Spatial Variation of Diapycnal Diffusivity Estimated From Seismic Imaging of Internal Wave Field, Gulf of Mexico

Bright reflections are observed within the upper 1000~m of the water column along a seismic reflection profile that traverses the northern margin of the Gulf of Mexico. Independent hydrographic calibration demonstrates that these reflections are primarily caused by temperature changes associated with different water masses that are entrained into the Gulf along the Loop Current. The internal wave field is analyzed by automatically tracking 1171 reflections, each of which is greater than 2~km in length. Power spectra of the horizontal gradient of isopycnal displacement, $\phi_{\xi_x}$, are calculated from these tracked reflections. At low horizontal wavenumbers ($k_x < 10^{-2}$ cpm), $\phi_{\xi_x} \propto k_x^{-0.2 \pm 0.6}$, in agreement with hydrographic observations of the internal wave field. The turbulent spectral subrange is rarely observed. Diapycnal diffusivity, $K$, is estimated from the observed internal wave spectral subrange of each tracked reflection using a fine-scale parametrization of turbulent mixing. Calculated values of $K$ vary between $10^{-8}$ and $10^{-4}$~m$^{2}$~s$^{-1}$ with a mean value of $K \sim 4 \times 10^{-6}$~m$^{2}$~s$^{-1}$. The spatial distribution of turbulent mixing shows that $K \sim 10^{-7}$~m$^{2}$~s$^{-1}$ away from the shelf edge in the upper 300~m where stratification is strong. Mixing is enhanced by up to four orders of magnitude adjacent to the shoaling bathymetry of the continental slope. This overall pattern matches that determined by analyzing nearby suites of CTD casts. However, the range of values recovered by spectral analysis of the seismic image is greater as a consequence of significantly better horizontal resolution

Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics

We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) ows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several special applications in heliophysics and astrophysics, assessing triumphs, challenges,and future directions