Transverse acoustic spin and torque from pure spinning of objects

Acoustic spin has been recently explored for many applications. In particular, transverse acoustic spin was demonstrated for inhomogeneous acoustic fields. In this Letter, we show the emergence of acoustic spin and torque in rotating acoustic objects of the same physical properties as the surrounding, to single out the effects purely due to rotation. The spinning of a cylindrical column of air or water in the same medium possesses intrinsic spin angular momentum, and we study the torque and force it experiences in evanescent acoustic fields. The resulting discontinuity can thus scatter sound in unusual ways, including a negative radiation force, although it has no imaginary part in its parameters.

Figure 1

(a) Schematic view ($x-y$ plane) of the single cylindrical scattering particle of radius $a$ (in gray color) lying inside a homogeneous infinitely extended medium (here air, in yellow color, with the dashed circle meaning the domain extends to infinity) and the incident plane wave excitation impinging on it. The acoustic monopole scattering is due to pure spinning, resulting from expansion and compression of the object. (b) Schematic representation of the acoustic dipole scattering, resulting in oscillatory linear motion of the object. The scales of motion in this figure are exaggerated, as in reality the motion or expansion of the particle are only perturbations.

Figure 2

(a) Absolute value of (top) the monopole polarizability ${\alpha }_m$ and (bottom) the dipole polarizability ${\alpha }_d^y$, in logarithmic scale (i.e., $10{log}_{10}$) vs $\alpha =\mathrm{\Omega }/\omega$. The solid lines give the numerical results of both real and imaginary parts of $({\alpha }_m,{\alpha }_d^y)$ computed with Eq. (4) and Eqs. (13) and(14), while the dashed lines give analytical expressions obtained when $k_{0}a\ll 1$, using Eqs. (15) and (16). The radius of the object is $a=1$ m and $\mathrm{\Omega }/\left(2\pi \right)=10$ Hz. (b) Same as in (a) but for $a=10$ m and $\mathrm{\Omega }/\left(2\pi \right)=100$ Hz. Please note that in (b) the scale is linear, unlike in (a), and that there is no analytical approximation, since $k_{0}a\approx 1$.

Figure 3

(a) Logarithmic scale plot of the (top) normalized torque $10{log}_{10}(T_z/T_0)$, (middle) normalized gradient force $10{log}_{10}(F_y^{\text{grad}}/F_0)$, and (bottom) normalized scattering force $10{log}_{10}(F_x^{\text{scatt}}/F_0$), vs $\alpha$. The solid (dashed) lines give the numerical (analytical) calculations, for the same object as of Fig. 2 and for $k_y/k_0=1.2$ and $\kappa /k_0=0.6633$. The insets in these plots show the linear scale plot of these parameters in a magnified view to showcase the regions where resonances occur and positive to negative values are obtained. (b) Same as in (a) but for the same object of Fig. 2. Please note that in (b) the scale is linear, unlike in (a). The red dashed lines denote zero values of the considered parameters.