“ Yet there shall be a space between you and it, about two thousand cubits by measure, come not near it, that you may know the way by which you must go, for you have not crossed over this way up to now.”
This suggests that the Ark was uncovered, which was why it was being borne by the priests (see Numbers 4). Compare the similar sized gap around Levitical cities (Numbers 35:5). Note that the gap was between the Ark and the people. It would not have been empty for it would contain all the priests going ahead, followed by the Levites, marching ahead of the people. This was similar to the Tabernacle where the priests could enter the Holy Place, and the Levites the outer court, forbidden to the people.
The gap would have been maintained while crossing the Jordan with the people crossing on both sides, either one or two thousand cubits away from the Ark depending on whether we interpret the two thousand cubits as the total gap (one thousand on each side), or as two thousand in both sides. In the case of the Levitical cities the former appears to be the case.
The priests, and even possibly the Levites, formed a protective wall around the Ark. The standard cubit was about Joshua 17:5 inches (just over half a metre). The purpose of the Ark going ahead was to show them the route to take over the Jordan. ‘Passed this way' or ‘crossed over this way' is a verb largely used in this narrative of crossing the Jordan (Joshua 2:23; Joshua 3:1; Joshua 3:6; Joshua 3:11; Joshua 3:14; Joshua 3:16-17). The point here is that they had never experienced YHWH's unique power in the way that it would be revealed here as they crossed over into a land they had never seen.
In view of the fact that this gap is not mentioned in the Law, and is not mentioned elsewhere, we are justified in seeing it as a unique requirement only for this occasion. The reason for it would seem to be because of the unique revelation of His power to be given here. He wanted them to be aware that He was there, invisibly but certainly, thus rendering the area around the Ark ‘holy'. This was also one reason why they had to sanctify themselves before the event. He was about to reveal Himself as Lord of all the earth by His power expressed in the stopping of the Jordan. During this manifestation of power, this ‘doing of wonders', this personal revelation of His presence, none must be near, except for the priests and the Levites. God wanted His people to remember this occasion vividly and to be aware that He had been there in numinous power.