the 'sand' is very silty all along that part of the coast ie. soil washed down by the rivers. therefore shore wave action causes the 'mud' to disperse thru the water column. that's the brown stain.

If you see "brown" water in Cairns, it is usually not a sign of pollution, but a natural result of the region’s geography and seasonal weather patterns. Cairns is surrounded by mangrove forests and estuaries. During the "Wet Season" (November to April), heavy tropical rains cause local rivers—like the Barron River—to swell, washing large amounts of organic sediment, silt, and tannins (natural "tea-like" dyes from leaves) from the rainforest into the ocean. This process is known as river plumes. Additionally, the beaches in Cairns are often "muddy" rather than "sandy" because the coast is protected by the Great Barrier Reef, which prevents large waves from crashing on the shore and cleaning away the fine silt. If the brown color appears in patches further out at sea, it might be trichodesmium (sea sawdust), a natural bloom of blue-green algae that turns a rust-brown color as it ages. For crystal clear blue water, visitors in Cairns usually take a boat trip further out to the "Outer Reef," where the water is too far from the mainland's river runoff to be affected by the coastal silt.