Dirty Price is the price of the bond, plus part of coupon the seller expects in form of accrued interest for holding the bond for certain days. In most of the European markets, bond prices are quoted in dirty price, and this is what a buyer has to pay to procure a bond. Dirty price is calculated on the basis of settlement date of purchase (T+2, T+3 etc).
Clean Price here is the price of the bond, which is calculated by adding all future payments of the bond, it is also called the market price of the bond.
Accrued interest depends upon how long its been passed since the last payment, and considers day-count convention to calculate that.
Since dirty price depends on how long the bond has been held since the last coupon and is directly related to accrued interest, is it zero on the day of coupon payment and highest just the day before. If we plot a curve of the evolution of accrued interest over a period of time, it exhibits a shark tooth pattern. Lets take an example of Gilt GB0008931148 for a sample period of 10 years between 2010 and 2017 and assuming clean price to be par.
Since dirty price is directly related to accrued interest, its graph will show a relative pattern. Consider for clean price to be the par value.
However in reality, clean price is not always at par value, and fluctuates depending upon prevalent interest rates and other risks factors. Thus a more practical evolution of dirty price looks as below.