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Definition of elements of transformed waves



 

In case of waves distribution from deep water area to shallow area, i.e. to coastal line subject to decrease of depth, the phenomena of transformation and refraction is accompanied by energy loss. Height and length of wave are changed, but the period stays constant.

Wave transformation – means the phenomena of wave profile transformation and wave elements change in case of shoaling waters due to the bottom influence.

Wave refraction – means the phenomena of wave turn in parallel to sea contour due to the dependence of wave development velocity from depth.

The influence of transformation and refraction upon wave elements shall be considered separately subject to the application of corresponding coefficients.

 

Coefficient of refraction:

 ,

where S0 – is a distance between two adjacent deep water beams at the refraction plan (S0=2 l r); S – is the shortest distance between the same beams at the refraction plan regarding calculated point.

 

 

Wave height:

 ,

Wave length:

 

 

 

 

 

 

 

where kr – coefficient of transformed wave;  - wave refraction coefficient;  - average coefficient of loss; - height of initial wave with i%-th cumulative probability.

Transformation coefficient shall be defined in compliance as an ordinate (left axis) for point with abscissa  (where Н – is a depth of water for considered area).

Refraction coefficient  shall be defined using the refraction plan. Refraction plan means the plan of water area with wave beams.

Each beam of refraction plan shall be formed separately. Beam curving is started from isobaths . Depending from angle αi of beam approach to i-1 isobaths, inclusive of relation  for the next isobaths i-1

Angle  of beam deviation from the initial direction shall be defined. Cross point of this beam and isobaths provides wave beam point with consideration of refraction. Then, considering the angle between the new direction of beam and i-1 isobaths , for i-1 and i-2 isobaths, new parameter of wave beam deviation shall be defined, etc.

The construction shall be up to the border of designed structure, but less than the inshore area.

Generalized coefficient of losses kп shall be defined with due consideration of i bottom incline and relation value .

 

 

 

 

Length of transformed wave. The length of transformed wave shall be defined subject to defined adjustable values  and . Wave period is equal to deep water area period.

Wave top shall be calculated  in compliance with the rated level as per Figure 2.10 subject to  and .

Figure 2 Diagram for identification of transformation coefficient and critical depth.

 

 

Figure 3 Diagram for refraction plan development.

 

Figure 4 Construction of diffracted wave beam considering α>80°.

 

 

Figure 5 Dependence of angular deflection from

Definition of inshore wave elements

Wave height. Inshore wave height ,m, shall be defined for specified bottom incline i as per diagrams 2, 3, and 4 (Figure 2.5). Subject to adjustable values  it can be defined by the diagram , as follows .

Wave length. Inshore wave length ,m, shall be defined as per diagram on Figure 2.9. Subject to adjustable values  it can be defined using the upper turned curve by the diagram , as follows .

Exceeding of wave over rated level , m, shall be defined using diagram 2.10. Subject to adjustable values  it can be defined using the upper turned curve by the diagram , as follows .

 

Table 10. Dependence of index  from bottom inclines i

Bottom incline i  0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05
Coefficient   0.75 0.63 0.56 0.5 0.45 0.42 0.4 0.37 0.35

 

Table 11. Definition of elements of transformed waves

  H,m i Кт Кп Кр ki hi,m hc,m

20

6.6

188.8

11

0.11

0.011

0.14

0.92

0.867

0.67

2.57

1.4

0.008

139.7

1.98

1.8

NW

15

1.2

39

5

0.38

0.014

1.47

0.98

0.97

1

2.95

1.5

0.014

37.8

2.3

1.95

20

6.25

178.6

10.7

0.112

0.112

0.16

0.92

0.87

0.68

2.58

1.4

0.008

132.1

1.99


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