Thanks for the questions Stefan.
Stated many times that evaporation is required to alter the density of the sap in the upper part of the tree, releasing pulses of salts down the phloem to induce a positive pressure in front of the falling sap and a negative pressure / tension on the xylem sap affording bulk flow back to the leaf. So clearly transpiration is important when leaves are on the tree but not required for inducing the circulation when there are no leaves on the tree. Yet the stored solutes in the upper parts of the tree as you rightly state move down the tree over the winter towards the roots and this cannot take place without affecting a return flow of dilute sap back up the tree.
Even when the tree has shed it's leaves root growth requires there to be circulation and the change in pressures brought about by shedding the leaves would undoubtedly influence a downward growth at the roots providing an increase in pressure within the roots.
Have already demonstrated circulation inside tubular experiments using tea, liberated from tea leaves, urine, milk, juiced fruit, juiced leafy vegetables, demonstrating slight changes in density at an elevated point will cause both a downward flow and a return flow.
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Mathematical calculations designed to show it can't happen or can happen appears a little pointless when we can show it taking place experimentally and reliably so. Has anyone done the maths on the Atlantic conveyor system? If you feel this can contribute anything please feel free to share your results.
Over a prolonged winter when hypothetically all of the sugars and salts have reached the roots which incidentally could not happen without a continual flow and return circulation taking place, all that would be required to trigger circulation in the spring would be a density change in the sap. Warming the outer part of the trunk first from the seasonal change in temperature would provide such a density change and induce circulation together with an increase in head of water at the tips of the branches to induce bud burst and the blooms of blossom and leaves.
Also, the last ice age that is believed to have been started by a sudden influx of salt free water flowing onto the ocean surface and causing the Atlantic Conveyor system to shut down. See film: After the Warming. Offers an understanding of the sudden increase in rainfall in the Autumn diluting the sugars and solutes in the tree and effectively washing out the nutrients from the leaves returning them to the trunk and branches and in doing so altering the circulation causing the leaves to wilt and fall.
The fact that the leaves fall from the tree indicates they are in danger given that the deciduous trees that normally shed leaves hang on to them when planted in warmer dryer conditions. And when a tree is in trouble from water stress it is generally the upper parts of the tree that die back again indicating a reduction in water within the tree.
Andrew