Figure 1

The function ${\beta }^2{k}^3\mathrm{Re}[P_s(k,k,k)]$ for the incoherent case, as a function of $k/\beta$. The three curves correspond to $g(t)$ given by (16, 17, 18), and the velocities are $v=1.0$ (left curves) and $v=0.01$ (right curves).Reuse & Permissions

Figure 2

The qualitative behavior of the function $P_s(k,\omega ,\omega )$ is shown for the totally coherent case. The diagonal $P_s(k,k,k)$ is also plotted. In the region $\omega <\beta$ and $k<\beta /v$ we expect a white noise spectrum of the anisotropic stress. For $\omega >\beta$ and $k>\beta /v$ the spectrum is expected to decrease. Since the gravity wave spectrum only probes the diagonal $\omega =k$, we expect, in the separable case with constant $R^{-1}=\beta /v$ a first change of slope at $\omega =k=\beta$ and a second at $\omega =k=\beta /v$. Whether the first or the second is the peak frequency depends on the space and time continuity and differentiability properties of $P_s(k,\omega ,\omega )$.Reuse & Permissions

Figure 3

The function ${\beta }^2{k}^3\mathrm{Re}[P_s(k,k,k)]$ for the coherent case, as a function of $k/\beta$: left panel, $v=1$, right panel, $v=0.01$. The three curves correspond to $g(t)$ given by (16, 17, 18). Notice the different peak positions for $g_1$ with respect to the other two.Reuse & Permissions

Figure 4

The function ${\beta }^2{k}^3\mathrm{Re}[P_s(k,k,k)]$ for the top hat case (with $x_c=1$), as a function of $k/\beta$. The three curves correspond to $g(t)$ given by (16, 17, 18) and the velocities are $v=1.0$ (left curves) and $v=0.01$ (right curves).Reuse & Permissions

Figure 5

Typical time evolution of the correlation length (corresponding to the characteristic scale of the colliding region) and therefore of the source (anisotropic stress) generating the gravitational waves calculated in numerical simulations of bubble collisions [5].Reuse & Permissions

Figure 6

Qualitative behavior of the GW spectrum for the model of Eq. (35) that reproduces the results from numerical simulations of bubble collisions.Reuse & Permissions

Figure 7

The qualitative behavior of the GW spectrum is shown for the model in Eq. (35), however replacing $L(t)\sqrt{R_{*}ϵ}$ by $L(t{)}^{3/2}$.Reuse & Permissions

Figure 8

The qualitative behavior of the GW spectrum is shown for the model of Eq. (36).Reuse & Permissions