Tuesday, August 9, 2016

Pellet guns in Kashmir Valley

Pellet guns in the Kashmir Valley
For a month I have been following with fascinated horror the injuries and killings by pellet guns in the Kashmir Valley. These pellet guns were introduced after the last major bout of stone pelting in 2010 as a ‘non-lethal’ mode of crowd control – because they do not kill (only maim). Today the Indian Army distances itself from the mess by saying that it’s the CRPF which is tackling the protesters. There are three main arguments that I have heard so far:

a    a)  The CRPF has instructions to fire below the waist so if any protester got injured in the head it was because he or she bent down to pick up a rock
      b) In the heat of trying to quell the protests, the aim of the CRPF may have been a bit off
      c) Although pellet guns are (‘properly used’) ‘nonlethal’, they are used in the last resort – and when anyone is being attacked by a murderous mob (possibly containing armed militants)
that is much larger than your own forces, then they will use the pellet guns in self-defence in the most effective way and even at distances much lower than the ‘recommended range’.

I think that any dispassionate examination of the facts will show that there was either criminal incompetence or murderous intent at work here. Even the fascist Israelis faced by hostile (and suicidal) Palestinians do not use metal pellets; they use rubber- or polyethylene-coated metal pellets. Even these coated pellets cause fatal injuries at short range, but uncoated metal pellets are bound to be much worse.
Having said that, I think that Kashmiri protesters are also being extremely callous in bringing, day after day, young boys to the protests: if the CRPF actually abide by the policy of aiming for boots, the children are much more likely to be hit.

I have tried to analyze the available data – although even thinking about somebody getting pellet injuries in the body, head or eyes is difficult – it is important to do it so that such stupid and inhuman methods are banned – just as land mines were. Even if he did not do the math, any competent and experienced Indian Army officer should have been able to foresee the kind of damage that pellet guns will do to crowds of civilians.

India has not done itself any favours by refusing to stop the use of pellet guns in the Kashmir Valley. With the huge amount of data available in the media or the internet, India is very likely to be attacked for human rights violations – not just by Pakistan – but by the whole world, maybe in the International Court of Justice. Forget about winning hearts and minds in Kashmir, and concentrate on just basic human decency. The defence  analyst Ajai Sahni (mentioned below) doubts whether there are any truly non-lethal weapons, since they all have ‘issues’. But the use of pellet guns should be beyond the pale even as ostensibly ‘non-lethal’ weapons: the scatter of pellets is too much for them to be ‘aimed’ with any tolerable degree of accuracy. Only Egypt and Bahrain use pellet guns – not the best of company for India to keep.

Even the hard-line Kashmiri, Sushil Pandit agreed that the huge damage inflicted on protesters is ‘gut-wrenching’, while Sitaram Yechury called the use of these weapons as ‘criminal’ and ‘inhuman’.


In the fortnight since the killing of Hizbul Mujahideen commander Burhan Wani, personnel of the Central Reserve Police Force (CRPF) have fired as many as 2,102 pellet
cartridges in the Valley to disperse protesters.
The Sunday Express has learnt that over 50 per cent of the 317 people, who sustained pellet injuries, have been hit in the eye.
The CRPF is also looking at the use of Condor guns used by UN peacekeeping forces. The guns fire spherical rubber pellets which cause painful bruises.
The use of pellet guns by CRPF is second only to tear smoke shells which have been fired over 4,500 times. The CRPF has ten mandated non-lethal weapons
for use in different situations. Other non-lethal weapons used by CRPF in the Valley include plastic pellet guns, rubber bullets, stun grenades, multi-button shells,
blank rounds, pepper balls and capsicum grenades. All have been used in the recent protests.
CRPF Director General K Durga Prasad, while expressing concern over civilian injuries, said: “Only after all non-lethal options are exhausted, pellet guns are used.
CRPF sources said that pellet guns are most effective because the cartridge contains hundreds of small pellets which spread out after being fired and cover a large part of the
crowd. Plastic cartridges, on the other hand, fire just three plastic pellets while rubber bullets are for target firing. There is a peculiar problem with tear smoke shells.
“If the wind is not favourable, it will blow away from the crowd without much impact. Protesters also have become smart over the years. They throw back the shells
towards us, forcing us to retreat,” a CRPF officer said.
Similarly, pepper balls and capsicum grenades (cause severe burning sensation) are best suited for targeting small crowds in alleys and lanes.
There is no such problem with pellet guns. “They also cause prolonged physical pain, forcing the injured to retreat. Earlier, forces used No. 4 pellets which are bigger
in size. But injuries caused by them were potentially fatal. We have now shifted to No. 9 pellets and occasionally use No. 8 pellets,” the officer said.
Standard Operating Procedures (SOP) for use of non-lethal weapons and training of men who fire them has been a cause of concern.
CRPF sources maintain that the SOP prepared by Bureau of Police Research and Development (BPR&D) has no mention of pellet guns.
“We (CRPF) have our own SOPs. We have to ensure that pellets guns are fired from a distance of at least 50 metres and are aimed at boots. Also, in a group of 20 CRPF men,
only three carry pellet guns. The rest carry other non-lethal weapons,” another CRPF officer said.


“Aiming it wrong”    Justice Harjit Singh Bedi Ind Exp. 23rd July 2016:

The data about pellet guns has been taken from the article by H.S.Bedi, sourced from “Forensic Science in criminal investigations and trials”:

Range (metres)
Diameter of spread circle (metres)
10
0.54
15
0.71
20
0.88
25
1.05
30
1.22
35
1.44


This data is plotted and fitted to a straight line:
The data from the article by Bedi is fitted (see above plot) to:
D = 0.19524 + 0.03429 R
where D is the diameter of spread at a distance R.
According to C. G. G. Aitken and David A. Stoney in,“The Use Of Statistics In Forensic Science” (CRC, 1991) pp. 170-5 :
D is a linear function of range R, and D is the diameter of the circle that encloses all the pellets at a distance R.

The slope of D vs R (0.03429) corresponds to an angular spread of 1.96° - that is at a fairly short distance there is not much spread.
At a distance of 10 metres, the angle subtended by a human face is about: 1.2°.
A human face is typically 15 cms wide and 23 cms high.
Note that this is a simple approximation of a face projected on to a rectangle. It disregards the curvature of the face. An example is that the projected area of a sphere is half that of
its frontal surface area:
                                                            

Where beta is the angle between the normal to the area element dA and the normal to the arbitrary plane on which we wish to project – in this case, the frontal plane.
However, one can think of the 15x23 cm2 as the smallest rectangle completely covering the face as seen from the front.

A pellet gun emits 600 pellets in a circle of diameter 0.54 metres at a distance of 10 metres, and each pellet is of 1.22 mm diameter.

If the circle is centred (aimed) around the face, it will be hit by: 600 * (15)(23)/[(3.14)(27)(27)] =   90 pellets.

Radiographs of the heads of Kashmiris hit by pellets show a large number of pellets – maybe around 100 in the head. 
The radiographs are there in thequint.com:


There are three images of human heads: the one on the left has more than 120 pellets, the one in the middle more than 40, and the one on the right about 10. These pellets are clearly
visible and the scanned images are not of diagnostic quality, so the actual number is probably more. And the images are taken from one side of the head, so there may be more pellets on the
other side of the head that is not shown.


The size of a human eye is roughly 2.5 x 1.5 cms.
What is the chance a pellet will hit an eye?
The total area is 7.5 cm2 for both eyes.
The chance of a single pellet hitting the eye is: (7.5)/[(15)(23)] = -0217. About 2%.
So the chances of it missing the eye are about: 97.83%.
But if we assume that 90 pellets may hit the face, the chances that all of them will miss an eye is:
(0.9783)90 = 0.139.
That is, 86% probability of hitting an eye at a distance of 10 metres.

R (m)
Probability of
Hitting an eye (%)
10
86
20
53
30
32
40
21
50
15
60
11
70
8
80
6
90
5
100
4

Let us assume only 30 pellets actually hit the face, then the chance that one of them will hit the eye is: 0.483, or 48.3%.

In today’s Indian Express article by Deeptiman Tiwary, the report is that over 50% of 317 patients have been hit in the eye (24th July 2016).

The number of cartridges has been given as 2,102. The fact that 317 people were hit means that they were quite accurate: they hit 15% of
the time – and they hit an eye with more than 7% of the cartridges used.

This would argue that the people who have been hit have all been deliberately targeted by firing at the head. If the crowds were all dense, then it is possible
That about 85% of the shots were not targeted directly at people – either deliberately or by bad aim.


“There is a pattern behind the action by forces on the protesters. At least 90 percent of these persons had firearm injuries above waist—in head, chest, and abdomen,” said a
senior doctor at the SHMS hospital. This refers to all firearm injuries - including bullets and pellets.

In any case, the fact that >50% of those hit were hit in the eye implies that the aim was above the waist.
The argument by some military participants on TV has been that the victim may have been hit in the face by pellets because he bent down
– but this argument is difficult to sustain for more than a hundred victims.

At a distance of 10 metres, a human who is 1.5 metres tall subtends an angle of 8.5°, as compared to about 1.2° for the face – while the angular range of the pellet gun is 1.96°.  Firing below the waist should indeed be possible. Also, considering the total number of pellets embedded in the bodies of the victims, it is extremely unlikely that the CRPF
actually aimed from a distance of 50 metres. If they had, the spread of the pellets would have been D = 1.7 m.
Suppose we consider a distance R =43.7 m. At this distance, D = 1.5 m.
Assume a human being has a projected frontal area of 1.5 x 0.4 m2 (i.e. 0.6 m2). Then the number of pellets that will hit him, assuming that the pellet gun is perfectly aimed is: 300*(0.6/1.77) = 102,
where the pellets are distributed across an area (pi)D2/4 = 1.77 m2.

Some of the radiograph images in thequint (mentioned above) show this kind of distribution of pellets across the whole body of the victim, and in the two images of the front view of the body the numbers of pellets is clearly more than 40.
 This would seem to imply that, in some cases at least, the victim was fired upon by CRPF at the mandated distance of 50 metres.
Unless a comprehensive database is produced by doctors in the Valley, it will be difficult to draw more accurate conclusions.

Either the CRPF personnel were untrained – or some of them deliberately targeted their victims. Also, see Ajai Sahni’s comments below:

PHR report:
Smaller pellets may have wider dispersal patterns and less accurate aim; larger pellets may have higher kinetic energy.
Metal shot has been banned in most countries as excessively dangerous, but it is still used regularly in Egypt & Bahrain.

The UNDP report, ”Crowd Control: Israel’s use of crowd control weapons in the West Bank” (Jan.2013)  researched by B’Tselem does not mention metal pellets at all: the only pellets used are coated with rubber or polyethylene. And rubber bullets were taken out of use before the second intifada.

The pellets being used by CRPF in Kashmir are not Israeli, and are manufactured in India by the Ordinance Factory in Ishapore, according to The Hindu:

.


In Kashmir, the Battle of Stones and Rubber Pellets is Politics by Other Means


It is not the brutality of the police or forces that has caused blinding injuries among agitators – it is the evaluation and selection process that resulted in the acquisition and deployment of pellet guns, despite well documented and recurrent evidence of the unacceptable consequences of their use in the control of violent crowds, globally (and even in J&K where they were first used in 2010).

The Ministry of Home Affairs has now belatedly announced the formation of a committee to evaluate options to pellet guns.

However, even a cursory examination of available ‘non-lethal’ technologies would demonstrate that none of these are without their own risks.” 

Another Kashmiri protester succumbs to pellets

8th Aug.2016 Srinagar Peerzada Ashiq
“Doctors who performed surgeries on those hit by pellets in SMHS and SKIMS hospitals in Srinagar told The Hindu that the three civilians died because they were shot from “a very very close range with the intention to kill.”
A pellet victim Riyaz Ahmad Shah, 21, a resident of Srinagar’s Chattabal locality, had his abdomen ripped apart last week. “More than 300 pellets were lodged inside his body, affecting all vital organs.
This only shows the gun was emptied by keeping barrel close to the victim’s body,” said a doctor. 
Figures at the Valley’s premier SMHS hospital paint a grim picture.
Of 933 pellet cases, 356 suffered eye injuries and 324 extra-ocular injuries. Similarly, the hospital treated 67 bullet injury cases.
Non-lethal tear-smoke shell injuries are less at 35.

The fact that 356 patients suffered eye injuries, 324 suffered extra-ocular injuries – presumably to the head – and the remaining 253 suffered injuries to the rest of the body shows a clear trend, that is not in line with the stated policy of shooting below the waist – since the number of protesters who have that particular type of injury seems relatively small.

The case of the ATM guard who was killed and whose body was hit by more than 300 pellets shows that he was shot at short range (a few metres) and with – as indicated above in Peerzada Ashiq’s report – ‘with the intention to kill.’

Tuesday, July 26, 2016

Beta effect

The Beta Effect

First, a mea culpa: in my last post I showed a diagram of the Coriolis deflection of an inertial circle in the counterclockwise direction - so that the cyclone would avoid the West Coast of India. Well, that's wrong. The rotation is clockwise in the Northern Hemisphere as can be seen in the Figure below (taken from one of Anders Persson's papers, I think):


So, having got that out of the way, let me meander a bit into some background, on the way to the beta effect - which actually explains the northwestwards (NW) motion of cyclones in the Northern Hemisphere (NH), which causes cyclones to avoid India's West Coast - and prefer to hit the East Coast (to disastrous effect).

Without going into the derivation (which could vary in length depending upon the level of rigour), the Coriolis force, which arises in a rotating frame, such as the Earth itself, is given by:

                                                F = 2m w ´ v

where the Coriolis force F results from the vector cross-product of the angular velocity w and the linear velocity v, all three vectors pointing along 3 perpendicular axes (as given by the right hand rule, w along the thumb, v along the forefinger and F along the middle finger). For the right-hand rule, see the website:

http://phys420.phas.ubc.ca/p420_12/tony/Coriolis_Force/Home.html


For the Earth, the angular velocity vector points through the poles, the velocity is along the surface of the Earth at some given latitude j, and the force F deflects the cyclone in a direction perpendicular to its motion (v). For horizontal motion, the magnitude of the Coriolis force is given by:

                                                F = 2m w v sin(j)

and so its magnitude is exactly zero at the Equator.

Since the Coriolis force acts to deflect any moving object perpendicular to its motion, that motion is likely to become a vortex or a circle. Specifically, the motion is clockwise (CW) in the Northern Hemisphere (NH) and counterclockwise (CCW) in the Southern Hemisphere (SH).
Equating the Coriolis force to the centripetal force mv2/r, the radius of the inertial circle is:

                                                R = v/(2wsin(j))

The latitude of Kanyakumari is 8.1°, of Mangalore is 12.9° and of Mumbai is 19.1°. Corresponding values of sin(j): 0.141, 0.223 and 0.327. The angular velocity of the Earth is w = 7.29x10-5 rad/sec and so the radius of the inertial circles at these points, assuming that the cyclone speed is 50 m/s (180 km/hr) is: 2,437 kms (KK), 1,537 kms (Man), and 1048 kms (Mum). 
Tabulated:

Latitude
Sin(l)
Radius of inertial circle (kms)
Kanyakumari
8.1°
0.141
2,437
Mangalore
12.9°
0.223
1,537
Mumbai
19.1°
0.327
1,048

Due to the latitudinal variation, the radius of the inertial circle is much greater closer to the Equator.

The fact that the Coriolis force deflects westwards is not obvious  – considering that the motion in the NH is clockwise, and circular motion along inertial circles should just keep on regularly returning the moving mass back to its pre-existing path - and the explanation is the beta effect (see below for a  sketchy description).

The equations that deal with this are discussed in the website quoted below, for a particle moving with a velocity vector (V0 cos(q), -V0 sin(q ), 0 ) with z = 0 along the surface of the Earth, and q = 0  as the reference direction, pointing north:


The end result of solving the equations of motion, assuming that w is small,  is:
Vx = V0 cos(q + 2wt sin(l))
And
 Vy = -V0 sin(q + 2wt sin(l))
Which means that the angle q changes at the rate:

(dq/dt) =  2w sin(l)

Since this quantity is positive, the angle q increases, and the mass moves in a clockwise direction (in the NH)..
The magnitude of dq/dt is 4.66x10-5  rad/sec (assuming sin(l) = 0.32), or 2.67x10-3 deg/sec.

In other words, the cyclone would get deflected by 9.6 deg/hr, or 230 deg/day.

According to a course document on “Inertial Oscillations” by Thompson (Ocean420) in Winter 2005 in a book by Susan Hautala, LuAnne Thompson, and Kathryn Kelly:

The time period of the inertial oscillation is given by: 

Tin = TE/[2 sin (l)]

Where TE = Earth’s rotation period (24 hrs), and gives some values at different latitudes: 69 hrs at 10°, 24 hrs at 30° (obviously), and 16.9 hrs at 45°. The radius of the inertial circle is also much greater near the Equator (as shown above).


The UTexas website makes a number of other things clear:

      a)   In the Northern Hemisphere, cool winds from the North (that move towards the Equator to replace hot air that rises), are deflected in a clockwise direction, giving rise to the trade winds which blow towards the southwest (SW).

b    b)  Cyclones originate because winds that blow from a high pressure area to a low pressure area are deflected clockwise in the NH (as seen in the Figure below, taken from the UTexas website), and this sets up the cyclonic rotation. Note that the winds blowing towards the South are deflected westwards, while the wind blowing to the North is deflected towards the East. 


c    c) The related point – not mentioned by Thompson (in this document) – is that the Coriolis force is too weak near the Equator to set up the cyclonic rotation, which accounts for the fact that cyclones mostly originate at latitudes with l >7°.






In the North Indian Ocean, a tropical cyclone usually lasts 5-6 days, and they remain at hurricane intensity for 2-4 days (compared to a global average of 6 days).
Another important quantity to evaluate is the dimensionless Rossby number Ro, which is the ratio of inertial to Coriolis forces as mentioned in wiki:


                                       Ro = V/(2w sin(l)L)
Where L is the spatial scale of the system, in this case a cyclone. Only if Ro £ 1, is the effect of Coriolis force significant relative to the inertial force.


A cyclone with a wind speed of 10-14 km/hr is slow-moving, 15-25 km/hr is a moderate cyclone, and for >25 km/hr it is a fast-moving cyclone.
The size of a cyclone in Indian seas varies between 50 and 2000 kms, but most of them are in the size range of 300-600 kms.
For a cyclone with V = 10 m/s (36 km/hr) in the Bay of Bengal or the Arabian Sea, with a spatial dimension of 500 kms, the dimensionless Rossby number Ro becomes:

                                            Ro = 10/[(2)(7.29x10-5)(0.32)(5x105)] = 0.43

It seems that the Ro number will be even lower for a larger cyclone (say 1000 kms) or a slower moving cyclone at a higher latitude.
Note that the highly contentious case of water draining out in spiral fashion from a kitchen sink: does it go CW in the NH? The answer is that, whatever happens, it’s not due to the Coriolis force. The Rossby factor for this case is (roughly), assuming L = 0.1 m, V = 1 m/s and in India:

                                               Ro = 1/[(2) )(7.29x10-5)(0.32)(0.1)] = 2x105

So the Coriolis effect doesn’t have a chance compared to inertial effects!


“Cyclones that form over the Bay of Bengal are either those develop in situ over southeast Bay of Bengal and adjoining Andaman Sea or remnants of typhoons over Northwest Pacific and move across south China sea to Indian Seas. As the frequency of typhoons over Northwest Pacific is quite high (about 35 % of the global annual average), the Bay of Bengal also gets its increased quota.
The cyclones over the Arabian Sea either originate in situ over southeast Arabian Sea (which includes Lakshadweep area also) or remnants of cyclones from the Bay of Bengal that move across south peninsula. As the majority of Cyclones over the Bay of Bengal weaken over land after landfall, the frequency of migration into Arabian Sea is low.
In addition to all the above the Arabian Sea is relatively colder than Bay of Bengal and hence inhibits the formation and intensification of the system.”

I am currently reading Amitava Ghosh’s “The Great Derangement: Climate Change and the Unthinkable“ (Penguin Random House India, 2016) and he observes that (possibly due to global warming) for the first time, in 2015, the number of cyclones originating in the Arabian Sea was known to be greater in number originating in the Bay of Bengal (p.58). He also notes that: “The cyclones that have struck the west coast of Indiain the past have all traveled upwards on a northeasterly tack, from the southern quadrant of the Arabian Sea” (p.66). He is extremely worried that such a cyclone may hit the highly populated, low-lying coastal megacity of Mumbai, with lethal consequences. With global warming, the intensity of cyclones has been observed to have increased, even though the frequency may not have.

According to Persson, since inertia circles have a lower diameter at higher latitudes (than at lower latitudes), the inertia circles are actually spirals transporting mass westwards, (Anders O.Persson, History of Meteorology 2 (2005)3). Elsewhere in this paper, Persson refers to the phenomenon of beta drift, which explains the northwestward movement (in the Northern Hemisphere) of cyclones. This is complicated but I will summarise what I got out of the flash simulation in the following website:
For an axisymmetric cyclone, the vorticity is conserved (under some reasonable conditions).
The vorticity (vector) is defined as: W = curl(v), where v is the velocity vector. Anyway, there are two components of vorticity: the local vorticity due to the spin of the cyclone around its central axis and the vorticity  f due to the spin of the Earth around its axis. The latter is given by:
f = 2sin(l)
 it is zero at the Equator, and it increases as the latitude increases.
If an air parcel in or near the cyclone moves Northwards, its Earth vorticity increases, and since the total vorticity is conserved, its local vorticity decreases. Similarly, an air parcel that moves South, finds its Earth vorticity decrease and its local vorticity increase. Air parcels that move East or West do not change their latitude or Earth vorticity.
These increases and decreases in local vorticity cause the formation of two secondary (beta) gyres (see the Figure below, from the above website) that rotate in opposite directions: the local vorticity has a minimum that is NE (CW rotation) of the main cyclone vortex (CW rotation), and a maximum SW  (rotating CCW) of the main vortex. These two gyres are much weaker (by orders of magnitude) than the main vortex – and they are not visible in satellite pictures of cyclones.      
At this point, the website unabashedly declares that ‘numerical simulation’ shows that these two gyres displace the main vortex of the cyclone in a NW direction (in the NH), and a speed of, at most, a few metres/sec. Note that the beta effect will displace the cyclone in the NW direction even if it is embedded in ‘calm winds’ (a slow or almost static’ cyclone).
For me, this constitutes a ‘ne plus ultra’ – because I am not about to get embroiled in numerical simulation of meteorology!   
About 10-20% of the storm’s motion arises from the beta effect.
 Please note that you can't observe these circulations on satellite loops because their orders of magnitude are so much smaller than the hurricane's circulation. 

Nonetheless, these circulations associated with the Beta effect are sufficiently large to cause a westward-moving hurricane to drift northwestward. Moreover, the Beta effect is the reason why tropical cyclones flirting with crossing the equator swerve to the northeast before it's too late.
 
The Earth vorticity parameter f arises due to the Coriolis force, and the beta effect arises due to the variation of the vorticity f with latitude (X.Liang and J.C.L.Chan J.Atmosph.Soc. (Oct.2005) p.3825)
Bottomline: The beta effect does cause the cyclone to move away from the West Coast of India (although it also causes cyclones to move towards the East Coast), while the frequency of cyclones in the Arabian Sea seems to have gone up in 2015, above that in the Bay of Bengal – according to Amitava Ghosh.


















Wednesday, July 20, 2016

More cyclones hit the East Coast of India

Just by reading the newspapers over the years, one can recall more cyclones hitting the East Coast of India than hitting the West Coast.
I thought that I would check online if somebody else has observed, and explained, this observation.

I found one post which I reproduce below, from an IAS (aspirants/trainees?) discussion forum:

http://discuss.forumias.com/discussion/595/gs-geography-questions


“Why do cyclones strike at the Eastern coast in India and not much in the Western coast. As if we notice it is seen that cyclones typically create much havoc in the Eastern coast rather the Western coast?
The main cause is Coriolis effect.
Since India is in Northern Hemisphere, so in here, due to Coriolis force, winds tend to turn toward their right while moving.
So, whatever cyclones are formed in Bay of Bengal, they turn toward their right, hitting our Eastern coast.When cyclones are formed in Arabian sea, they get deflected away from india.
But, they are exceptions also, since this is not the only factor.”

The explanation seems to be correct - except for the fact that in the Northern Hemisphere (NH) the deflection is towards the left, or the North-West. The diagram below indicates this:

I also put a very rough approximation of the Indian peninsula as a triangle, with the East Coast making a shallower angle of 35°  at Kanyakumari, than the West Coast which makes an angle of 21°.
Also, Kanyakumari is at 8.08° N latitude.

Why does India’s West Coast get hit by cyclones less often than the East Coast? 
a)  Cyclones form over water, because they pick up energy from evaporating water 
b)  Cyclones are mostly observed to originate between 7 and 15 degrees of latitude; they form at latitudes greater than 7 degrees (in the NH), and do not originate at all in the zone of +/- 7 degrees about the Equator.
c)  Cyclones move counterclockwise in the NH because of the Coriolis force
d      The East Coast is at an angle to the cyclone so it tends to miss it. The position of Kanyakumauri at 8 degrees N is significant in view of c).  
     
       Another factor is the frequency of storms in the Bay of Bengal and in the Arabian Sea (4:1):

“       "Historical records suggest that for every four cyclones in the Bay of Bengal, there is one in the Arabian Sea,” said Basab Bandopadhyay, a scientist in the cyclone warning division at the India Meteorological Department, New Delhi.
Subtle differences between the way that convective currents behave over the Arabian Sea and over the Bay of Bengal may explain this higher frequency of cyclones forming over the Bay, scientists said."



Q: Why are there fewer cyclones in the Arabian Sea compared to the Bay of Bengal?

The Arabian Sea is relatively colder than the Bay of Bengal and this inhibits formation of cyclones.
"Bay of Bengal cyclones either originate in situ or come from the South China Sea (also NW Pacific) (the latter has 35% of all global cyclones every year, so this is a large number). Arabian Sea cyclones either originate in situ or are remnants of cyclones that come from the Bay of Bengal overland across the Southern Peninsula (and so have become weaker, and are less in number)." 

Generally storms do not cross the Equator - but this rule is probably not inviolable.


"The developing (storm) system must be at least 500 km (300 miles) away from the Equator. For the development of the rapid rotation characteristic of tropical cyclones, the low-pressure centre must be located at least 500 km (300 miles) away from the Equator. If the initial disturbance is too close to the Equator, then the effect of the Coriolis force will be too small to provide the necessary spin. The Coriolis force deflects the air that is being drawn into the surface low-pressure centre, setting up a cyclonic rotation. In the Northern Hemisphere the direction of the resulting circulation around the low is counterclockwise, and in the Southern Hemisphere it is clockwise".
Note that the distance between Kanyakumari and the Equator is about 900 Kms. This implies that the cyclones that form in the Bay of Bengal and in the Arabian Sea are 'separate' - to some extent - because a cyclone crossing land tends to weaken (as mentioned above), but, again, this is not an insurmountable barrier, so there will be some crosstalk between the two.

A similar phenomenon - the East Coast getting more hurricanes - has been observed in the U.S.:

Why do hurricanes hit the East coast of the U.S., but never the West coast? Contributed by Chris Landsea (NHC)
"Hurricanes form both in the Atlantic basin (i.e. the Atlantic Ocean, Gulf of Mexico and Caribbean Sea) to the east of the continental U.S. and in the Northeast Pacific basin to the west of the U.S. However, the ones in the Northeast Pacific almost never hit the U.S., while the ones in the Atlantic basin strike the U.S. mainland just less than twice a year on average. There are two main reasons. 
The first is that hurricanes tend to move toward the west-northwest after they form in the tropical and subtropical latitudes. In the Atlantic, such a motion often brings the hurricane into the vicinity of the U.S. east coast. In the Northeast Pacific, a west-northwest track takes those hurricanes farther off-shore, well away from the U.S. west coast. 
In addition to the general track, a second factor is the difference in water temperatures along the U.S. east and west coasts. Along the U.S. east coast, the Gulf Stream provides a source of warm (> 26.5°C) waters to help maintain the hurricane. However, along the U.S. west coast, the ocean temperatures rarely get above the lower 20's, even in the midst of summer. Such relatively cool temperatures are not energetic enough to sustain a hurricane's strength. So for the occasional Northeast Pacific hurricane that does track back toward the U.S. west coast, the cooler waters can quickly reduce the strength of the storm."

Ok, so this is where I'm going to stop for today. I'll continue in the next post to add some more details about the Coriolis force. The reason that I have to go into more detail is that the deflection in the Northern Hemisphere is counterclockwise, but a cyclone can last several days, and in this process the continued CCW deflection causes the cyclone to trace a circle (called an inertial circle). So where does this leave us, going round and round? On an average is the motion of the cyclone an undeflected straight line (or whatever it was going to do anyway in the absence of the Coriolis force)?









Friday, July 1, 2016

Just a few add-ons to the previous post: a log-log graph of extra time vs altitude h (in kms):
in which points for Burj Dubai, Mt.Everest and the 12 kms cruising height of commercial jet-liners are indicated. The point to be emphasized is that the extra time is proportional to the square root of the altitude.
Of course, one could increase the altitude beyond 12 kms. At an altitude of 100 kms (the 'edge of outer space'), the extra time is 40.34 mins, and at 400 kms (the mean altitude of the International Space Station), it is 79.17 mins.
At an altitude equal to the Earth's radius, the angle q = 60° (which is easy to verify) and the extra time is 240 mins or 4 hrs.
You need to go infinitely far to get q=90° and a time of 6 hrs.
That's it - I can't think of any reason to bang on about this any more!