Relatively late with starting this new thread. Before we look at the foreseeable future, let's have a look at the previous season although I don't think many want to
The season was dominated by a much stronger than normal stratospheric polar vortex (SPV) which meant the Northern Hemisphere had a very mild winter, in fact the mildest on record for many. There was very little blocking on offer in the high latitudes and there was very little warming to disturb this strong SPV from developing. There were 2 minor warming events through the season, first one in early November and the other in early February but the latter did not do much at all.
The final warming took place on 29 April which was 14 days later than average. This was unusual as winters with a major SSW event tend to have very late dynamical final warmings (such as 2019 did) but 2019-20 had no major SSW.
It certainly was no varied season like the previous two, 2017-18 and 2018-19, were but it was yet another notable season for the stratosphere.
You can look at other years back to 1979 here for yourself if you so wish to.
For those that are new, the earth's atmosphere is divided into different layers. The troposphere is where weather occurs and the stratosphere is just above the troposphere. Much like the weather around the earth, the stratospheric temperature varies by season with it reaching its lowest point in December on average. Each autumn, a phenomena known as the stratospheric polar vortex forms within the Arctic Circle. This is an upper-level area of low pressure formed by the temperature difference between the equator and the pole. The vortex weakens and strengthens from year to year via dynamic events like stratospheric warming or the annual summer hibernation where the SPV "goes to sleep" due to a lower temperature gradient between the equator and the pole. The SPV is well defined when it's strong with a single vortex lying within the Arctic Circle.
Normally, the troposphere and stratosphere are in sync with each other which results in downwelling. This is when planetary waves are propagated to either level of the atmosphere via the weather patterns that occur. For example, an Aleutian Low (low pressure over or around Alaska) / Scandinavian High (high pressure over Scandinavia) combination can be a sign of disrupting the Polar Vortex and a precursor to a SSW event as a result. Another example is that with a cold stratosphere and healthy SPV, the North Atlantic jet stream is powered up bringing mild and moist conditions to western Europe with low pressure centred over Iceland. Tropospheric patterns that can have an impact on the SPV are defined by zonal wavenumbers which I would like to direct you to GL's excellent post from a 2018-19 thread here as I couldn't have explained it better myself.
There are different types of warming that occur and can have different degrees of impacts on the weather around the Northern Hemisphere if a tropospheric response occurs.
There is a minor stratospheric warming which involves the stratospheric temperature rising but less dramatically compared to a major warming and the zonal mean zonal winds do not reverse.
A major sudden stratospheric warming involves the zonal mean zonal winds at 60N 10hPa in the stratosphere to reverse from westerly to easterly. The SPV is completely disrupted and it will either be split into two or more vortices OR displaced from its normal location over the North Pole. Major SSW events are forced by tropospheric patterns disturbing the SPV but sometimes, these events can propagate back down into the troposphere and result in anomalously blocked patterns which gives a higher chance of colder weather for Europe. However, even if a SSW downwells successfully into the troposphere, the positioning of the blocking is a factor to consider also.
Cohen and Jones (2011) did a good paper on tropospheric precursors and categorising past SSW events into splits and displacements here, it's free access to everybody.
Met Éireann highlighted previous Irish cold spells and if a SSW could have caused them in their Storm Emma paper here.
Other warming events that occur include final warming events which indicate the transition into stratospheric summer hibernation mode and Canadian warming events which occur earlier in the winter.
The foreseeable future shows the stratospheric polar vortex continuing to strengthen at a greater amplitude than normal. No signs of weakening any time soon.