Energy cascades in the upper ocean

Abstract

Wave-wave interactions cause energy cascades. These are the most important processes in the upper ocean because they govern wave-growth and dissipation. Through indirect cascades, wave energy is transferred from higher frequencies to lower frequencies, leading to wave growth. In direct cascades, energy is transferred from lower frequencies to the higher frequencies, which causes waves to break, and dissipation of wave energy. However, the evolution and origin of energy cascade processes are still not fully understood. In particular, for example, results from a recent theory (Kalmykov, 1998) suggest that the class I wave-wave interactions (defined by situations involving 4-, 6-, 8-, etc, even numbers of resonantly interacting waves) cause indirect cascades, and Class II wave-wave interactions (involving, 5-, 7-, 9-, etc,.., odd numbers of waves) cause direct cascades. In contrast to this theory, our model results indicate the 4-wave interactions can cause significant transfer of wave energy through both direct and indirect cascades. In most situations, 4-wave interactions provide the major source of energy transfer for both direct cascades and indirect cascades, except when the wave steepness is larger than 0.28. Our model results agree well with wave measurements, obtained using field buoy data (for example, Lin and Lin, 2002). In particular, in these observations, asymmetrical wave-wave interactions were studied. They found that direct and indirect cascades both are mainly due to the 4-wave interactions when wave steepness is less than 0.3.