Bay of Bengal:
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It is concave or shallow due to which when strong winds push water, it gets concentrated as a storm.
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It is shaped like a trough that makes it more hospitable for storms to gain force.
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High sea surface temperature makes matters more worse in the Bay triggering the intensity of the storms.
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It gets more rainfall with sluggish winds and warm air currents around it that keep temperatures relatively high all year.
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The constant inflow of fresh warm water from the perennial rivers like Brahmaputra, Ganga makes it further impossible to mix with the cooler water below.
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Lack of landmass between the Pacific Ocean and the Bay of Bengal tend cyclonic winds to move into the coastal areas causing heavy rainfall.
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The absence of air movements from north-western India towards the Bay in the post-monsoon phase is also another reason for the chances of cyclones in the Bay of Bengal.
Arabian Sea:
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It is much calmer as the stronger winds help dissipate the heat and lack of constant fresh water helps the warm water to mix with the cool water underneath, reducing the surface temperature.
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The Arabian Sea enjoys the locational advantage as the winds from the Pacific Ocean encounter the Western Ghats and the Himalayas cutting down on its intensity and sometimes never reaching the Arabian Sea.