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Most areas of deep low pressure create their own area of minimal shear as latent heat from condensation is released into the environment directly above the storm. This is what aids in development of these deep lows. As the center weakens, cloud tops cool, and this heat transfer slows down. All the 40 and 50 knot shear surrounding the storm then has a chance to start attacking the periphery of the storm, eventually creating a sheared environment and killing the low.