Aerodynamics properties:

The Golden Spiral Turbine has no straight lines or surfaces:  

• When a fluid current impacts the blade of the logarithmic spiral turbine, it never hit a flat surface or a straight line on all three dimensions.

The blade surface actually curves from front to end, from inside out and around the axis.  

• This configuration helps minimize turbulence on the surface facing the current and increasing lift on the opposite side.

If looking at both turbines from front their swept area appear to be the same.

Swept area of a conventional turbine is usually that of a disc minus the area in the center where the blades are mounted to the generator.

The center area where the blades connect to the generator is used more efficiently in the logarithmic spiral turbine giving it a larger swept area.

From a profile view angle, the logarithmic spiral turbine has a whole new concept.

One of the other main characteristics of the Logarithmic spiral turbine is its relatively long horizontal axis compared to a conventional turbine.

 The fluid current is channeled in a spiral around the rotational axis

so it has a longer way to travel than surrounding fluids traveling in a straight line.

 This imbalance causes the spiraling fluids inside the turbine to increase velocity in order to meet the surrounding fluids at the same time

and fill in the vacuum behind the blades. This property in negligible in conventional turbines.

 A computer simulation shows the fluid flow trajectory between and around the blades;

The test results of the simulation below displays a 10m/s wind current applied to a a standstill logarithmic spiral turbine,

 velocity increased by up to 50% while passing inside the turbine and forming a vortex around the rotary axis.

The fluid velocity (thus pressure) is greatest on the surface facing the current

and reduced on the surface behind the blades. 

This difference in pressure reached between -5 and +15 m/s.  (blue to orange)

The Logarithmic spiral turbine is cone shaped when it reaches maximum velocity.

giving the whole design an aerodynamic profile versus a disc shaped profile found in conventional turbines.

Of course, the logarithmic spiral turbine does have some disandvantages, and it is not yet measured and proven to be more efficent than conventional turbines;

Because of its large surface it could generate more torque but may not reach a conventional turbines' velocity.  However, i think it would do much better if used in slow water currents. Not to mention that it would be relatively safe for marine life. 

Watch this youtube video to learn more about the Golden spiral: Nature by Numbers
 

Any contribution to continue research and development will be greatly appreciated.