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If κ is the wavenumber and ε is the rate of dissipation of turbulent energy, which of these is proportional to the spectral energy of the inertial sub-range of turbulence?

If κ is the wavenumber and ε is the rate of dissipation of turbulent energy, which of these is proportional to the spectral energy of the inertial sub-range of turbulence? Correct Answer κ-5/3ε2/3

The spectral energy in terms of the wavenumber and the rate of dissipation of turbulent energy is given by E(κ) ∝ κ-5/3 ε2/3. Where the proportionality constant is 1.5 (obtained experimentally)

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Modern civilization is completely dependent on energy, which has therefore to be abundant and also economical. About 85% of the world's energy is supplied by oil, coal and natural gas while nuclear, hydro, wind and solar power and biomass supply the rest. Coal, nuclear and hydro are used primarily to generate electricity while natural gas is widely used for heating. Biomass is used both for heating and cooking. The wind and solar power is the future's hope as they are sustainable energy sources. Oil powers almost all machines that move and that makes oil uniquely versatile. Oil powered airplanes carry 500 people across the widest oceans at nearly the speed of sound. Oil powered machines produce and transport food. Oil powered machines are ubiquitous. Clearly, we live in the age of oil but it is drawing to a close. According to data available if oil production remains constant until it's gone, there is enough to last 42 years. Oil wells will produce less as they become depleted, which will make it impossible to keep production constant. Similarly natural gas and coal will last another 61 years and 133 years respectively. Naturally, as they become scarce, they become expensive, leading to a worldwide energy crisis. If we are to survive on this planet, we have to make a transition to sustainable energy sources. The transition may be willy-nilly or planned - the choice is ours. The dawning era of limited and expensive energy will be very difficult for everyone on earth but will be even more difficult if it is not anticipated. It is of utmost importance that the public and policymakers understand the global energy crisis and act in tandem to ensure that the species 'homo sapiens' does not become extinct. Biomass is an energy source used in
Read the passage carefully and choose the best answer to each question out of the four alternatives and click the button corresponding to it.
Modern civilisation is completely dependent on energy, which has therefore to be abundant and also economical. About 85% of the world's energy is supplied by oil, coal and natural gas while nuclear, hydro, wind and solar power and biomass supply the rest. Coal, nuclear and hydro are used primarily to generate electricity while natural gas is widely used for heating. Biomass is used both for heating and cooking. The wind and solar power is the future's hope as they are sustainable energy sources. Oil powers almost all machines that move and that makes oil uniquely versatile. Oil powered airplanes carry 500 people across the widest oceans at nearly the speed of sound. Oil powered machines produce and transport food. Oil powered machines are ubiquitous. Clearly, we live in the age of oil but it is drawing to a close. According to data available if oil production remains constant until it's gone, there is enough to last 42 years. Oil wells will produce less as they become depleted, which will make it impossible to keep production constant. Similarly natural gas and coal will last another 61 years and 133 years respectively. Naturally, as they become scarce, they become expensive, leading to a worldwide energy crisis. If we are to survive on this planet, we have to make a transition to sustainable energy sources. The transition may be willy-nilly or planned - the choice is ours. The dawning era of limited and expensive energy will be very difficult for everyone on earth but will be even more difficult if it is not anticipated. It is of utmost importance that the public and policymakers understand the global energy crisis and act in tandem to ensure that the species 'homo sapiens' does not become extinct. The energy sources of the future are
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