Ramanujan Auditorium

Turbulence, Kolmogorov Spectrum and its different variations

Jayanta Kumar Bhattacharjee

IACS Kolkata

Fully developed turbulence is known to be a rather difficult problem to handle. But Kolmogorov (1941) found a result which was strikingly simple. He considered the energy spectrum E(k) of maintained turbulence, defining it by E=∫E(k)dk, where k is the wave-number and E is the total energy – a quantity conserved in the inviscid, unforced limit. Physical reasoning and dimensional analysis led to E(k) ∝ k^{-5/3}. More than eighty years later, the goal of many turbulence researchers is to find something as elegant as that. We will discuss a number of related situations and also the difficulties still encountered in making the proportionality an equality.