Typically this is the case because
In a nutshell yes, because the stronger system has a deeper rossby penetration depth (defined here by the height at which the circulation of the TC is very evident in the column, stronger TCs w/ larger circulations & generally taller/more persistent convection = deeper rossby penetration depth). This means that a stronger TC is also steered by a deeper layer of the troposphere and given that the winds become increasingly westerly with height as a tropical cyclone ventures away from the tropics this often implies faster recurvature for stronger storms. In addition, a stronger storm is liable to gain latitude for another reason: beta drift, which refers to a tropical cyclones' tendency to move in the absence of any steering! Beta drift/the beta effect usually accounts for about 10% of a tropical cyclone's motion and is estimated to add ~2-5 m/s to its translational speed and would be the net movement a TC would undergo if there was no net steering influence from a trough or ridge. Coriolis deflection increases w/ increasing latitude from the equator, as does the planetary vorticity (planetary vorticity is just the spin imparted on phenomena simply from earth's rotation). Effectively what occurs especially as a tropical cyclone becomes fairly intense, is that the differential in planetary vorticity advection across the storm increases and this leads to a net NW motion as a pair of beta gyres (w/ opposing signs) forms on opposite ends of the storm in the northern hemisphere this happens in the NW & SE quadrants. To understand how this works (as shown in the diagram below) and how we get an anticyclonic beta gyre and vis versa in the SE quadrant, we have to know that for example on the east side of the cyclone in the northern hemisphere, as air blows northward it gains planetary vorticity, as the impact of earth's spin becomes greater closer to the pole and thus, going back to the statement of the conservation of absolute vorticity (where absolute vorticity is the sum of planetary + relative vorticity) relative vorticity must decrease if planetary vorticity increases, thereby forming and an anticyclonic beta gyre in the NW quadrant of the storm. On the other hand, as northerly flow occurs on the western side of the hurricane, air moving southward loses planetary vorticity (f becomes smaller), thus in order to conserve absolute vorticity again, relative vorticity has to increase, thereby forming a cyclonic gyre. The net flow between these two beta gyres in the northern hemisphere is to the northwest and this flow which essentially accounts for the beta effect becomes more prominent for stronger hurricanes because their circulations are larger and stronger and thus there's a larger gradient in planetary vorticity (f) across them!
There are certainly other ways to understand the impact of the beta effect on tropical cyclone track but I think this way is much easier to digest but it still can be difficult (as it was for me) the first few times I learned/read about it.
This diagram below shows what I was talking about above, notice the pair of opposing beta gyres orientated from SW-NE across the tropical cyclone's circulation and that the flow between them is to the northwest. This essentially means that in the absence of any steering flow, a tropical cyclone in the northern hemisphere will tend to move to the northwest, with stronger/larger tropical cyclones having a greater tendency to do so vs smaller/weaker TCs.
Hope this helps!
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