A 43-year-old woman is evaluated for acute-onset vertigo of 3 days' duration. She reports that severe vertigo accompanied by nausea and vomiting began abruptly and has been persistent. There are no maneuvers that accentuate or totally relieve her symptoms, and the severity of the vertigo prevents her from conducting her usual activities at work and home. She prefers to lie in bed with her eyes closed. She has had neither head trauma nor headaches and reports no motor weakness, numbness, tingling, otalgia, dysarthria, diplopia, hearing loss, tinnitus, fevers, or chills. Ten days ago, she had an upper respiratory tract infection. Medical history is otherwise unremarkable, and she takes no medications.

On physical examination, the patient is afebrile, blood pressure is 135/80 mm Hg, pulse rate is 98/min, and respiration rate is 14/min. BMI is 22. She appears uncomfortable and is lying down on the examination table with her eyes closed. She is unable to walk because of the vertigo. Hearing is normal. Pupils are equal, round, and reactive to light. Funduscopic examination reveals normal discs and vasculature. The remainder of the general medical examination is normal. On neurologic examination, finger-to-nose, rapid alternating movements, and heel-to-knee-to-shin tests are normal. The Dix-Hallpike maneuver evokes mixed upbeat-torsional nystagmus after 6 seconds that lasts for about 30 seconds; she then becomes very symptomatic and vomits. The remainder of the neurologic examination is normal.

Which of the following is the most likely diagnosis?