Potential explanations of Red Sea crossing
To my knowledge, the best study looking at potential explanations for the Red Sea crossing is the one by Nof and Paldor (1992). They present a couple of plausible scenarios for the crossing. The main one is the effect of strong winds blowing along the Gulf of Suez and they find that the sea level drop could be sufficient: 


  It is found that, even for moderate storms with wind speed of about 20 s−1 receding distance of more than 1 km and a sea level drop of more than 2.5 m are obtained. These relatively high values are a result of the unique geometry of the gulf (i.e., its rather small width-to-length and depth-to-length ratios) and the nonlinearity of the governing equation. Upon an abrupt relaxation of the wind, the water returns to its prewind position as a fast (nonlinear) gravity wave that floods the entire receding zone within minutes.


The second mechanism involves a tsunami propagating along the Gulf of Suez from the Red Sea, but it seems like way more of a stretch.

Nof D. and N. Paldor, 1992: Are There Oceanographic Explanations for the Israelites'Crossing of the Red Sea?. Bull. Amer. Meteor. Soc., 73, 305–314.
doi: http://dx.doi.org/10.1175/1520-0477(1992)073%3C0305:ATOEFT%3E2.0.CO;2