Thunderstorm downdraft on Meal Fell

We were caught in a developing thunderstorm on Meal Fell. The winds suddenly rose to over 30mph out of nothing. Now I knew that thunderstorms are driven by convection. Hot air rises quickly. I assumed that the winds were caused by air rushing in from outside the area at ground level to fill the space. However it seems that downdrafts are the most likely cause. The initial rising air contains water vapour that condenses into big droplets that fall down. These droplets drag colder denser air with them. This rushing air pulls the surrounding air in to join it. This process is called entrainment and I am wondering if this is linked to the Bernoulli Effect. The mass of colder air rushing downwards results in the strong winds we experienced.