An improved model of near-inertial wave dynamics
 作者： Olivier Asselin,  William R. Young 作者单位： 11 Scripps Institution of Oceanography , University of California San Diego , La Jolla , CA 90293-0213 , USA 刊名： Journal of Fluid Mechanics, 2019, Vol.876 , pp.428-448 来源数据库： Cambridge University Press Journal DOI： 10.1017/jfm.2019.557 原始语种摘要： $\mathit{Bu}\rightarrow 0$]]> , where is the Burger number of the NIWs. Here we develop an improved version, the YBJ+ equation. In common with an earlier improvement proposed by Thomas, Smith & Bühler ( J. Fluid Mech. , vol. 817, 2017, pp. 406–438), YBJ+ has a dispersion relation that is second-order accurate in . (YBJ is first-order accurate.) Thus both improvements have the same formal justification. But the dispersion relation of YBJ+ is a Padé approximant to the exact dispersion relation and with ... xlink:type="simple" xlink:href="S0022112019005573_inline4"/> of order unity this is significantly more accurate than the power-series approximation of Thomas et al. (2017). Moreover, in the limit of high horizontal wavenumber , the wave frequency of YBJ+ asymptotes to twice the inertial frequency . This enables solution of YBJ+ with explicit time-stepping schemes using a time step determined by stable integration of oscillations with frequency . Other phase-averaged equations have dispersion relations with frequency increasing as (YBJ) or (Thomas et al. 2017): in these cases stable integration with an explicit scheme becomes impractical with increasing horizontal resolution. The YBJ+ equation is tested by comparing its numerical solutions with those of the Boussinesq and YBJ equations. In virtually all cases, YBJ+ is more accurate than YBJ. The error, however, does not go rapidly to zero as the Burger number characterizing the initial condition is reduced: advection and refraction by geostrophic eddies reduces in the initial length scale of NIWs so that increases with time. This increase, if unchecked, would destroy the approximation. We show, however, that dispersion limits the damage by confining most of the wave energy to low

• inline　顺列式布置
• graphic　图示的
• integration　集成
• accurate　精确的
• destroy　消灭
• unchecked　非复选
• inertial　惯性的
• horizontal　水平线
• dispersion　分散
• subtype　亚型