Relation between direction of shear and tropical cyclone formation
The direction of the vertical shear plays a large role in cyclogenesis, where easterly shear tends to enhance the formation of cylones and westerly shear tends to suppress it (Tuleya and Kurihara, 1981).

Internal waves are responsible for large transfers of energy across vast distances. Therefore, they play important roles in a wide array of atmospherical (and oceanic) processes, such as tropical cyclogenesis (TC). These waves are capable of depositing energy that was created far away in an already active region. This energy may manifest itself in the form of an easterly shear. Depending on the type of wave, there is evidence that some waves play an important role in triggering cyclogenesis.


  It has been known for decades that about half of the hurricanes in the
  North Atlantic form from African waves (e.g., Frank and Clark 1980),
  and there have been many studies of this type of genesis (e.g.,
  Carlson, 1969; Landsea, 1993; Thorncroft and Hodges, 2001; and
  others). Molinari and Vollaro (2000), Mal- oney and Hartmann (2001),
  Liebmann et al. (1994).


There are three main classes of equatorial internal waves to consider when it comes to TC. Namely, the MJO, equatorial Rossby (ER) waves and other large wavenumber, high frequency waves that propagate towards the west (mixed Rossby gravity waves). Note that equatorial Kelvin waves are thought to have little effect on cyclogenesis. This animation from NOAA shows the internal waves (as OLR anomalies) over a period of 40 days: 

Specifically: 


the MJO and ER waves produce easterly shear anomaly at the generation location, while the MJO tends to reduce westerly shear over the atlantic.



  the MJO enhances both the convergence and the low-level rotation at the genesis location. [...] shows a tendency for the MJO to cause easterly vertical shear anomalies at the genesis location in most basins, and this would tend to be favorable for storm formation.  [...] The ER waves also appear to enhance genesis by increasing both the
   large-scale rotation and convection, as in this band the storms form
   within the low-level cyclonic gyre and about two days after the wave’s
   convective anomaly first reaches the genesis point. The ER waves also
   cause significant easterly shear anomalies at the genesis locations in
   about half of the basins.


Basically, internal waves enhance the formation of cyclones by increasing the vorticity of the local flow.

References:

Anantha R. Aiyyer and Chris Thorncroft, 2006: Climatology of Vertical Wind Shear over the Tropical Atlantic. J. Climate, 19, 2969–2983. 

Tuleya, Robert E., and Yoshio Kurihara. "A numerical study on the effects of environmental flow on tropical storm genesis." Monthly Weather Review 109.12 (1981): 2487-2506.

William M. Frank and Paul E. Roundy, 2006: The Role of Tropical Waves in Tropical Cyclogenesis. Mon. Wea. Rev., 134, 2397–2417.