Wind waves within THE enclosed water areas

 

3.1 General provision

Required wave regime for unprotected or partly protected water areas is provided by separate protective structures (for example, Figure3.1; Figure3.2; Figure3.3, Figure3.4).

Initial waves for calculation of wave regime of protected water area shall be assumed as waves occurred outside the protective area next to the port entrance. Initial wave parameters next to port area shall be defined in compliance with section 2 considering barrier structures location (port entrance).

Usually waves are diffracted subject to development over area with barriers. Diffraction means passing of barriers by waves. Waves after passing through the port entrance have lost some energy outside the entrance. The terms of wave shade and wave border are used. Wave shade means the part of water area protected from wave impact subject to direction of the initial wave beam. The border of wave shade means straight line within the water area plane through the extreme point of barrier structure top considering the direction of initial wave beam.

As of calculation all these variants of port area protection from wind waves can be subdivided as follows:

ü Single barrier;

ü Two barrier walls;

ü Wave breaker.

There are several wave systems that can be formed within the enclosed water area. Wave systems include diffracted and reflected waves (from hydrotechnical structures and coastal line) inclusive of waves from internal acceleration and corresponding reflected waves. Waves parameters can be influenced by bottom. So, the height of wave with i-th cumulative probability at any point of water area considering transformation and refraction shall be defined as follows:

                                    ,                            (3.1)

where h_{di -} wave height with i%-th cumulative probability at i-th point of water area, m; k_Т - transformation coefficient at i-th point k_р - refraction coefficient at i-th point; k_di- diffraction coefficient at i-th point; h_i0  - wave height with i-th cumulative probability within water area entrance, m.

Waves are reflected from barriers. So, diffracted wave height at the i-th point considering reflection from barriers shall be defined as follows:

 ,                                (3.2)

where h_di,r - wave height at i-th point of water area considering reflection from barriers; k_r - coefficient assuming reflection from barriers.

Reflection coefficient shall be defined as follows:

,                           (3.3)

where k_d0 - coefficient for reflective area; k_r0 and k_p0 -coefficients as per Table 3.1 [1]; Θ_r - angle between wave and reflective surface, deg.;  - relative distance from protective surface up to rated point subject to wave reflection beam; at this the direction of reflective wave beam shall be assumed as approach angle equality; k_{r,i -} reflection coefficient as per Table 3.2.

 

Table 3.1

Coefficients k_r0  and k_p0

Slope support structure	relative roughness r/h1%	kr0	kp0
Concrete (reinforced concrete) slabs	-	1	0.9
Gravel-pebble stony or concrete (reinforced-concrete) block support	Less than 0.002	1	0.9
	0.005+0.01	0.95	0.85
	0.02	0.9	0.8
	0.05	0.8	0.7
	0.1	0.75	0.6
	Over 0.2	0.7	0.5

Notes Roughness size and particulars r, m, equals to average diameter of material grains and average dimension of reinforced (concrete) blocks.

 

 

Table 3.2

Coefficient  subject to wave flatness and reflective surface incline

Wave flatness	Values  subject to incline of reflective surface
	1	0.5	0.25
10	0.5	0.02	0.0
15	0.8	0.15	0.0
20	1.0	0.5	0.0
30	1.0	0.7	0.05
40	1.0	0.9	018

For water areas with constant or significant depth ( ) water length is equal to length within the water area entrance without transformation and refraction correspondingly.

                                                   (3.4)

For incline angle of reflected surface to the horizontal plane more than 45⁰ reflection coefficient is equal to k_r,i=1.

The result of height calculation for enclosed water area shall be provided as a map with different height lines.

 

3.2 Wave regime within the water area with single barrier walls

 

Identification of wave regime for any direction shall be performed as follows:

- diffracted waves beams without consideration of refraction and transformation shall be shown on water area plan; k_g coefficients for rated points of water area shall be defined;

- diffracted waves beams location inclusive of refraction shall be shown; refraction index k_p; wave transformation index k_r shall be defined; averaged coefficients of losses shall be defined in compliance with special justification, i.e. k_p = k_r= =1.0;

- h_d,i height of diffracted waves shall be calculated as per (3.1) formula; lines of equal wave height shall be shown;

- h_di,r height of reflected waves shall be calculated as per (3.2) formula;

- wave heights subject to internal acceleration and corresponding reflected waves shall be defined;

- h_р calculated height of waves as a sum of straight and reflected waves;

Some port areas have no protection from barriers, so wave height shall be defined without diffraction. It is assumed that quays are protected once being located within the protective area. The protective area of such structure shall be limited by structure size, wave diffraction border and section between protective structure and diffraction border (see Figure 3.1). The location of each diffraction border point shall be defined by two coordinates l and r (see Figure 3.1). The development of diffraction border shall be performed as follows: In order to calculate wave area featured with r value, , shall be defined with further calculation of l value.

The height of wave within the water area with single barrier shall be defined using (3.1) or (3.2). Diffraction index within carrier wall protection area shall be defined as follows (see Figure 3.2).

Initial wave beam

Wave front

Figure 3.1 Water area with single barrier wall

 

Figure 3.2 Diagram for identification of diffraction coefficient for water area with single barrier.

 

1. Coordinates  and r shall be defined for approved point subject to diffraction coefficient.

2.  Considering obtained angle , deg., and relative distance from barrier to point r/  and angle , deg., diffraction index shall be defined in compliance with diagram on Figure 3.3 subject to long-dotted line with arrow.

 

3.2 Wave regime within the water area with two barrier walls

 

In this case each barrier wall protection area shall be defined (see Figure 3.3). The protective area of the first barrier is limited by its size, water side from В₁ point up to В_гл point, main beam from В_гл  point up to В point and wave diffraction border from В point up to the first barrier top. The protective area of the second barrier is limited by its size, water side from В₂ point up to В_гл point, main beam from В_гл  point up to В point and wave diffraction border from В point up to the second barrier top. Point B is located at the crossing of diffraction borders. Diffraction borders shall be defined as for single barrier walls. The main beam shall be constructed via points using coordinate х, standing over from wave shade border (WSB) of the barrier with less angle , deg., and coordinate х as per formula [1]:

                                          ,                    (3.5)

where х - distance from the main beam up to wave shade border for barrier with less angle , m; l₁  - distance from WSB to WSB of the first barrier up to crossing of wave front passing via х, subject to the first barrier diffraction border, m; l_a1 and l_a2  - coefficients in compliance with diagram on Figure 3.4; в - width of port enter assumed as a distance between barriers against initial wave, m; l₂ - distance from WSB to WSB of the second barrier up to crossing of wave front passing via х, subject to the second barrier diffraction border, m.

 

 

Initial wave beam

Main beam

Zone 1

Barrier 1

Barrier 2

Zone 2

Rated section

 

Figure 3.3 Diagram of main beam development

Rated section

Barrier 2

Barrier 1

Initial wave beam

Main beam

Zone 2

Zone 1

Figure 3.4 Diagram for identification of l and l₀ values.

Figure 3.5 Diagram for identification of convergence index

The height of wave within water area with barrier shall be defined using (3.1) or (3.2). Diffraction coefficient for i-th point shall be defined as follows:

1. Across i point (see Figure 3.2) using compasses placing on barrier top (i.e. from the first barrier top, as i point is located within the corresponding protection area), line shall be constructed as a wave front. Wave front shall be constructed up to the crossing with WSB of corresponding barrier from which the wave front is constructed. From crossing point of WSB and wave front the perpendicular line shall be constructed up to the main beam. x_i point shall be defined on the crossing of main beam and perpendicular line.

2. Foe x_i  point the value d_c shall be defined as follows [1]:

 ,                                                (3.6)

where l₁ - distance measured on perpendicular line and WSB, stood over from WSB and wave front crossing point across i point, m; l₂ - distance according to perpendicular line up to WSB₂ with wave front across i point, m; b - port entrance width, m.

3. For x_i point the diffraction coefficient k_d,.ср shall be defined as for single barrier in compliance with diagram shown on Figure 3.2.

4. Assuming d_i and  k_d,ср, values defined for x_i  point in compliance with diagram on Figure 3.5, the coefficient shall be defined.

5. Diffraction coefficient for i-th point shall be defined as follows:

 ,                                             (3.7)

where  diffraction index at i-th point of water area with barriers;  - diffraction index at i-th point of water area assumed for a single barrier with i-th point;  - convergence index.

The head of one barrier can be located within the protection area of the other barrier (see Figure 3.6). In this case one part of water area is protected by the first barrier wall, and the other - by the second barrier wall. The task is to define the areas of protection and waves from which each barrier is protected this water area. The height of wave reaching the head of the second barrier. It shall be defined as for water area protected by the first barrier considered as a single one at the point with coordinated of the second barrier head. The direction of wave front reaching the second barrier head shall be defined by the line matching both barriers. Once diffraction borders are defined for both barriers, so protection area shall be defined. Area of the second barrier wall protection is limited by ВЕ, ED, DB lines (see Figure 3.6). Area of the first barrier wall protection is limited by AC, CB, DB, DF, FA lines (see Figure 3.6).

 

Barrier 2

Initial wave beam

Barrier 1

 

 

Figure 3.6 Diagram for identification of diffraction coefficient subject to location of one barrier top within protective area of another barrier.

 

Diffraction coefficient for i-th point shall be defined as for single barrier

 

3.4 Wave regime within water area with barrier walls

 

The diagram for water area with barrier walls is shown on Figure 3.7. The height of wave within water area with barrier shall be defined using (3.1) or (3.2).

Once wave breaker length is more than , so the calculation of diffraction index for the half of barrier shall be performed regardless the other half as for a single barrier. Once wave breaker length is less than  , so the diffraction fields are overlaid. In this case diffraction coefficient shall be defined using [2]:

,                                                          (3.8)

where k_di,1 - diffraction index for the first head assumed as a single barrier; k_di,2 - diffraction index for the second head assumed as a single barrier.

Figure 3.7 Diagram for diffraction coefficient definition for water area with barriers

Literature

 

1. SNiP 206.04-82*. Loads and impacts on hydraulic structures (wave, ice and navigational). - М.: “Strroyizdat”, 1989. - 40 pages
2. Recommendations for identification of loads and impacts on hydraulic structures (wave, ice and navigational). P58-76/VNIIG. - L.: VNIIG Publishing House named after Vedeneyev B. E., 1977 - page
3. USSR Climate Guide. C. Z. Veter. - L.: HydroMeteoIzdat, -1968. - pages
4. Smirnov G. N. Oceanology - М.: "Vysshaya Shkola" Publishing house, 1974. - pages
5. SNiP 2.01.07-85. Loads and Impacts - М.: StroyIzdat, 1986 - pages

 

 

Content

Introduction

1. Basic terms and definitions

1.1. Wave profile and elements

1.2. Rated wave elements

1.3. Rated water levels

1.4. Waves transformation next to shore

2. Wave formation factors. Identification of wave elements within opened water areas………………..………………12

2.1 Identification of waves elements subject to simple conditions of waves formation

2.2 Identification of waves elements subject to complex conditions of waves formation

2.3. Identification of transformed waves elements

2.4. Definition of inshore wave elements

3. Wind waves within enclosed water areas

3.1. General provisions

3.2. Wave regime within water area with single barrier walls

3.3. Wave regime within water area with two barrier walls

3.4. Wave regime within water area with barrier walls

LITERATURE

 

Sabodash Olga Alekseyevna, Seliverstov Vladimir Ivanovich

 

CALCULATION OF WAVES ELEMENTS WITHIN WATER AREAS

Methodical recommendations for practical trainings, course and graduation paper development majoring 270104 and 270105

 

 

Printed from ready-to-print file prepared by the author

 

Editor V. V. Sizova

Technical Editor N. M. Belokhonova

Signed for publishing

Cond. print. sh. 2.5. Acc. publ. sh.   

Quantity (100 copies); Order

FESTU Publishing House, 690950 Vladivostok 10 Pushkinskaya Street

FESTU Publishing House, 690950 Vladivostok 10 Pushkinskaya Street

 

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