed asymmetry of the radial dynamics between the expansion and the contraction phases of the cavity. It reproduces the scaling of the closure depth and total depth of the cavity which are both found to scale roughly as ∝ Fr1/2 with a weakly Froude-number-dependent prefactor. In addition, the model accurately captures the dynamics of the minimal radius of the cavity and the scaling of the volume Vbubble of air entrained by the process, namely, Vbubble/h03∝(1 + 0.26Fr1/2)Fr1/2.

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