Where to download NATs (North Atlantic Tracks) information?
Your question


  I cannot find information from [Shanwick Oceanic Control and Gander
  Oceanic Control] What are their websites?


Direct answer

ATC centers have no public websites in general. Aeronautical information is distributed by a fixed dedicated network, the aeronautical fixed service (AFS) and its data network AFTN.

From ICAO North Atlantic Operations and Airspace Manual (NAT Doc 007):


  The agreed OTS is promulgated by means of the NAT Track Message 
  via the AFTN to all interested addressees. A typical time of
  publication of the day-time OTS is 2200 UTC and of the night-time OTS
  is 1400 UTC.


FAA, other agencies and aviation blogs relay the NAT-OTS notam on the web.

You can read below if you are interested in jet streams and how the track system is rebuilt twice a day to take advantage of current winds.



Polar jet stream

The jet streams are extremely strong west winds blowing at cruise (tropopause) altitude. The polar jet streams blow at about 50/60° latitude, and the northern polar jet stream is the one blowing over the North Atlantic ocean, the busy route between North America and Europe.

According to the theory, still in discussion, the prevalent wind in altitude in this area is due to the interaction between interleaved Ferrel cells (high pressure) and polar cells (low pressure):


Atmospheric circulation (source)

(Note the tropopause is lower at the pole than at the equator.)

This results in a wind blowing from a south cell to the closest north cell, speed is often between 50 and 150 kt, but 200 kt has been seen. However, for an observer on the ground, due to Earth rotation (Coriolis force) the flow is meandering eastwards from Canada to northern Europe at an altitude of about 8-10 km, as visible on this image of today's polar jet at 250 hPa isobar:


Source: NullSchool

Colored curves are isotachs, areas of equal air speed. Blue is 0 and purple is more than 200 km/h.

The thickness of the polar jet streams is usually less than 5 km and their width a few hundreds of km. To take advantage of jet streams when flying to Europe, aircraft must be packed into this area.

Daily updated organized track system

Aircraft fuel consumption and ground speed can be significantly improved by using tailwinds when flying eastwards, and minimizing headwinds when flying westwards, rather than just following the shortest path (great circle) between two locations. The North Atlantic Organized Track System (NAT-OTS) is a set of eastbound and westbound routes over North Atlantic, computed twice a day to this effect.

Tracks to North America are named starting at letter A, tracks to Europe are named starting at letter Z. Routes for Europe are in the middle of the polar jet, routes to North America are the northernmost, where the jet is the weakest.

Today's polar jet stream and corresponding NAT-OTS (look at eastwards tracks S/T/U tightly packed in the channel where the wind is most beneficial):



NAT-OTS vs. polar jet stream at 250 hPa isobar on 17 Feb 2020. On top, blue is 0 and purple is more than 200 km/h.
Sources: NullSchool (top), SkyVector (bottom)

North Atlantic track system

ICAO guidance for planning and using this airspace between FL285 and FL420, where almost all commercial traffic occurs, is described in NAT Doc 007.

Crossing the ocean is currently done without radar surveillance and coordinated by five oceanic area control centers (OAC): Gander, Shanwick, Reykjavik, Santa-Maria and New York East. The tracks use a set of fixed entry and exist points at their extremities:


Overall structure, with entry and exist points (source)

Those points change over time when the NAT airspace is reorganized, e.g. with the adoption of HLA in replacement of MNPS.

Track system construction

The process is collaborative between airlines and ATC.

From Wikipedia:


  The day prior to the tracks being published, airlines that fly the
  North Atlantic regularly send a preferred route message (PRM) to
  Gander and Shanwick. This allows the ATC agency to know what the route
  preferences are of the bulk of the North Atlantic traffic


From SKYbrary:


  The night-time OTS (eastbound) is produced by Gander OAC and the
  daytime OTS (westbound) by Shanwick OAC, each incorporating any
  requirement for tracks within the New York, Reykjavik, Bodø and Santa
  Maria Oceanic Control Areas (OCAs). The OTS planners co-ordinate with
  adjacent OACs and with domestic ATC agencies to ensure that the
  proposed system is viable. They also take into account the
  requirements of opposite direction traffic and ensure that sufficient
  track/flight level profiles are provided to satisfy anticipated
  traffic demand.


and:


  Following the initial construction of the NAT tracks by the
  appropriate OCA, the proposed tracks are published on an NAV Canada
  operated internet site for review and discussion by interested
  parties. One hour is allocated for this process during which any
  comments will be considered by the publishing agency and any agreed
  changes are then incorporated into the final track design.


OTS Changeover Period

From SKYbrary:


  To provide a smooth transition between the night-time and the daytime
  OTS, a period of several hours is allocated between the termination of
  one system and the commencement of the next. These periods are from
  0801 to 1129 UTC and from 1901 to 0059 UTC.
  
  During the changeover periods, some restrictions to flight planned
  routes and levels are imposed and opposite direction traffic must
  remain clear of the inbound (terminating) OTS.


Suggested (good) reading


Flying the North Atlantic Tracks, from AeroSavvy.
North Atlantic MNPS Airspace, from Airline Pilots Forum and Resource