Sauce – Non-alcoholic substitution for dry white wine in bolognese sauce and other tomato sauces

It depends what the recipe is, but I've successfully replaced brandy with orange juice or apple juice in the past. It's not a direct replacement for the flavour, of course, but gives a similar strength of flavour, if you see what I mean.

Short answer: tomato sauce is a non-Newtonian fluid. Another interesting link can be found here.

Tomato sauce is an interesting creature. Think about ketchup. You try to shake some out and nothing happens. So you tap the bottle a little bit, still nothing. Tap it a little harder, and a little harder, and suddenly boom: a flood of ketchup. The "jumpiness" of tomato sauce is caused by the same physics.

Basically, tomato sauce has two things in it that contribute to this characteristic: water and tomato pulp. At first, the tomato pulp is just lying around every which way, which makes the sauce act a lot thicker. But when the strands of pulp are aligned, it makes the sauce act a lot more like water. Heating up the sauce increases the pressure on the sauce, allowing areas of the sauce to become much more fluid, resulting in bubbling, popping, and the flinging of tomato sauce all over your clean white shirt. The same effect is what makes ketchup come flying out of the bottle - when you whack it hard enough, the pressure changes the state of the ketchup, and the ketchup literally flows like water.

Edit: updated with relevant information

Unfortunately, when I managed to get a hold of Mr. Steingarten's lovely book, The Man Who Ate Everything,* I discovered that the passage regarding tomato sauce as a non-Newtonian fluid was exclusively regarding ketchup, and not general tomato sauce as I thought I remembered. However, this description is still a valuable one, and it does help explain this particular characteristic of tomato-based sauces (after all, ketchup is a tomato based sauce) [p 96]:

It was only after I had send a stream of ketchup streaking across my wife's favorite tablecloth, a lovely hand-printed Indian cotton from a shop on the rue Jacob, that I telephoned Professor Malcolm Bourne at Cornell for a lesson in non-Newtonian fluids. Sir Isaac Newton wrote the laws governing liquids that flow like water: the more force you exert on them, the faster they flow. But ketchup is different. Composed of tangled red tomato fibers suspended in a sweet and acidic colorless serum, ketchup behaves like a solid both at rest and under low levels of pressure: but then, at some higher threshold, it suddenly begins flowing like an ordinary fluid. That's why the frustrated ketchup lover who loses patience with gentle taps on the bottle's bottom and prematurely shifts to a powerful wallop ends up with a gush of ketchup over everything. Ketchup and mayonnaise are known as Bingham fluids, named after the scientist who characterized them early [last] century.

_{*Personally, I think that The Man Who Ate Everything is a must-read for anyone interested in culinary science, and a should-read for anyone interested in food.}

Second Edit:
Due to a handful of downvotes that I received while I slept last night, I guess some clarification is needed:

1. I just want to be absolutely clear here, I am in no way implying that ketchup == tomato sauce. I offer this information as an example of how tomato pulp suspended in liquid acts.
2. The fact that "tomato sauce is thick" doesn't really hold up. The question even clearly states: "Of all the sauces and creams I prepare in a hot pot, tomato sauce is the most jumpy", which presumably includes thick ones. If thickness was the only factor (and I'm not saying that it isn't a factor), we would see similar actions from cheese sauces, bechamels, gravies, and a variety of soups. While these sauces/soups do splatter, tomato sauce is significantly more "splattery." Put a pot of tomato sauce next to any other sauce/soup, take your pick, and heat them to the same temperature. I can pretty much guarantee that given similar conditions, you're going to be wiping up a lot more tomato sauce than the other one.

One last edit: This article on Slate indicates that it's a combination of the above (being a "plastic liquid"), the viscosity, and pectin, as pointed out by Brendan in a comment below.