Q:

Does steady flow imply laminar?

Most secondary school textbooks, in their chapter about fluid dynamics, seem to suggest that "steady flow" and "laminar flow" are synonyms.
Though I never received any fluid mechanics course when I was at the university, it's pretty obvious to me that flows can be laminar but non-steady.
But what about the converse? Can a steady flow be non-laminar?
If I skim through more advanced textbooks and lecture notes, I can't find any direct reference of a strict relation between the two concepts, neither positive nor negative. Yet "between the lines" most of the texts seem to take as a fact that steady implies laminar. 
Is that true? Is a steady non-laminar flow something theoretically possible in some context (eg. inviscid flow in a purely continuum-mechanical model of a fluid) but physically unobtainable in any actual fluid? Is the implication blatantly false? 
My imagination has apparently no problem at visualizing some sort of weird self-intersecting (and consequently non-laminar?) flow which doesn't vary over time. 
Am I missing something? I definitely guess that I am.

A:

The answer depends on your definition of "steady". A flow is called turbulent when small oscillations are no longer damped, but instead excited. Therefore when looking at the fluid on a microscopic scale, a turbulent flow is not steady.
However, turbulence can be modeled on a macroscopic scale (cf. https://en.wikipedia.org/wiki/Turbulence_modeling), effectively encapsulating the local non-steadiness. Thus on a macroscopic scale, turbulent flow can be steady.
An example for a (macroscopic) partially turbulent steady flow is the flow around an airfoil. At the nose, the flow is laminar. At some point (the transition point) at both upper and lower surface, the flow becomes turbulent. (The location of the transition point for a dedicated airfoils is depending on flow velocity and the angle of attack.)

A:

Most secondary school textbooks, in their chapter about fluid dynamics, seem to suggest that "steady flow" and "laminar flow" are synonyms. 

You'll have to point to specific textbooks because mine don't say that, primarily because it is incorrect.
By steady flow simply understand constant flow rate. Understood that way, steady flow can be laminar, turbulent (or in that grey area between the two). Constant (volumetric) flow rate says nothing about the Reynolds Number at all.

Edit:
Illustrating laminar (top) and turbulent (bottom) flow, with associated radial flow speed gradients:

For laminar flow the radial speed distribution is given by:
$$v(r)=v_m\bigg(1-\frac{r^2}{R^2}\bigg)$$
Suitable integration between $0$ and $R$ gives the volumetric flow rate $F$:
$$F=A\frac{v_m}{2}$$
With $A$ the cross-section.
For turbulent flow (velocity profile not very well drawn), the exponent $2$ becomes much higher and the velocity gradient $v(r)$ much flatter near the centre. Here too, volumetric flow rate can be obtained by integration over $0$ to $R$. At very high Reynolds Numbers, then $\frac{dv(r)}{dt} \approx 0$.

