Intial Regime - When a channel is first put into service, then the channel tries to attain its "intial regime" condition. When the channel is excavated with small width and flatter slope, then the bed slope gets increased due to deposition of sediment, in order to develop increased flow velocity. The increased velocity enables the discharge to pass through the channel having small width.
Here with the increased bed slope the depth of the channel also varies, how ever the width of the channel does not vary and remains constant. So kepping constant discharge, constant width, constant silt charge and constant silt grade and only by varying bed slope and depth of channel, the channel attains stability, such a condition is known as initial regime condition.
Final Regime :- This is the ultimate regime condition attained by the channel when, in addition to varying bed slope and depth of the channel, the width of the channel is also allowed to vary.
What happen exactly is that with the passage of time, the resistance offered by the sides of the channel against erosion comes to an end due to continuous action of water, so the channel adjusts its bed slope, depth and width in order to attain stability. Such a condition is known as final regime condition.
Such a channel where all the parameters such as width, depth and bed slope are allowed to vary freely, has the tendency to attain a semi-elliptical shape. So coarser the silt, flatter would be the semi-ellipse and finer the silt, the shape would be more or less of a semi-circle.