Offshore Structures by Arun Krishna

Waves - Waves are periodic undulations of the sea surface

krishnaarun750 — 2020-05-21 06:21:57 UTC

According To Apparent Shape

krishnaarun750 — 2020-05-21 06:23:42 UTC

According to relative water depth

krishnaarun750 — 2020-05-21 06:24:27 UTC

According to origin

krishnaarun750 — 2020-05-21 06:24:50 UTC

Progressive waves

krishnaarun750 — 2020-05-21 06:27:15 UTC

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.

Standing waves (Clapotis)

krishnaarun750 — 2020-05-21 06:27:34 UTC

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

Small amplitude waves (Airy’s theory is used)

krishnaarun750 — 2020-05-21 06:27:48 UTC

Finite Amplitude waves

krishnaarun750 — 2020-05-21 06:28:04 UTC

krishnaarun750 — 2020-05-21 06:29:25 UTC

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

Oscillatory waves

krishnaarun750 — 2020-05-21 06:32:28 UTC

Solitary waves

krishnaarun750 — 2020-05-21 06:32:45 UTC

Intermediate depth waves (Stoke’s waves)

krishnaarun750 — 2020-05-21 06:33:09 UTC

Shallow water waves

krishnaarun750 — 2020-05-21 06:33:27 UTC

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

krishnaarun750 — 2020-05-21 06:44:39 UTC

(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.

Factors controlling wind motion

krishnaarun750 — 2020-05-21 06:49:52 UTC

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

Pressure Gradient

krishnaarun750 — 2020-05-21 06:51:05 UTC

Ratio of pressure difference between two region and distance between them

Coriolis Force

krishnaarun750 — 2020-05-21 06:53:36 UTC

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

Geostrophic Wind

krishnaarun750 — 2020-05-21 06:54:37 UTC

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

Beaufort Scale

krishnaarun750 — 2020-05-21 06:58:23 UTC

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

Cyclone

krishnaarun750 — 2020-05-21 07:02:28 UTC

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

Extra-tropical Cyclone

krishnaarun750 — 2020-05-21 07:02:52 UTC

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.

Tropical Cyclone

krishnaarun750 — 2020-05-21 07:06:17 UTC

Formed due to temperature gradient

Wind velocity for open sea conditon

krishnaarun750 — 2020-05-21 07:07:52 UTC

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

Interaction of wind with Ocean water masses

krishnaarun750 — 2020-05-21 07:16:04 UTC

Storm Surge

krishnaarun750 — 2020-05-21 07:22:45 UTC

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.

Components of Storm surge

krishnaarun750 — 2020-05-21 07:26:21 UTC

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

Classification of waves based on energy and period

krishnaarun750 — 2020-05-21 07:34:29 UTC

Wave Characteristics

krishnaarun750 — 2020-05-21 07:51:08 UTC

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

krishnaarun750 — 2020-05-21 08:06:55 UTC

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

Airy's Wave Theory

krishnaarun750 — 2020-05-21 08:09:56 UTC

Boundary Condition

krishnaarun750 — 2020-05-21 08:25:20 UTC

1) The Laplace equation is to be satisfied in the region -d≤z≤η-∞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

Dispersion Relationship

krishnaarun750 — 2020-05-21 08:32:02 UTC

Classification of ocean waves according to water depth

krishnaarun750 — 2020-05-21 08:35:52 UTC

LOCAL FLUID PARTICLE VELOCITIES AND ACCELERATION UNDER PROGRESSIVE WAVES:

krishnaarun750 — 2020-05-21 08:39:29 UTC

WATER PARTICLE DISPLACEMENT UNDER PROGRESSIVE WAVES

krishnaarun750 — 2020-05-21 08:48:50 UTC

SHALLOW WATER CONDITION

krishnaarun750 — 2020-05-21 08:54:38 UTC

DEEP WATER CONDITION

krishnaarun750 — 2020-05-21 08:58:07 UTC

SKETCH OF ORBITS IN WAVES IN DIFFERENT WATER CONDITIONS

krishnaarun750 — 2020-05-21 09:03:10 UTC

WAVE ENERGY

krishnaarun750 — 2020-05-21 09:12:19 UTC

MASS TRANSPORT VELOCITY

krishnaarun750 — 2020-05-21 09:16:12 UTC

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.

WAVE DEFORMATION

krishnaarun750 — 2020-05-21 09:19:49 UTC

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.

WAVE REFRACTION

krishnaarun750 — 2020-05-21 09:30:21 UTC

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.

WAVE DIFFRACTION

krishnaarun750 — 2020-05-21 09:32:41 UTC

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.

krishnaarun750 — 2020-05-21 09:36:38 UTC

WAVE LOADS

krishnaarun750 — 2020-05-21 09:48:09 UTC

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.

FORCE REGIMES

krishnaarun750 — 2020-05-21 10:02:44 UTC

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

D/L < 0.2 Diffraction is negligible

D/L_o > 0.2 Inertia dominate

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

krishnaarun750 — 2020-05-21 10:09:28 UTC

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

Keulegan and Carpenter Number

krishnaarun750 — 2020-05-21 10:14:34 UTC

Drag Force

krishnaarun750 — 2020-05-21 13:38:22 UTC

Inertia Force

krishnaarun750 — 2020-05-21 13:39:38 UTC

Froude Krylov Force

krishnaarun750 — 2020-05-21 13:42:05 UTC

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