Currents may also be generated by density differences in water masses caused by temperature and salinity variations. These currents move water masses through the deep ocean—taking nutrients, oxygen, and heat with them. Occasional events also trigger serious currents. Huge storms move water masses. Underwater earthquakes may trigger devastating tsunamis. Both move masses of water inland when they reach shallow water and coastlines.
http://oceanexplorer.noaa.gov/facts/currents.html
Wind-driven surface currents (such as the Gulf Stream) travel polewards from the equatorial Atlantic Ocean, cooling en route, and eventually sinking at high latitudes (forming North Atlantic Deep Water).
https://en.wikipedia.org/wiki/Thermohaline_circulation
Ocean currents can be generated by wind, density differences in water masses caused by temperature and salinity variations, gravity, and events such as earthquakes. Currents are cohesive streams of seawater that circulate through the ocean.
http://oceanexplorer.noaa.gov/facts/currents.html
Surface currents are generated largely by wind. Their patterns are determined by wind direction, Coriolis forces from the Earth’s rotation, and the position of landforms that interact with the currents. Surface wind-driven currents generate upwelling currents in conjunction with landforms, creating deepwater currents.
http://oceanexplorer.noaa.gov/facts/currents.html
In the deep ocean, the predominant driving force is differences in density, caused by salinity and temperature variations (increasing salinity and lowering the temperature of a fluid both increase its density). There is often confusion over the components of the circulation that are wind and density driven.
https://en.wikipedia.org/wiki/Thermohaline_circulation
1 Thermohaline Circulation: As surface water is made denser through the removal of heat or freshwater, the surface layer descends to deeper depths. 2  If the stratification is weak and the buoyancy removal sufficient, the descent would reach the deep sea floor.
http://eesc.columbia.edu/courses/ees/climate/lectures/o_circ.html
The thermohaline circulation is mainly triggered by the formation of deep water masses in the North Atlantic and the Southern Ocean caused by differences in temperature and salinity of the water.
https://en.wikipedia.org/wiki/Thermohaline_circulation
Formation and movement of the deep water masses at the North Atlantic Ocean, creates sinking water masses that fill the basin and flows very slowly into the deep abyssal plains of the Atlantic. This high latitude cooling and the low latitude heating drives the movement of the deep water in a polar southward flow.
https://en.wikipedia.org/wiki/Thermohaline_circulation
The Coriolis Force strength is proportional to the strength of the ocean current. In short: the wind produces convergences and divergences of surface water, which causes hills and valleys of sea level, which then produce a horizontal gradient of pressure.
http://eesc.columbia.edu/courses/ees/climate/lectures/o_circ.html
1 The thermohaline circulation engages the full volume of the ocean into the climate system, by allowing all of the ocean water to 'meet' and interact directly the atmosphere (on a time scale of 100-1000 years).
http://eesc.columbia.edu/courses/ees/climate/lectures/o_circ.html
what factors will influence deep water currents
The factors  will Wind, density differences in water masses caused by temperature and salinity variations, gravity, and events such as earthquakes  influence deep water currents.  The factors that influence deep water currents are wind, density differences in water masses caused by temperature and salinity variations, gravity, and events such as earthquakes.