Magnetic reconnection facilitates the conversion of magnetic energy to thermal energy and plasma flows. Reconnection occurs at the magnetopause, the magnetic boundary between the plasmas of the terrestrial magnetosphere and the heliosphere. Turbulence is known to develop at this boundary, but its influence on reconnection, particularly on small scales, is unknown. In light of this, an important goal of NASA's Magnetospheric Multiscale (MMS) Mission is to understand the role turbulence plays in the development of reconnection.

We present two- and three-dimensional particle-in-cell simulations of the 16 October 2015 MMS magnetopause reconnection event. While the two-dimensional simulation is laminar, turbulence develops at

both the x-line and along the magnetic separatrices in the

three-dimensional simulation. This turbulence is electromagnetic, is characterized by a wavevector $k$ given by

$k\rho_e\sim(m_e/m_i)^{0.25}$ with $\rho_e$ the electron Larmor

radius, and appears to have the ion pressure gradient as its source of free

energy. Taken together, these results suggest the instability is a

variant of the lower-hybrid drift instability. The turbulence

produces electric field fluctuations in the out-of-plane direction with an amplitude

of around $\pm 10$ mV/m, which is much greater than the reconnection

electric field of around $0.1$ mV/m. Such large values of the

out-of-plane electric field have been identified in the MMS data. The

turbulence in the simulation controls the scale lengths of the

density profile and current layers, driving

them closer to $\sqrt{\rho_e\rho_i}$ than the $\rho_e$ or $d_e$

scalings seen in 2D reconnection simulations, where $d_e$ is the electron inertial length. The turbulence

produces

both anomalous resistivity and anomalous viscosity. Each contribute

significantly to breaking the frozen-in condition in the electron

diffusion region. The crescent-shaped features in

velocity space seen both in MMS observations and in two-dimensional

simulations survive. We compare and contrast these results to a three-dimensional simulation of the 8 December 2015 MMS magnetopause reconnection event in which the reconnecting and out-of-plane guide fields are comparable. LHDI is still present in this event, although its appearance is modified by the presence of the guide field. The crescents also survive although, in agreement with MMS, their intensity decreases. Nevertheless, the developing turbulence remains strong.