Kelvin wake in the presence of surface waves

Shugan, Igor V.; Lee, Kwi-Joo; Sun, An Jung

doi:10.1016/j.physleta.2006.06.062

Cited by 6 publications

(4 citation statements)

References 8 publications

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“…This angle is labeled as the Kelvin angle in the present paper. However, many observations of wakes show this angle is variable depending on the water depth and the streamwise length of the object producing the disturbance [9,[15][16][17][18]. While the theoretical exploration of the wake generation is besides the scope of the present paper, we summarize here for completeness.…”

Section: Methodology Backgroundmentioning

confidence: 95%

Velocimetry Based on Self-Generated Surface Wave Patterns

Lin

Muste

2020

Water

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This paper introduces an image analysis technique applied to an artificially-created disturbance at the free surface of a moving water body as a means of quantifying the average velocity of the water stream for shallow flows. The disturbance was created by a thin object penetrating the free surface with different submerged distances. A V-shaped wake pattern was created by the object of interest through its variation with the water body velocity, the submergence and shape of the piercing body. The angle of the wake pattern decreased with the increase of the velocity for a depth-based Froude number ranging from 0.15 to 0.96. The proof-of-concept experiments presented in this paper, therefore, are usable to quantify the velocity based on the wake angle only in subcritical flow conditions. The results showed the shape of the wake was only slightly influenced by the shape of the object geometry and its submergence. Observations on various types of surface wakes have been documented before, but it is the conversion of these observations into a relatively inexpensive and robust method to estimate the velocity of the moving body that is deemed innovative.

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Section: Methodology Backgroundmentioning

confidence: 95%

Velocimetry Based on Self-Generated Surface Wave Patterns

Lin

Muste

2020

Water

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“…First of all, the classical model is based on the approximation of deep water and the movement of the ship in the absence of wind waves and currents in calm water. Accounting for the finite depth of the sea and the presence of wind surface waves can significantly change the structure of the ship wake [17,18]. The angle of the wake and the characteristics of the ship's waves in this case fundamentally depend on the speed of the ship, the depth of the water and the field of wind surface waves.…”

Section: Introductionmentioning

confidence: 99%

“…The presented kinematic model reproduced the main features of the Kelvin solution and attracted attention with its simplicity and clarity. An extension of the ship's wake kinematic model for a finite water depth and in the presence of wind waves was carried out in [17,18]. More recently, we presented a model of a ship wake on a shear flow at an infinite water depth [33].…”

Section: Introductionmentioning

confidence: 99%

Ship’s Wake on a Finite Water Depth in the Presence of a Shear Flow

Shugan

Chen

2022

JMSE

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The ship’s wake in the presence of a shear flow of constant vorticity at a finite water depth is investigated by expanding the Whitham-Lighthill kinematic theory. It has been established that the structure of a wave ship wake radically depends on Froude number Fr (in terms of water depth) and especially on the critical Froude number Frcr, which depends on the magnitude and direction of the shear flow. At its subcritical values Fr<Frcr two types of waves are presented: long transverse and short divergent waves inside the wedge area with an angle depending on Fr For the supercritical range Fr>Frcr only divergent waves are presented inside the wake region. Critical Froude number Frcr is variable and mostly depends on collinear with the ship path component of the shear flow: it decreases with the unidirectional shear flow and increases on the counter shear current. The wedge angle of the ship wake expands with an increase in the unidirectional shear flow and narrows in the oncoming flow in the subcritical mode of the ship’s motion Fr<Frcr. Wake angle decreased with Froude number for Fr>Frcr and only divergent waves with the crests almost collinear with ship path are finally presented in the narrow ship wake. For a critical value of the Froude number Fr=Frcr, the ship’s wake has a total wedge angle of 1800 with waves directed parallel to the ship’s motion. The presence of a shear flow crossing the path of the ship gives a strong asymmetry to the wake. An increase in the perpendicular shear flow leads to an increase in the difference between the angles of the wake arms.

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“…Modeling a ship's wake in calm water and in deep water approaching is one of the main reasons for this discrepancy. Wind waves and a finite sea depth approach can significantly alter a ship's wake [19,20]. The wake angle and the cusp waves' characteristics in this case strongly depend on the ship's speed and the depth of the water.…”

Section: Introductionmentioning

confidence: 99%

Kinematics of the Ship’s Wake in the Presence of a Shear Flow

Shugan

Chen

2020

JMSE

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We present the kinematic model of the ship wake in the presence of horizontal subsurface current linearly varying with the depth of water. An extension of the Whitham–Lighthill theory for calm water is developed. It has been established that the structure of ship waves under the action of a shear flow can radically differ from the classical Kelvin ship wake model. Co propagating ship and shear current lead to increasing the total wedge angle up to full one 180° and decreases for the counter shear current. At relatively large unidirectional values of the shear current, cusp waves in the vicinity of the wedge boundary are represented by transverse waves and, conversely, by diverging waves directed almost perpendicular to the ship track for the opposite shear current. The presence of a shear flow crossing the direction of the ship’s movement gives a strong asymmetry of the wake. An increase in the perpendicular shear flow leads to an increase in the difference between the angles of the wake arms. The limiting value of the shear current corresponds to one or both arms angles equal to 90°. Transverse and divergent edge waves for this limiting case coincide.

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Kelvin wake in the presence of surface waves

Cited by 6 publications

References 8 publications

Velocimetry Based on Self-Generated Surface Wave Patterns

Velocimetry Based on Self-Generated Surface Wave Patterns

Ship’s Wake on a Finite Water Depth in the Presence of a Shear Flow

Kinematics of the Ship’s Wake in the Presence of a Shear Flow

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