5. (a) Use Figure Q5 to introduce the concept of energy cascade and how it affects the motion scales in fluid turbulence. (10 marks) (b) What is meant by the mixture-fraction PDF? And briefly state the advantages and disadvantages with beta-PDF. (10 marks) (c) What is the definition of Dahmkhler number (Da)? And briefly discuss the differences and technical difficulties between 3 conditions when Da < >1, Da1. (5 marks) Dissipation & n {DI T(l) Transfer of energy to successively smaller scales Inertial subrange Production P LEI lo Dissipation range Energy-containing range Figure Q5. A schematic diagram of energy cascade in turbulent flows C