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Froude theory can be applied if flow separation is not significant, reflection from the cylinder is minimum and diameter of structure is not very small when compared to its wavelength

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1) The wave forces on a submerged member of an offshore platform is generally determined from the Morison equation
2) This equation is applicable for members of offshore structures when D/L < 0.2

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D/L > 1    Conditons approximate to pure reflection
D/L > 0.2  Diffraction is increasingly important

D/L < 0.2  Diffraction is negligible

D/Lo > 0.2  Inertia dominate

D/Lo < 0.2   Drag dominate
D: Diameter of structure, L: wave length and Lo: Deepwater wave length

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1)  Functional loads are loads due to the existence, use and treatment of the structure under ideal circumstances for each design condition.
2) Environmental loads defined as loads, which are not a necessary consequence of the structure. Such loads are loads due to wind, wave currents, ice etc.

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Diffraction of water waves is a phenomenon in which energy is transferred laterally along a wave crest. It is most noticeable where a barrier such as a breakwater interrupts an otherwise regular train of waves.

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The bending effect of the wave called refraction.
Variation in wave celerity occurs along the crest of a wave moving at an angle to under water contours because that part of the wave crest in deeper waters will be moving faster than the part in shallower waters. This variation causes the wave crest to bend towards the alignment with the contours.

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Wave deformation may occur due to:

(i) Lateral diffraction of wave energy

(ii) By the process of attenuation

(iii) Air resistance encountered by the waves or by directly opposing winds

(iv) By the tendency of the waves to overrun the currents.

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When waves are in motion, the particles upon completion of each nearly an elliptical or circular motion would have advanced a short distance in the direction of propagation, consequently there is a mass transport in the direction of progress of the wave.

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SKETCH OF ORBITS IN WAVES IN DIFFERENT WATER CONDITIONS

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SKETCH OF ORBITS IN WAVES IN DIFFERENT WATER CONDITIONS

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WATER PARTICLE DISPLACEMENT UNDER PROGRESSIVE WAVES

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WATER PARTICLE DISPLACEMENT UNDER PROGRESSIVE WAVES

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LOCAL FLUID PARTICLE VELOCITIES AND ACCELERATION UNDER PROGRESSIVE WAVES:

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LOCAL FLUID PARTICLE VELOCITIES AND ACCELERATION UNDER PROGRESSIVE WAVES:

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Classification of ocean waves according to water depth

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Classification of ocean waves according to water depth

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1) The Laplace equation is to be satisfied in the region -d≤z≤η-∞<x<∞ where ‘η’ is the water surface elevation measured from the Still Water Level, SWL.
2) The kinematic bottom boundary condition meaning, that the vertical velocity component at the sea bottom is zero.
3) The pressure at the free surface is zero or at z = η

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1) Laplace Equation
2) Continuity Equation
3) Bernoulli's Equation

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Wave are generated mainly due to:
1) Wind
2) Gravitational attraction between Sun, Moon and Earth
3) Catastrophic Events

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Classification of waves based on energy and period

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Classification of waves based on energy and period

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1) Initial Setup
2) Pressure setup
3) Long wave setup
4) Wave setup
5) Wind stress setup
6) Coriolis setup

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Storm surge is simply rise in water level due to storm predominantly caused by:
1) Pressure variation between center of cyclone and periphery
2) Wind stress directed from continental shelf towards shallow water.

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Interaction of wind with Ocean water masses

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Interaction of wind with Ocean water masses

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Vz = Wind Velocity at any elevation z from sea surface
V10= Wind velocity at 10m from ocean surface
Cd = Drag Coefficient
K = Von karman Coefficient

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Formed due to temperature gradient

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Used to refer to cold-core in the upper troposphere and often form along fronts in higher latitudes. It is developed in the mid and high latitude beyond tropics which causes abrupt changes in the weather conditions over an area in the middle and high latitudes.

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Cyclone is a large scale air mass that rotates around a strong center of low atmospheric pressure

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The Beaufort gave a description of wind in terms of its strength and numbered from 0 to 17.

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The wind formed as result of coriolis effect on wind flowing along pressure gradient. This deflects the wind, parallel to pressure isobars.

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The Coriolis Effect describes the turn of the wind to the right in the Northern Hemisphere caused by earth's rotation.
The Coriolis Effect contributes to the circular motion of the wind around pressure systems

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Ratio of pressure difference between two region and distance between them

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1) Pressure gradient
2) Coriolis force
3) Friction force
4) Centrifugal force

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The assumptions in deriving the expression for the velocity potential due to propagating ocean waves

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The assumptions in deriving the expression for the velocity potential due to propagating ocean waves

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(a) Flow is said to be irrotational.
(b) Fluid is ideal.
(c) Surface tension is neglected.
(d) Pressure at the free surface is uniform and constant.
(e) The seabed is rigid, horizontal and impermeable.
(f) Wave height is small compared to its length.
(g) Potential flow theory is applicable.
(h) A velocity potential Φexists and the velocity components u and ω in the x and z directions.

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Intermediate depth waves (Stoke’s waves)

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Intermediate depth waves (Stoke’s waves)

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a. Capillary wave (due to surface tension) T upto 0.1 sec
b. Ultragravity waves (Surface tension and gravity T upto 0.1 sec
c. Gravity wave (wind) T upto 30 sec
d. Infra gravity waves (storms) T = 30 sec to 5 min
e. Long period waves (storms) T = 5 mins to 12 hrs
g. transtidal waves (storms, Tsunamis – due to under sea explosives)
f. Ordinary tidal waves (attraction of  astronomical bodies)
T = 12 hrs to 24 hrs

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Small amplitude waves (Airy’s theory is used)

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Small amplitude waves (Airy’s theory is used)

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Wave which oscillates in time but whose peak amplitude profile does not move in space

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A wave which travels continuously in a medium in the same direction without the change in its amplitude is called a travelling wave or a progressive wave.

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Waves - Waves are periodic undulations of the sea surface

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Waves - Waves are periodic undulations of the sea surface