As the airplane descended from about 38,000 feet, the flight crew observed that they had a tailwind of between 60 and 70 knots and that cumulonimbus clouds were ahead of the airplane. Descending through 34,668 feet, the tailwind suddenly decreased and the indicated speed of the airplane quickly increased. The captain activated the speed brakes and disengaged the autopilot. Subsequently, the airplane began to slow. As the captain was slowly retarding the speed brakes, the airplane started to climb and the captain slowly lowered the nose of the airplane. The digital flight data recorder revealed that over a 30-second period the airplane’s vertical acceleration decreased to 0.75 g, then increased to 2.33 g, decreased to 0.05 g, then stabilized at 0.9 g (normal). During the event, one passenger broke her femur; two cabin attendants and four passengers received minor injuries. The airplane was not damaged. Convective activity was located immediately west of where the event occurred, likely blocking the wind flow and causing a wave-like disturbance downstream of the storms, which would result in unanticipated convectively induced turbulence. Since the event occurred in clear air downstream of the cumulonimbus clouds, the airplane likely encountered an undulating turbulence under a strong temperature inversion and strong windshear. The turbulence was not predicted by weather forecasters. Probable Cause: An encounter with unanticipated convectively induced windshear and turbulence during descent.