That would trigger an ice age. The earth loses heat in low latitudes and mid latitudes in summer but not in winter or in high latitudes. If it does, then the oceans will cool rather rapidly starting at the poles and permanent snow will quickly build up on the continents. That would continue as long as the meridional flow you described continued.
That would trigger an ice age.
BTW, in the book I mentioned. the author makes the argument that the earth had a close encounter with another planet (say mars or Venus or some other) that also had an ice moon. This ice moon was the rain as well as a fair amount of our polar ice caps. It may be that the continental shelves really were below sea level before that. He also suggested that the earth and this other planet spinning around each other ripped up a new mountain range with each revolution.