Provided that the performer is able to whistle, it is possible to amplify this sound through the tuba/euphonium via the mouthpiece opening.
The largest hurdle to overcome with this technique is the ability of the performer to whistle in the first place. If not, then the technique must be approximated or omitted in performance. If there is an extensive section of whistling and the performer is physically incapable of whistling, then this is a huge obstacle for the performance of the work. With that being said, it is vital that the composer be aware of the fact that some tubists/euphonists will not be able to perform the work as intended.
Because of the shape of the mouthpiece opening, the whistle must be performed with a loose seal. This means that some of the sound will bleed out through the sides of the mouthpiece, which in turn will result in an effective dynamic range that eschews towards the softer end of the spectrum.
Performing a whistle into the mouthpiece also tends to diffuse the sound, creating a very airy whistle with a less-defined pitch center. As long as this is acceptable within the context in which it is used, the technique will be successful.
If specifics pitches are called for, it is acceptable to notate this technique in a relatively normal way. This assumes that some direction will be given to indicate that the intended passage is to be whistled, and not sung/buzzed. Because of its status as a separate technique from normal buzzing, it is helpful to use a clear and distinguishable alternative notehead; the provided example uses x-shape noteheads, which work well for this scenario.
Intermediate to Professional
Works to consider (bolded titles are particularly representative examples of this technique)
From the Quiet… – Peter Hoch
Helpless Before a Creature Which Defies Physical Laws and Communicates Only Through Death – Ray Evanoff
Bi[cusp]id – Brian Griffeath-Loeb