Model Classes

Abstract

In the first-generation wave models, each spectral component evolves essentially independently of all other components in accordance with the linear input source function (1.2) until it approaches its limiting saturation level, which is again defined independently of the energy in other spectral components by a universal equilibrium distribution. The weak coupling by the nonlinear transfer, if considered at all, represents a relatively small modification and is parameterized rather simply in terms of only one or two integral spectral parameters. It is therefore natural to represent the spectrum in these models directly as a two-dimensional discretized array of frequency—direction energy “packets,” each of which propagates at its appropriate group velocity along its own ray path, responding only to the wind history sampled along this particular path. The numerical integration is carried out either in natural characteristic coordinates along individual rays, or in terms of a discretized advection operator within a common grid point representation for all wave components. We refer to these essentially linear, decoupled first-generation wave models as decoupled propagation (DP) models. [Although Barnett (1968) and Ewing (1971) include the nonlinear transfer explicitly and therefore have to contend with some of the numerical complications of coupled rays encountered in the later second-generation models, we nevertheless class these models physically as first-rather than second-generation models since the wave growth and spectral form are dominated by the wind input rather than the nonlinear transfer.]