Yes, that's why it sinks.
The process you are referring to is called convection. Warm air rises because it is less dense than cool air, which causes it to displace the cooler, denser air and sink. This cycle creates a convection current that plays a key role in atmospheric circulation and weather patterns.
rising
Rising and sinking air is called up draft and down draft, respectively.
A high pressure system is characterized by sinking air. This sinking air creates dry and stable weather conditions with clear skies and little precipitation.
tornado
In areas of high pressure, air is generally sinking rather than rising. High-pressure systems are characterized by descending air, which leads to clearer skies and stable weather conditions. This sinking motion suppresses cloud formation and precipitation. In contrast, rising air is typically associated with low-pressure systems, where clouds and storms can develop.
The vertical rising or sinking of air is known as the air current
Sinking air produces clear skies and dry conditions.
it is rising think of clear skies with a high pressure rising the air up.
Convection.
The process of warm rising and cool air sinking is called convection. Convection is the concerted, collective movement of groups or aggregates of molecules within fluids and rheids, either through advection or through diffusion or as a combination of both of them.
Cold sinking air refers to air masses that are denser and heavier than the surrounding air, causing them to sink towards the surface. This process can lead to stable atmospheric conditions and inhibit cloud formation and precipitation. Cold sinking air is often associated with high pressure systems and clear weather.