Wave elements. Sea waves By the action of force after the formation of a wave

Sea waves

periodic oscillations of the surface of the sea or ocean caused by back-and-forth or circular movements of water. Depending on the reasons causing the movement, wind waves, tidal waves ( tides And low tides), pressure (seiches) and seismic ( tsunami). The waves are characterized height, equal to the vertical distance between the crest and the bottom of the wave, length– horizontal distance between two adjacent ridges, speed of spread And period. For wind waves it lasts approx. 30 s, for pressure and seismic - from several minutes to several hours, for tidal it is measured in hours.

Most common in reservoirs wind waves. They are formed and developed thanks to wind energy transferred to water due to friction and by the pressure of the air flow on the slopes of wave crests. They always exist in the open ocean and can have a wide variety of sizes, reaching lengths. up to 400 m, altitude 12–13 m and propagation speed 14–15 m/s. Max. registered high wind waves are 25–26 m, and higher waves are possible. In the initial stage of development, wind waves run in parallel rows, which then break up into separate crests. In deep water, the size and nature of the waves are determined by the speed of the wind, the duration of its action and the distance from the leeward space; shallow depths limit wave growth. If the wind that caused the disturbance subsides, then the wind waves turn into the so-called. swell. It is often observed simultaneously with wind waves, although not always coinciding with them in direction and height.

In the surf zone, so-called surf beats– periodic rises in water level when a group of high waves approaches. High the rise can be from 10 cm to 2 m, rarely up to 2.5 m. Seiches are usually observed in limited bodies of water (seas, bays, straits, lakes) and are standing waves, most often caused by a rapid change in the atmosphere. pressure, less often for other reasons (sudden influx of flood waters, heavy rains, etc.). Once caused, the deformation of the water level leads to gradually damped oscillations in it. At the same time, at some points the water level remains constant - this is the so-called. standing wave nodes. High Such waves are insignificant - usually a few tens of centimeters, rarely up to 1–2 m.

Geography. Modern illustrated encyclopedia. - M.: Rosman. Edited by prof. A. P. Gorkina. 2006 .

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The disturbance is accompanied by the movement of water masses. The movement of water particles during waves occurs in open orbits and is a random, disordered process that is difficult to theoretically describe and depends on many factors.

The main elements of sea wind waves are as follows: height h - vertical distance from the wave trough to the crest; length X - horizontal distance between two successive ridges or depressions; period T, is the time interval between the passage of the tops of two successive waves through a fixed vertical.

The height of sea wind waves decreases as they move from the surface to the seabed. According to the classical trochoidal theory of waves, their height decreases with depth according to the exponential law

h 2 = he -2r/ ^ (3.1)

where z is the depth from the sea surface; h z and h are the height of waves at depth z and on the sea surface, respectively.

In fact, the attenuation of waves with depth occurs somewhat faster than it follows from the classical wave theory. The results of field studies show that the decrease in the height of surface waves with depth for aquatic

thorium, the depth of which is 2 times or more greater than the wavelength, is more correctly estimated by the expression

h z = he -5.5(z/X)0.8. (3.2)

However, for engineering calculations such clarifications are not significant. In the indicated water areas, the wave height h z at depth z can be approximately calculated based on a simple rule: if the depth increases in an arithmetic progression, then the wave height decreases in a geometric progression (Table 3.1).

Wind waves are divided into forced waves, which arise and are under the influence of wind pressure, and free waves, which occur after the wind stops or go beyond the zone of its action. Free waves are also called swell waves. The results of numerous observations of waves in natural conditions show that for deep-water areas, where the bottom does not affect the shape and size of wind waves, we can assume that X « 20h for wind waves and X « 30h for swell waves (Table 3.2). Obstacles encountered along the path of waves are subject to hydrodynamic loads. According to modern concepts of hydrodynamics, the main components of the total force of wave pressure on any cylindrical obstacle are the drag force, the inertial force and the force of the impact of water on the obstacle.

The drag force is proportional to the square of the linear speed of orbital motion. Its maximum value is achieved when the top of the wave crest passes at the monosupport. The force of drag is due to the fact that on the surface of an obstacle, when a viscous fluid flows around it, a boundary layer of a vortex structure appears, and under certain conditions periodically breaks off. Energy,

Table 3.1

Decrease in wave height with sea depth (in relative units)

Table 3.2

Scales for the degree of wind waves (numerator) and swell (denominator)

< 0, 25 - 0,75

Moderate

spent on the formation of vortices and overcoming the friction of water against an obstacle creates a drag force.

The inertial force is explained by the fact that, under wave conditions, the obstacle flows around a water flow of varying speed. A change in the speed of water movement over time creates a force, the magnitude of which is directly proportional to the acceleration of the flow. The maximum value of this force is achieved in the wave section, the position of which approximately corresponds to the undisturbed sea level. Thus, with respect to the drag force, the inertial force has a phase shift equal to r/2.

The force of the impact is caused by a sudden loss of flow velocity and is accompanied by a splash. This force is proportional to the square

rate of flow speed. Its maximum value is achieved in phase with the maximum drag force.

The role of individual components in the total force for waves and obstacles of various parameters is different. For relatively small waves not accompanied by a burst, the inertial component plays the greatest role. For large steep waves, especially when splashing, the forces of drag and impact play a major role.

One of the important criteria in determining wave pressure forces is the relative depth parameter - the ratio of the depth of the water area H to the wavelength X. If H/ X > 0.5, then the water area is considered deep-water and it is assumed that the seabed does not have a significant effect on the process of flow around the obstacle .

From the table 3.1 it is clear that already at 2/X = 5/9 the wave height is only about 3% of the surface one. Obviously, at a depth where the wave heights are small, the wave pressure on the obstacles is also small. This determines the independence of the values of the resultant wave pressure on the obstacle from the depth of the water area if H/X > 0.5.

The stable nature of the relationship between wave elements X and h (see Table 3.2) allows us to move from the H/X parameter to the H/h parameter, which is more convenient for calculations in practice. Then we can conclude that when determining the force of wave pressure, the influence of the bottom on the nature of waves flowing around an obstacle can be ignored if H/h > 10.

In shallow water and in the surf zone, the increase in wavelength lags behind the increase in their height. The flatness of the waves here decreases and reaches the value X/h = 8+12. Therefore, the influence of the bottom on the process of flow around an obstacle in shallow water can be ignored at lower values of the parameter H/h.

Classification of sea waves.

Plan

Lecture No. 4. Topic. Sea waves

UDC: 656.62.052.4:551.5 (075) Kuznetsov Yu.M. Ph.D., Associate Professor,

Department of Navigation

1. Classification of sea waves.

2. Elements of waves.

3. Watching the waves.

As a result of the influence of various natural forces on the waters of the oceans and seas, oscillatory and translational movements of water particles arise.

Sea waves mean a form of periodic, continuously changing movement in which water particles oscillate around their equilibrium position.

Sea waves are classified according to various criteria:

By origin The following types of waves are distinguished:

Wind, formed under the influence of wind,

Tidal waves, which arise under the influence of the attraction of the Moon and the Sun,

Anemobaric, formed when the sea surface level deviates from the equilibrium position, occurring under the influence of wind and changes in atmospheric pressure,

Seismic (tsunamis) resulting from underwater earthquakes and eruptions of underwater or coastal volcanoes,

Ship damage, formed during the movement of the vessel.

According to the forces tending to return the water particle to the equilibrium position:

Capillary waves (ripples),

Gravitational.

According to the action of force after the formation of a wave:

Free (the force has ceased),

Forced (the action of force has not stopped.

According to the variability of elements over time:

Steady (do not change their elements),

Unsteady, developing, fading, (changing their elements over time).

By location in the water column:

Superficial, arising on the surface of the sea ,

Internal, arising at depth.

By form:

Two-dimensional, representing long parallel shafts following each other,

Three-dimensional, not forming parallel shafts. The length of the crest is commensurate with the wavelength (wind waves),

Solitary (single), having only a dome-shaped crest without a wave base.

According to the ratio of wavelength and sea depth:

Short (wavelength is significantly less than the depth of the sea),

Long (the wavelength is much greater than the depth of the sea).

By moving the waveform:

Translational, characterized by visible movement of the wave profile. Water particles move in circular orbits.

Standing (seiche), do not move in space. Water particles move only in the vertical direction. Seiches occur when the water level rises at one edge of a reservoir and simultaneously falls at the other, usually after the wind stops.

In small basins (harbours, bays, etc.), a seiche can occur when ships pass.

Most often in the seas and oceans, navigators have to encounter wind waves, which cause the ship to rock, flood the deck, reduce the speed, and in a strong storm cause damage that leads to the death of the ship.

Wind waves are divided into three main types:

Vetrovoe- this is the excitement that is formed by the wind blowing in a given place at a given moment. When the wind weakens or completely stops, the waves turn into swells.

Swell is a wave that propagates by inertia in the form of free waves after the wind weakens or stops. A swell that spreads during calm conditions is called dead. Swell waves are usually longer than wind waves, flatter and have an almost symmetrical shape. The direction of the swell may differ from the direction of the wind and often the swell propagates towards the wind or at right angles to it.

Surf- These are waves formed by wind waves or swells near the coast. Propagating from the deep water of the open sea towards the shore in shallow water, the waves are transformed. Three-dimensional waves turn into two-dimensional ones, having the form of long crests parallel to each other. Their height, steepness and destructive force increase. The impact force of a breaking wave can reach 90 t/m2. In the surf zone, capsizing and turning over moments occur, which are dangerous for watercraft.

Therefore, swimming in the shallow coastal zone and landing on the shore here is very difficult, dangerous, and sometimes impossible.

Warnings about underwater obstacles can be breakers.

A breaker is a phenomenon where waves overturn and break over shoals, banks, reefs and other rises in the bottom.

One type of wave is crowd - This is the meeting of waves from different directions, as a result of which they lose a certain direction of movement and represent random standing waves.

Each wave is characterized by certain elements, such as:

Crest waves - the part of the wave located above the calm level.

Vertex waves - the highest point of a wave crest.

Hollow waves - the part of the wave located below the calm level.

Waves are characterized by the following elements (Fig. 1):

Rice. 1 Wave elements

The bottom is the lowest point of the wave trough;

Height h- vertical distance from the base to the top of the wave;

Length λ - horizontal distance between the tops of two adjacent ridges;

Slope – the ratio of wave height to its length ();

Period τ – the time interval between the passage of two adjacent vertices through the same fixed point;

Front – a line running along the crest of a given wave; the line perpendicular to the wave front is called a wave ray;

Spread speed c - the distance traveled by a certain point of the wave per unit time;

The direction of propagation is the angle measured from the north in the direction of wave movement (or the true direction from which the waves are moving).

Based on the hydrodynamic theory of waves, formulas were obtained that connect the individual elements of waves in deep water (when the sea depth is >);

With= 1.56 τ,

λ = 0.64 With 2 ,

τ = 0.64 With,

The wave height is measured directly or determined approximately using a special nomogram.

It has been established that with depth the disturbance quickly subsides and spreads to depths equal to the wavelength. Thus, at a depth equal to half the wavelength, the wave height is 23 times less than on the surface, and at a depth equal to the wavelength it is 535 times less.

In navigation, it should be taken into account that large waves arise when there is a very strong wind of a constant direction, blowing for a long time

(more than a day), in basins of significant size and depth, and that in the coastal zone, wave formation, in addition to depth, is greatly influenced by the configuration of the coastline and the direction of the wind relative to the shore (wind from the shore or from the sea).

Wind waves are caused by the action of wind and are called forward waves. After the wind stops, the waves still continue due to inertia, and such waves are called swell (on the image).

The waves are distinguished height(h) - vertical distance between adjacent ridge and valley; wavelength (λ) - horizontal distance between adjacent crests or troughs ( hollows).

Rice. Wave profile and its elements (Sudolsky, 1991):

1 - static level, 2 - average wave line, 3 - wave profile, 4 - wave top, 5 - wave crest, 6 - wave bottom, 7 - wave trough: λ - wave length, λ g - crest length, λ l - length of the trough, h - wave height, h r - crest height, h n - depth of the base

Wave steepness(ϵ) is determined by dividing the wave height (h) by its length (λ).

ϵ = h/λ

Wave period(T) is the time during which the wave travels a distance equal to its length. Wave age (B) is the ratio of wave speed (s) to wind speed (W).

The wave speed is

c = λ/T

Relationships between elements trochoidal wave are given in the table below. Moreover, the wavelength (λ), wave period (T) and wave speed (c) are interdependent, and they can be determined by formulas. The wave height (h) is not included in the indicated dependencies, and it is determined by observation or other methods, for example, according to the nomogram of A.P. Braslavsky (1952).

Table. Relationship between elements of trochoidal waves

To calculate height and wavelength The formulas of V. G. Andriyanov (1957) are often used:

h=0.0208 W 5/4 D 1/3 and λ = 0.304 W D 1/2

and N. A. Labzovsky (1976):

h= 0.073 W √E D and λ = 0.073 W √D/E,

where h and λ are the height and wavelength, m; W - wind speed, m/s; D - acceleration length, km; E - wave steepness (h/λ).

h = 0.33 √L

and small lakes(L<60 км):

h = 0.33 √L + 0.76 - 0.26 4 √L

But in lakes with L less than 1 km, the formula does not always give a real indicator of wave height.

In the formulas of E. A. Dyakova and N. D. Shitov, in addition to the acceleration length (D) and wind speed (W), the depth of the reservoir (N, m) is taken into account:

h = 0.0186 W 0.71 D 0.24 H 0.54

h = 0.151 H 0.34 W D 0.33

λ = 0.104 H 0.57 W D 0.33

To quickly assess wave elements (height, length, period and propagation speed) depending on the acceleration length and wind speed, you can use the table of N. A. Labzovsky (1952).

The characteristics of waves and the state of reservoirs are assessed according to the scale of the degree of wind waves and the scale of the state of the surface of the lake and reservoir under the influence of wind (see table).

At critical depth(Nkr ≥ h with a tailwind) near the coast and in shallows (shoals), waves are destroyed, which are called offshore surf , on luds (shallows) - breakers .

The water of bottom compensation currents in elevated areas of the bottom or in narrow shallow bays rises upward. This is expressed in abnormally low temperatures compared to temperatures in neighboring deep areas.

Each wave is characterized by certain elements. The common elements for waves are: 1. vertex- the highest point of the wave crest; 2. sole- the lowest point of the wave trough; 3. height(h) - exceeding the top of the wave; 4. length() - horizontal distance between the tops of two adjacent ridges on a wave profile drawn in the general direction of wave propagation; 5. period(T) is the time interval between the passage of two adjacent wave peaks through a fixed vertical; in other words, it is the period of time during which the wave travels a distance equal to its length; 6. steepness(e)- the ratio of the height of a given wave to its length. The steepness of the wave at different points of the wave profile is different. The average wave steepness is determined by the ratio:

7. wave speed(c) is the speed of movement of the wave crest in the direction of its propagation, determined over a short time interval of the order of the period; waves; 8. wave front- a line on the plan of the rough surface, passing along the vertices of the crest of a given wave, which are determined by the blade of the wave profiles drawn parallel to the general direction of propagation.

Figure 1. Basic wave elements

2.2 Wind wave speed

Wind waves are characterized by only minor horizontal movement of water. With increasing depth, horizontal displacement becomes negligibly small even at a depth exceeding the wavelength. As a result, in deep water, waves practically do not interact with the bottom and their behavior does not depend on depth. Therefore, the phase speed of a wave is a function of wavelength only. In deep water

Any system in which the speed of a wave depends on its length is called dispersed. Therefore, the deep ocean is a typical disperse system. When the wave speed becomes independent of (the system ceases to be dispersed). But at the same time it becomes dependent on depth.

In shallow water

All of the above refers to the phase velocity of the wave. Group velocity, i.e. the speed of energy propagation differs from the phase speed in a dispersed medium. For two limiting cases (deep and shallow waves), the following relations are true:

in deep water:

in shallow water:

2.3.Wave height

The wave height depends on:

wave acceleration;

duration of wind action;

wind speed.

Figure 2. Graph of wave height versus wind speed

The maximum recorded wave height was 34 m; its length was 342 m; period 14.8 s.. It had a phase speed of 23.1 m/s and a group speed of about 11.5 m/s

2.4 Wave energy

According to the hydrodynamic theory, the wave energy consists of the kinetic energy E k of the fluid particles participating in the wave motion and the potential energy E p, determined by the position of the fluid mass raised above the level of the calm surface. In waves of small amplitude, the energy per area having a wavelength and unit width:

, (6)

where is the density of the liquid; is the acceleration of gravity;