If inertial waves in a uniformly rotating fluid reflect from a rigid plane surface, it is shown that the magnitudes of the incident and reflected wavenumbers are generally unequal. The reflection process thus provides an interchange of energy among different scalar wavenumbers k. In an inviscid fluid, the ratio α(k)/k is conserved on reflection, where α is the particle orbit speed associated with the wavenumber k. In a viscous fluid the reflection coefficient is generally 1 ‐ O(R1/2), where R is the wave Reynolds number 2Ω/νk2, though there is an exceptional case in which the incident energy flux is totally absorbed. When the fluid is contained in a large rotating box of general shape, the energy interchanges from repeated reflections can result in a statistical radiative equilibrium over the high wavenumbers. A dynamical equation is derived that specifies Eϑ(k), the energy distribution among wavenumbers inclined at an angle ϑ to the rotation vector. An approximate solution shows that Eϑ(k) is constant when k « kν = (Ω/νL)1/3, where L is the size of the domain. When k » kν, the spectrum decreases exponentially.
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April 1963
Research Article|
April 01 1963
Energy Transfer in Rotating Fluids by Reflection of Inertial Waves
O. M. Phillips
O. M. Phillips
Mechanics Department, The Johns Hopkins University, Baltimore, Maryland
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Phys. Fluids 6, 513–520 (1963)
Article history
Received:
November 13 1962
Citation
O. M. Phillips; Energy Transfer in Rotating Fluids by Reflection of Inertial Waves. Phys. Fluids 1 April 1963; 6 (4): 513–520. https://doi.org/10.1063/1.1706766
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