 Award ID(s):
 1658564
 NSFPAR ID:
 10215027
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 912
 ISSN:
 00221120
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
More Like this

null (Ed.)Abstract Anticyclonic vortices focus and trap nearinertial waves so that nearinertial energy levels are elevated within the vortex core. Some aspects of this process, including the nonlinear modification of the vortex by the wave, are explained by the existence of trapped nearinertial eigenmodes. These vortex eigenmodes are easily excited by an initialwave with horizontal scale much larger than that of the vortex radius. We study this process using a waveaveraged model of nearinertial dynamics and compare its theoretical predictions with numerical solutions of the threedimensional Boussinesq equations. In the linear approximation, the model predicts the eigenmode frequencies and spatial structures, and a nearinertial wave energy signature that is characterized by an approximately timeperiodic, azimuthally invariant pattern. The waveaveraged model represents the nonlinear feedback of the waves on the vortex via a waveinduced contribution to the potential vorticity that is proportional to the Laplacian of the kinetic energy density of the waves. When this is taken into account, the modal frequency is predicted to increase linearly with the energy of the initial excitation. Both linear and nonlinear predictions agree convincingly with the Boussinesq results.more » « less

null (Ed.)In the presence of inertiagravity waves, the geostrophic and hydrostatic balance that characterises the slow dynamics of rapidly rotating, strongly stratified flows holds in a timeaveraged sense and applies to the Lagrangianmean velocity and buoyancy. We give an elementary derivation of this waveaveraged balance and illustrate its accuracy in numerical solutions of the threedimensional Boussinesq equations, using a simple configuration in which vertically planar nearinertial waves interact with a barotropic anticylonic vortex. We further use the conservation of the waveaveraged potential vorticity to predict the change in the barotropic vortex induced by the waves.more » « less

The data is from a direct numerical simulation of rotating stratified turbulence on a 4096cubed periodic grid using a pseudospectral parallel code, GHOST. The simulations are documented in Ref. 1. The relative strength of stratification vs. rotation is characterized by the ratio of the BruntVäisälä to inertial wave frequency, N/f = 4.95. The code solves the Boussinesq equations with a solid body rotation force acting as the only external forcing mechanism. Time integration uses fourthorder RungeKutta. The simulation is initialized with largescale isotropic conditions on a coarser grid. As the simulation progresses resolution is increased, peaking with 4096cubed at maximum dissipation. After the simulation has reached a statistical stationary state, 5 frames of data, which includes the 3 components of the velocity vector and the temperature fluctuations, are generated and written in files that can be accessed directly by the database (FileDB system).more » « less

The YBJ equation (Young & Ben Jelloul, J. Marine Res. , vol. 55, 1997, pp. 735–766) provides a phaseaveraged description of the propagation of nearinertial waves (NIWs) through a geostrophic flow. YBJ is obtained via an asymptotic expansion based on the limit $\mathit{Bu}\rightarrow 0$ , where $\mathit{Bu}$ 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 secondorder accurate in $\mathit{Bu}$ . (YBJ is firstorder 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 $\mathit{Bu}$ of order unity this is significantly more accurate than the powerseries approximation of Thomas et al. (2017). Moreover, in the limit of high horizontal wavenumber $k\rightarrow \infty$ , the wave frequency of YBJ + asymptotes to twice the inertial frequency $2f$ . This enables solution of YBJ + with explicit timestepping schemes using a time step determined by stable integration of oscillations with frequency $2f$ . Other phaseaveraged equations have dispersion relations with frequency increasing as $k^{2}$ (YBJ) or $k^{4}$ (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 $\mathit{Bu}$ 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 $\mathit{Bu}$ . In other words, advection and refraction by geostrophic flows does not result in a strong transfer of initially nearinertial energy out of the nearinertial frequency band.more » « less

Abstract The study reported here focuses on inertial internal wave currents on the west Florida midshelf in 50 m depth.
In situ observations showed that the seasonal shifts in stratification change both the frequency range of inertial internal waves and their modulation time scales. According to the analysis, the subinertial flow evolution time scales also undergo compatible seasonal variations, and the inertial internal wave currents appear to be temporally and spatially related to the subinertial flow. Specifically, the subinertial flow evolving on frontal/quasigeostrophic time scales appears to be accompanied by the nearinertial oscillations/inertiagravity waves in corresponding small/finite Burger number regimes, respectively. The quasigeostrophic subinertial currents on the west Florida shelf are probably associated with the synoptic windforced flow, whereas the frontalgeostrophic currents are related to the evolution of density fronts. Further details of this conceptual view should, however, be elucidated in the future.