Why do you expect thermal convection to mix the cold and hot water?
What could cause the hot water to move down and mix with the cold water?
as the element heeat the cold water gets warm and rises it soon mixes
with the cold water above the element and produces a slower less
heated current, this continues, you won't ge whole tank circulation
currents until the whole tank is essentially at the same temperature.
It's far from obvious that the mixing is that fast. Anyway, even the
mixed water is warmer than its surroundings, and will ascend. Eventually
it's at the same temperature as its surroundings, but it has an upward
velocity, so it will rise above its proper level, in the process
displacing some of the warmer water around it downwards. Throw in some
more mixing, and the next parcel of warmed water will climb higher,
causing yet more mixing. So even if the initial parcel of heated water
cannot reach the top, these processes will ensure that it will in due
course.
The tank may then indeed be essentially all at the same temperature, but
that temperature will be lower than the temperature of the water that
was initially at the top of the tank. Cut off the power then and you
have a tank full of lukewarm water rather than a tank containing hot
water at the top and cold water at the bottom.
Sylvia.