I think the question is ill-posed: what do you mean by meaningful? and what is the flow? TI is just a definition, if you define it as urms where u is the streamwise component, that's it, you defined a one-dimensional TI and you got it. if you define urms as something else, and you measure only one of the 3 components, the question is what is "meaningful" for your need? The suggestions of isotropy or homogeneity can be valid or not for your particular case, but you didn't define what kind of turbulent flows you're referring to. 

Hello,

Usually what we obtain from a simple hot wire is 1D information and it wont provide us the direction of the flow. For example if we have some recirculation we wont be able to interpret it very well.

For the 2D and 3D measurements we have X and tri-axial probes.

You may calculate a TI by using air speed data measured using an omnidirectional air velocity sensor such as a hot wire sensor. But you need to realize that these data has the effects caused by the fluctuations of the airflow direction also. Please notice that 1D and omnidirectional sensors/measurement are different.

If you know a priori that turbulence is isotropic, then unidirectional measurements can be used as surrogate.

Please use one-component TI if you don't need more careful description of the field. There are many cases when such simplification is reasonable.

Yes it is meaningful. You should use a 1D hot wires in a 1D flow though.

A single hot-wire anemometer can measure turbulence over a range of scales, typically preferably as the turbulent motions are swept past it via a mean flow which is perpendicular to the wire. See e.g. Wyngaard (1969) for 1-d vs. more dimensions.

  Note that the fluctuations can be isotropic in the inertial range of turbulence, but this over only a limited range of scales at scales larger than the inertial range (e.g. in the atmosphere, the energy-containing range, for L>~100m) then the fluctuations are not isotropic.  Isotropy can also be invalid for some (disturbed) flow configureations...

I think the question is ill-posed: what do you mean by meaningful? and what is the flow? TI is just a definition, if you define it as urms where u is the streamwise component, that's it, you defined a one-dimensional TI and you got it. if you define urms as something else, and you measure only one of the 3 components, the question is what is "meaningful" for your need? The suggestions of isotropy or homogeneity can be valid or not for your particular case, but you didn't define what kind of turbulent flows you're referring to. 

Hi,

You can use a one-directional hot wire anemometer to determine TI. The TI determined is velocity fluctuation normal to the wire. However, the applicability depends on the nature of the flow you are investigating. For example, if you have a reverse flow where you are taking the measurement, a one-directional hot wire anemometer can't resolve direction. As such, your TI calculation will not be correct. Also, measurement of velocity using a one-directional hot wire anemometer near and in the boundary layer is another issue. So, you should explain a little more about the nature of the flow you are investigating and how you measured the velocity data. 

I think if you consider an isotropy of the turbulence you can assume turbulence in the three directions are the same if not i think you can calibrate the hot wire in y direction and use it for measuring the v fluctuation componenent.

The TI obtained will be 1-D considering the case of isotropy of the turbulence.For that calibration of hot wire in other two directions also will be required.

You may use correlation function to find u( rms) in other directions provided the turbulent flow assumed to be isotropic.

Alex is right.

Now if you want to make computer runs and you need an initial estimate for say inlet boundaries you may start with the "1-d" wire value and then perform a couple of more runs with say + and - 20/% and see if there is any change.I bet it will not be if your wire has measured in the predominant flow direction!

Turbulent flow is a random, 3 dimensional and highly dissipative flow with eddies (can be assumed as a vortex for simplicity ) of size varying from micro scales to  problem domain. In reality, you need to take into consideration of all three fluctuating components of the velocity. However, in some specific cases, the flow is assumed to be isotropic (fluctuations in all three direction is same which is exists when there is a equilibrium between the energy input and dissipation).  For example flow inside the wind tunnel test section is assumed as isotropic. I do not know your situation, so I cannot comment about the applicability of the single wire hot wire anemometry results.