You'll see it said again and again: mead is a patient person's drink. Like wine, it benefits from aging, both before and after bottling. Mead can age just as long (or longer) than wine, under the right conditions.
A lot of the scientific information for aging is specific to wine, but seems to apply to mead as well.
To bulk age a mead simply means to give it additional time in a carboy prior to bottling. This allows it time to clear and mature as a single unit and creates higher consistency between future bottles.
During bulk aging, oxidation is a major concern and can be handled via several techniques. Techniques can be combined. Due diligence paid upfront will help protect the mead you earned.
There is often no immediate need to rack upon completion of primary fermentation. Yeast will flocculate (clump together and drop to the bottom) out over time at different rates (days to weeks to a month) depending on their strain. The concern about leaving a mead on the lees is autolysis, but is hardly a concern both on homebrew time scale and batch size. Even a month is not enough time to make a difference for that but can allow it to clear. It can reduce the amount of rackings needed which can reduce oxygen exposure. Cold crashing is often ineffective but time is the real winner for clearing the majority of meads (exceptions being fruited meads, pectins can cause persistent haze even after the yeast is gone). More time clearing in primary or secondary prevents yeast cakes from forming in the bottom of bottles.
Minimal headspace is the most ideal way to fight oxidation. Firstly, choose a narrow neck secondary container like a carboy and not a bucket or mason jar. Secondly, plan ahead and primary in a vessel slightly larger than your secondary one. For example, 6.5 gallon carboy with 5.5 gallons of mead in primary racked into a 5 gallon carboy. 2 gallon bucket with 1.25 gallons of mead racked into 1 gallon carboy, etc. Anticipate about 1/2 gallon (~2L) of losses on traditional batches around 5-6 gallons (~19-23L) and 1 quart (~1L) on traditional batches around 1 gallon (~4L). Both of those will keep airspace above mead to a minimal. Your mileage may vary depending on fermenter setup, adjunct use (this varies a lot), racking capability (siphon versus racking arm), etc. Heavily fruited meads and other absorbent adjuncts (like hops) will claim their share of your mead.
Headspace can be purged by inert gas such as CO2, nitrogen, or argon. CO2 is available to those who already have kegging equipment but others can easily be purchased online for cheap. Such as CO2 tire fillers. Just be sure to use food-grade CO2, which is a thing, when getting catridges. Argon is sometimes sold as wine preserver and serves a similar purpose. Spray the gas into the headspace for several seconds before quickly sealing it up.
The space can also be filled by topping up the carboy. When creating a batch, it can be beneficial to make (and seal in bottles early) an extra gallon for the purpose of topping up when necessary. Other batches can be used and a neutral trad will help top off a vessel and drop %ABV less than water. Water is acceptable too. It may seem like betrayal to pour in water but consider that water added is the like a slightly lower OG than when you started.
As a last ditch (not recommended by experienced members here, follow above guidelines instead) the extra space can also be neutralized with a filler material like marbles. If taking this route, be sure to thoroughly sanitize the filler. Also be aware that dropping glass marbles into a glass carboy is a good way to break the carboy. This will incur heavy losses as you will not be able to effectively siphon below the marbles. It is the least advisable for practicality and safety reasons. Plan ahead and keep more of your mead.
Use sulfites. Potassium metabisulfite or campden tablets can be used to add SO2 to your mead. This is beneficial since the SO2 scavenges free oxygen before it can get to other compounds in the mead, then off-gas. They are safe to use and used in many industries such as commercial wine and meadmaking. They do not change taste when used in appropriate amounts. 25-50 ppm are simple amounts which are beneficial to most styles of mead. There is a calculator for calculating what you need to get that. Other styles may have different needs, winemaking resources have lots of wisdom on that topic. Add sulfites each time you rack for maximum protection.
Use appropriate equipment, specifically a siphon and not pour. A pour introduces the most amount of oxygen possible in all ways of handling liquid and rapidly oxidizes mead. The high amount of surface area created as it flows through the air does this. A siphon will flow through a tube and fill a container from the bottom, minimizing interaction with air, thus oxygenation. Start high with the bottom of the siphon and go lower as the liquid level drops, this prevents siphoning any lees. Stop when the lees start to move to the siphon. Use two people, one to control each end of the siphon. They are exceptional mess-making devices when the receiving end goes somewhere you didn't expect.
A note about filtration: it is entirely ineffective without using specialized equipment. Coffee filters are entirely useless at catching yeast and do nothing but oxidize mead. You will need appropriate filters and a pump to accomplish it correctly without damaging the mead and is another topic. The main takeaway is do not pour mead through coffee filters.
There is no standard time frame for bulk aging; anywhere from 3-60 months is very common. It is style-dependent and driven by the goals you have.
Aging continues once the mead is put into bottles. Oxygen exchange, as allowed by natural cork, will speed this process, but even in an anaerobic environment like a perfectly sealed crown-capped bottle, chemical reactions will continue to take place which will mature the mead.
When using bottles sealed with corks, several factors can place a limit on the amount of time a bottle can be allowed to age.
Using standard wine bottles in the US, size #8 and #9 corks will both fit the bottle, and #8s are easier to apply with a double-lever corker, but they do not provide as good of a seal as #9s. This will decrease the amount of time mead will gracefully age in the bottle before becoming oxidized.
Cork quality matters. Agglomerated corks will only last a couple of years before they begin to fall apart and the mead becomes oxidized. There are a variety of corks available. Better corks last longer and cost more. Buy them with your purpose in mind. If you open a dead bottle in 10 years, you'll wish you'd spent a few extra cents on a better cork.
Corks work best when they're inserted all the way. This can be difficult with real #9 size solid cork with a handheld lever corker. A floor corker is much easier and more consistent. These are expensive to buy, but can sometimes be rented for a day from your local homebrew shop.
Get the headspace in corked bottles down to a millimeter or less if long-term aging is your goal. This takes some practice, but after ten years, a surprising amount of liquid will have evaporated through the cork.
Corks have a shelf life. Use corks within about 6 months of purchase for best results.
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Please see the article on fining.