Why does a coin go in a zigzag fashion and not straight down when dropped in a bucket of water?

When a coin is dropped in a bucket of water, the free fall is resisted by friction or drag due to the water. This force consists of two parts: 

1. Due to pressure acting perpendicular to the coin surface
2. Due to viscous forces acting along the coin surface.

The first part is the pressure drag and the second part is called the skin friction drag. Note that the pressure acting on the coin is not just hydrostatic (which generates the Archimedes buoyancy force) but pressure modified by the motion of the coin itself. Skin friction also depends on the motion of the coin. It is usually smaller than the pressure drag unless the body under consideration is highly streamlined like an aircraft wing. Vortices are formed behind (lee side) the falling coin and they grow in size and get detached periodically. This formation and shedding of the vortices drastically influences the pressure distribution on the coin, especially on the leeward side. This may lead to a sudden change in the motion of the coin including its rotation and hence a zigzag motion. 

The skin friction drag is small on the coin but it affects the vortex shedding and hence the pressure distribution on the coin. It is easy to imagine how complicated this water motion can be. A coin dropped in air, say from a high-rise building, is subjected to similar motion but the frictional forces are smaller due to low air density. We observe similar motion when the leaves are falling from a tree, especially in the absence of wind.Even a coin released carefully in a bucket of water starting from a vertical position soon turns inclined and then tumbles. The laws governing the motion of the coin and the fluid (Newton's laws for a fluid are known as the Navier-Stokes equations) are known but it is difficult to solve them accurately even using a supercomputer to predict the exact motion of this coin. But it is fun to release a coin gently in a bucket of water and try to hit a particular spot at the bottom.

Source: The Hindu