Motivation:

The motivation for this study comes from the fact that not all sources of oceanic internal waves have been identified. Wind and tidal forces are clearly major sources of waves but, away from the surface or from topographic features, no significant sources have been identified. Yet, field observations show that the internal wave spectrum is remarkably constant in amplitude and spectral shape everywhere in the open ocean.
Observations have shown enhanced wave activity in the vicinity of oceanic fronts (Tang, 1979; Kunze and Sanford, 1984; Mied et al., 1986; Merrifield and Pinkel, 1996; Lee and Eriksen, 1997). While some of these waves are undoubtedly wind-forced, others exhibit upward energy propagation and appear to originate in the ocean interior. It has been suggested that geostrophic adjustment of the ambient current could be responsible for some of these waves (e.g. Tang, 1979; Kunze and Sanford, 1984). Recent analysis of Synthetic perture Radar (SAR) images has led to speculation that highly sheared baroclinic currents such as the Gulf Stream or Kuroshio Current can act as sources for internal solitons (Apel, 1998). Given the highly energetic nature of Western boundary currents such as the Gulf Stream or the Kuroshio, even a tiny fraction of mean current energy converted to waves can constitute a significant source for the oceanic internal wave field.
Observationally, it remains quite difficult to distinguish wind-generated waves from waves due to other sources; however, this problem is well suited for a numerical modeling study where atmospheric forcing can be controlled.

Approach:

We have been studying inertia-gravity wave generation resulting from the instability of an energetic ocean current by means of high-resolution numerical simulations. In order to see whether local geostrophic adjustment on unstable ocean currents can be a significant source of IGWs, we have been modelling the evolution of barotropic and baroclinic instabilities on idealized ocean currents. Our ultimate goal is to assess the efficiency of the generation mechanism as a function of current parameters such as intensity, structure and position relative to lateral and bottom boundaries.

Numerically, this problem is quite challenging in the sense that a very broad range of spatial and temporal scales must be resolved simultaneously. Typical e-folding scales for the growth of baroclinic instability are on the order of 60 days. IGWs, on the other hand, evolve on timescales of hours. This very large timescale separation between the large-scale flow evolution and that of the IGWs is the primary reason why this mechanism has not been given serious consideration in the past. In the atmosphere, on the other hand, the timescale separation is not as drastic: baroclinic instabilities reach finite amplitude in a matter of days. This is because atmospheric vertical shears are much stronger than oceanic ones, implying a much faster instability growthrate. However, even slowly growing instabilities can develop localized regions where strong accelerations (or decelerations) can result in rapid local changes in the flow structure. These regions are precisely where one would expect IGWs to be generated since this is where the large-flow time and spatial scales project onto the IGW scales. This scale-matching is a necessary condition for IGW generation.

Our principal objectives have been:

1. To understand the dynamics of the wave generation process.
2. To identify the regions within the jet that are favorable to wave generation.
3. To quantify the resulting energy radiation away from sources.

The long-term goals of this study are to use our results to help interpret observational data and to assess the relative contribution of energetic unstable mean currents to the oceanic internal wave spectrum.

Results:
Our first set of simulations was performed with the Hallberg free-surface isopycnal model ( Hallberg Isopycnal Code ). We first simulated a developing baroclinic disturbance on a shallow, upper-ocean jet in a channel oriented along the east-west direction, away from any boundaries (Lelong et al., 1999). To maximize resolution, the computational domain was adjusted to encompass exactly one wavelength of the most unstable mode.
Our second set of simulations was performed with the Winters free-slip Boussinesq code on an f-plane ( Winters Spectral Code ). This code is better suited for identifying wave parameters such as vertical wavelength and frequency than an isopycnal code. The code is doubly periodic in the horizontal with free-slip conditions at the top and bottom. Sponges (using Rayleigh damping) have been implemented in the meridional direction. These serve the double purpose of absorbing outgoing waves and relaxing the meridional density profile back to periodicity (an artifact of periodic boundary conditions).

• How do we distinguish IGWs from balanced ageostrophic motions?
By definition, IGWs represent the unbalanced component of the flow. Away from the jet, in the far-field region, the horizontal divergence provides an accurate measure of IGW activity. One must be careful near the jet, however, since in that region the horizontal divergence is primarily associated with the secondary ageostrophic circulation and is therefore part of the balanced flow. To differentiate the unbalanced from the balanced horizontal divergence, we invoke a Lagrangian frequency. IGWs represent the propagating component of the flow and are characterized by a dispersion relation whereas the balanced component advects, but does not propagate.
• How do we identify IGW sources?
  A Lagrangian Rossby number, Ro_l, is a useful quantity for identifying IGW sources. It remains small over most of the instability lifecycle, but becomes locally O(1) once sharp fronts develop. The regions where Ro_l is large are preferred regions of IGW generation. These regions tend to be characterized by strong PV gradients.
  
  IGW sources can also be identified diagnostically by examining the spatial maps of the right-hand-side forcing terms of a linear wave equation

  

  Applying a high-pass filter to focus on the IGW frequency band, we find that the forcing terms remain small over most of the instability lifecycle except at times when IGWs are generated. Restricting our attention to the regions within the jet where these terms are not small enables us to identify IGW sources.
  Below is a sequence of horizontal cross-sections of the RHS forcing terms (left panels) and corresponding horizontal divergence patterns (right panels).

  

Here is an animation of a baroclinic instability illustrating the generation of waves. The waves occur in localized bursts and emanate from sharp frontal features. As the instability develops, local deviations from geostrophic equilibrium produce local adjustment, with IGWs generated in response to that process.