Preheat the oven to 350ºF.
If using a domestic duck, remove the neck flap. With the duck breast side up and the cavity facing you, make 1/2-inch slits on each side of the rib cage inside the cavity with a sharp pointed knife. The number of slits will vary according to the size of the duck. Insert a garlic clove in the neck cavity. Insert the quartered onion and celery pieces in the breast cavity. Rub the duck with some of the oil. Combine 2 teaspoons of the salt, the pepper, and 1/2 teaspoon cayenne. Season the outside of the duck with half of this mixture. Add the remaining half of the vegetables inside the cavity. Dust the duck with the flour.
Heat the remaining 1 tablespoon vegetable oil in a roasting pan over medium-high heat. Place the duck, breast side down, in the hot oil and brown for 2 to 3 minutes. Using a long-handled fork, turn the duck over and brown on the back and sides, until evenly browned.
Arrange the Jerusalem artichokes and chopped onions, celery, and carrots around the duck or ducks in the roasting pan. Sprinkle the vegetables with the remaining 1 teaspoon salt and remaining 1/2 teaspoon cayenne. Continue to cook for 3 to 4 minutes to slightly wilt the vegetables. Add the water and wine and cook for 5 to 6 minutes more. Cover and roast for about 1 hour 15 minutes, basting occasionally with the pan juices.
Remove from the oven. With a large spoon, mash the vegetables against the sides of the roasting pan.
Return the pan to the oven and roast, uncovered, for about 45 minutes, or until the duck is tender when pierced with the tip of a pointed knife. Let stand for about 10 minutes before carving,
To serve, carve the ducks into serving pieces and spoon vegetables and gravy over.
Yield: 4 servings