 Award ID(s):
 1813891
 NSFPAR ID:
 10309191
 Date Published:
 Journal Name:
 Journal of Fluid Mechanics
 Volume:
 905
 ISSN:
 00221120
 Format(s):
 Medium: X
 Sponsoring Org:
 National Science Foundation
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We use a multiplescale expansion to average the wave action balance equation over an ensemble of seasurface velocity fields characteristic of the ocean mesoscale and submesoscale. Assuming that the statistical properties of the flow are stationary and homogeneous, we derive an expression for a diffusivity tensor of surfacewave action density. The small parameter in this expansion is the ratio of surface current speed to gravity wave group speed. For isotropic currents, the action diffusivity is expressed in terms of the kinetic energy spectrum of the flow. A Helmholtz decomposition of the seasurface currents into solenoidal (vortical) and potential (divergent) components shows that, to leading order, the potential component of the surface velocity field has no effect on the diffusivity of wave action: only the vortical component of the seasurface velocity results in diffusion of surfacewave action. We validate our analytic results for the action diffusivity by Monte Carlo raytracing simulations through an ensemble of stochastic velocity fields.more » « less

Abstract The generation of broadband wave energy frequency spectra from narrowband wave forcing in geophysical flows remains a conundrum. In contrast to the longstanding view that nonlinear wave–wave interactions drive the spreading of wave energy in frequency space, recent work suggests that Dopplershifting by geostrophic flows may be the primary agent. We investigate this possibility by ray tracing a large number of inertia–gravity wave packets through threedimensional, geostrophically turbulent flows generated either by a quasigeostrophic (QG) simulation or by synthetic random processes. We find that, in all cases investigated, a broadband quasistationary inertia–gravity wave frequency spectrum forms, irrespective of the initial frequencies and wave vectors of the packets. The frequency spectrum is well represented by a power law. A possible theoretical explanation relies on the analogy between the kinematic stretching of passive tracer gradients and the refraction of wave vectors. Consistent with this hypothesis, the spectrum of eigenvalues of the background flow velocity gradients predicts a frequency spectrum that is nearly identical to that found by integration of the ray tracing equations.more » « less

Abstract We evaluate energetic electron scattering in pitch angle and energy using realistic magnetic field and density models due to whistler mode chorus waves in Jupiter's magnetosphere and study their dependences on various wave and background parameters. We calculate the bounce‐averaged diffusion coefficients by considering the latitudinal variation of total electron density and ambient magnetic field intensity, using the VIP4 internal magnetic field and CAN current sheet model. The electron phase space density evolution due to chorus waves is simulated at
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Turbulence and mixing in a nearbottom convectively driven flow are examined by numerical simulations of a model problem: a statically unstable disturbance at a slope with inclination $\unicode[STIX]{x1D6FD}$ in a stable background with buoyancy frequency $N$ . The influence of slope angle and initial disturbance amplitude are quantified in a parametric study. The flow evolution involves energy exchange between four energy reservoirs, namely the mean and turbulent components of kinetic energy (KE) and available potential energy (APE). In contrast to the zeroslope case where the mean flow is negligible, the presence of a slope leads to a current that oscillates with $\unicode[STIX]{x1D714}=N\sin \unicode[STIX]{x1D6FD}$ and qualitatively changes the subsequent evolution of the initial density disturbance. The frequency, $N\sin \unicode[STIX]{x1D6FD}$ , and the initial speed of the current are predicted using linear theory. The energy transfer in the sloping cases is dominated by an oscillatory exchange between mean APE and mean KE with a transfer to turbulence at specific phases. In all simulated cases, the positive buoyancy flux during episodes of convective instability at the zerovelocity phase is the dominant contributor to turbulent kinetic energy (TKE) although the shear production becomes increasingly important with increasing $\unicode[STIX]{x1D6FD}$ . Energy that initially resides wholly in mean available potential energy is lost through conversion to turbulence and the subsequent dissipation of TKE and turbulent available potential energy. A key result is that, in contrast to the explosive loss of energy during the initial convective instability in the nonsloping case, the sloping cases exhibit a more gradual energy loss that is sustained over a long time interval. The slopeparallel oscillation introduces a new flow time scale $T=2\unicode[STIX]{x03C0}/(N\sin \unicode[STIX]{x1D6FD})$ and, consequently, the fraction of initial APE that is converted to turbulence during convective instability progressively decreases with increasing $\unicode[STIX]{x1D6FD}$ . For moderate slopes with $\unicode[STIX]{x1D6FD}<10^{\circ }$ , most of the net energy loss takes place during an initial, short ( $Nt\approx 20$ ) interval with periodic convective overturns. For steeper slopes, most of the energy loss takes place during a later, long ( $Nt>100$ ) interval when both shear and convective instability occur, and the energy loss rate is approximately constant. The mixing efficiency during the initial period dominated by convectively driven turbulence is found to be substantially higher (exceeds 0.5) than the widely used value of 0.2. The mixing efficiency at long time in the present problem of a convective overturn at a boundary varies between 0.24 and 0.3.more » « less

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