A given fluid flowing through a given channel is laminar at low velocities. This means that the fluid particles move in sheets or laminae. Increasing the speed distorts this laminar flow and chaos creeps in. At very high velocity, the fluid becomes turbulent, i.e. the motion is random. Turbulence is one of the open problems in the field of mathematics. Although advanced numerical methods are good in predicting the turbulent behavior, yet they are based on many assumptions and this limits the generality of a particular turbulence model. It is obvious that understanding the transition from laminar to
turbulent flow might be very useful, since during transition, the motion is not random. In geophysical flows, for example oceans and lakes, the onset of this transition (or instability) occurs at places of sharp velocity gradient. This is why we see surface waves. The same process occurs during the production of internal waves. Another property which affects the stability behavior is density gradient (which is sharp between air and water at the surface). Both velocity and density gradients are also observed when fresh water mixes with salt water, especially in the estuaries. This makes the interface between the fresh and salt water unstable. The interplay between velocity and density gradients govern the laws of instability at the interface. This is what I intend to study for my Ph.D thesis work. Using both theoretical and numerical techniques, I will try to understand this behavior and perhaps formulate the smallest length scales involved in the flow. This will also help understanding the turbulence induced mixing between the fresh and salt water.