How to use the floris.utilities.sind function in FLORIS

dist_top = np.sqrt((coord.x1 - x_locations) ** 2 + ((coord.x2) - y_locations) ** 2 + (
                    z_locations - (turbine.hub_height + D / 2)) ** 2)
        idx_top = np.where(dist_top == np.min(dist_top))

        # bottom point of the rotor
        dist_bottom = np.sqrt((coord.x1 - x_locations) ** 2 + ((coord.x2) - y_locations) ** 2 + (
                z_locations - (turbine.hub_height - D / 2)) ** 2)
        idx_bottom = np.where(dist_bottom == np.min(dist_bottom))

        if len(idx_top) > 1:
            idx_top = idx_top[0]
        if len(idx_bottom) > 1:
            idx_bottom = idx_bottom[0]

        scale = 1.0
        Gamma_top = scale * (np.pi / 8) * rho * D * turbine.average_velocity * Ct * sind(yaw) * cosd(yaw) ** 2
        Gamma_bottom = scale*(np.pi/8) * rho * D * turbine.average_velocity * Ct * sind(yaw) * cosd(yaw)**2
        Gamma_wake_rotation = 0.5 * 2 * np.pi * D * (aI - aI ** 2) * turbine.average_velocity / TSR

        # compute the spanwise and vertical velocities induced by yaw
        # Use set value
        eps = self.eps_gain * D

        # decay the vortices as they move downstream - using mixing length
        lmda = D/8 #D/4 #D/4 #D/2
        kappa = 0.41
        lm = kappa * z_locations / (1 + kappa * z_locations / lmda)
        z = np.linspace(np.min(z_locations),np.max(z_locations),np.shape(flow_field.u_initial)[2])
        dudz_initial = np.gradient(flow_field.u_initial, z, axis=2)
        nu = lm ** 2 * np.abs(dudz_initial[0, :, :])

        # top vortex

velDef[x_locations < xR] = 0
            velDef[x_locations > x0] = 0

            # wake expansion in the lateral (y) and the vertical (z)
            sigma_y = ky * (x_locations - x0) + sigma_y0
            sigma_z = kz * (x_locations - x0) + sigma_z0

            sigma_y[x_locations < x0] = sigma_y0[x_locations < x0]
            sigma_z[x_locations < x0] = sigma_z0[x_locations < x0]

            # velocity deficit outside the near wake
            a = (cosd(veer)**2) / (2 * sigma_y**2) + \
                (sind(veer)**2) / (2 * sigma_z**2)
            b = -(sind(2 * veer)) / (4 * sigma_y**2) + \
                (sind(2 * veer)) / (4 * sigma_z**2)
            c = (sind(veer)**2) / (2 * sigma_y**2) + \
                (cosd(veer)**2) / (2 * sigma_z**2)
            totGauss = np.exp(-(a * ((y_locations - turbine_coord.x2) - delta)**2 \
                    - 2 * b * ((y_locations - turbine_coord.x2) - delta) \
                    * ((z_locations - HH)) + c * ((z_locations - HH))**2))

            # compute velocities in the far wake
            velDef1 = (U_local * (1 - np.sqrt(1 - ((Ct * cosd(yaw)) \
                    / (8.0 * sigma_y * sigma_z / D**2)))) * totGauss)
            velDef1[x_locations < x0] = 0

            # TEMP HACK: Store some variables for inspection
            # self.sigma_tilde = np.sqrt((sigma_y/D)**2 + (sigma_z/D)**2)
            self.sigma_tilde = np.sqrt((sigma_y/D) * (sigma_z/D))

            self.n = 2 * np.ones_like(self.sigma_tilde) # Always 2 for gauss
            self.beta_out = np.ones_like(self.sigma_tilde) * sigma_y0 /D

for k in range(len(zt)):
                    x_grid[i, j, k] = xt[i]
                    y_grid[i, j, k] = yt[j]
                    z_grid[i, j, k] = zt[k]

                    xoffset = x_grid[i, j, k] - coord.x1
                    yoffset = y_grid[i, j, k] - coord.x2
                    x_grid[i, j, k] = (
                        xoffset * cosd(-1 * self.wind_map.turbine_wind_direction[i])
                        - yoffset * sind(-1 * self.wind_map.turbine_wind_direction[i])
                        + coord.x1
                    )

                    y_grid[i, j, k] = (
                        yoffset * cosd(-1 * self.wind_map.turbine_wind_direction[i])
                        + xoffset * sind(-1 * self.wind_map.turbine_wind_direction[i])
                        + coord.x2
                    )

        return x_grid, y_grid, z_grid

def _rotated_grid(self, angle, center_of_rotation):
        """
        Rotate the discrete flow field grid.
        """
        xoffset = self.x - center_of_rotation.x1
        yoffset = self.y - center_of_rotation.x2
        rotated_x = (
            xoffset * cosd(angle) - yoffset * sind(angle) + center_of_rotation.x1
        )
        rotated_y = (
            xoffset * sind(angle) + yoffset * cosd(angle) + center_of_rotation.x2
        )
        return rotated_x, rotated_y, self.z

yR = y_locations - turbine_coord.x2
            xR = yR * tand(yaw) + turbine_coord.x1

            # velocity deficit in the near wake
            sigma_y = (((x0 - xR) - (x_locations - xR)) / (x0 - xR)) * 0.501 * \
                D * np.sqrt(Ct / 2.) + ((x_locations - xR) / (x0 - xR)) * sigma_y0
            sigma_z = (((x0 - xR) - (x_locations - xR)) / (x0 - xR)) * 0.501 * \
                D * np.sqrt(Ct / 2.) + ((x_locations - xR) / (x0 - xR)) * sigma_z0

            sigma_y[x_locations < xR] = 0.5 * D
            sigma_z[x_locations < xR] = 0.5 * D

            a = (cosd(veer)**2) / (2 * sigma_y**2) + \
                (sind(veer)**2) / (2 * sigma_z**2)
            b = -(sind(2 * veer)) / (4 * sigma_y**2) + \
                (sind(2 * veer)) / (4 * sigma_z**2)
            c = (sind(veer)**2) / (2 * sigma_y**2) + \
                (cosd(veer)**2) / (2 * sigma_z**2)
            totGauss = np.exp(-(a * ((y_locations - turbine_coord.x2) - delta)**2 \
                    - 2 * b * ((y_locations - turbine_coord.x2) - delta) \
                    * ((z_locations - HH)) + c * ((z_locations - HH))**2))

            velDef = (U_local * (1 - np.sqrt(1 - ((Ct * cosd(yaw)) \
                    / (8.0 * sigma_y * sigma_z / D**2)))) * totGauss)
            velDef[x_locations < xR] = 0
            velDef[x_locations > x0] = 0

            # wake expansion in the lateral (y) and the vertical (z)
            sigma_y = ky * (x_locations - x0) + sigma_y0
            sigma_z = kz * (x_locations - x0) + sigma_z0

            sigma_y[x_locations < x0] = sigma_y0[x_locations < x0]

)
            + turbine_coord.x1
        )

        # velocity deficit in the near wake
        sigma_y = (((x0 - xR) - (x_locations - xR)) / (x0 - xR)) * 0.501 * D * np.sqrt(
            Ct / 2.0
        ) + ((x_locations - xR) / (x0 - xR)) * sigma_y0
        sigma_z = (((x0 - xR) - (x_locations - xR)) / (x0 - xR)) * 0.501 * D * np.sqrt(
            Ct / 2.0
        ) + ((x_locations - xR) / (x0 - xR)) * sigma_z0
        sigma_y[x_locations < xR] = 0.5 * D
        sigma_z[x_locations < xR] = 0.5 * D

        a = cosd(veer) ** 2 / (2 * sigma_y ** 2) + sind(veer) ** 2 / (2 * sigma_z ** 2)
        b = -sind(2 * veer) / (4 * sigma_y ** 2) + sind(2 * veer) / (4 * sigma_z ** 2)
        c = sind(veer) ** 2 / (2 * sigma_y ** 2) + cosd(veer) ** 2 / (2 * sigma_z ** 2)
        r = (
            a * ((y_locations - turbine_coord.x2) - delta) ** 2
            - 2 * b * ((y_locations - turbine_coord.x2) - delta) * ((z_locations - HH))
            + c * ((z_locations - HH)) ** 2
        )
        C = 1 - np.sqrt(1 - (Ct * cosd(yaw) / (8.0 * sigma_y * sigma_z / D ** 2)))

        velDef = GaussianModel.gaussian_function(U_local, C, r, 1, np.sqrt(0.5))
        velDef[x_locations < xR] = 0
        velDef[x_locations > x0] = 0

        # wake expansion in the lateral (y) and the vertical (z)
        ky = self.ka * TI + self.kb  # wake expansion parameters
        kz = self.ka * TI + self.kb  # wake expansion parameters
        sigma_y = ky * (x_locations - x0) + sigma_y0

velDef = GaussianModel.gaussian_function(U_local, C, r, 1, np.sqrt(0.5))
        velDef[x_locations < xR] = 0
        velDef[x_locations > x0] = 0

        # wake expansion in the lateral (y) and the vertical (z)
        ky = self.ka * TI + self.kb  # wake expansion parameters
        kz = self.ka * TI + self.kb  # wake expansion parameters
        sigma_y = ky * (x_locations - x0) + sigma_y0
        sigma_z = kz * (x_locations - x0) + sigma_z0
        sigma_y[x_locations < x0] = sigma_y0[x_locations < x0]
        sigma_z[x_locations < x0] = sigma_z0[x_locations < x0]

        # velocity deficit outside the near wake
        a = cosd(veer) ** 2 / (2 * sigma_y ** 2) + sind(veer) ** 2 / (2 * sigma_z ** 2)
        b = -sind(2 * veer) / (4 * sigma_y ** 2) + sind(2 * veer) / (4 * sigma_z ** 2)
        c = sind(veer) ** 2 / (2 * sigma_y ** 2) + cosd(veer) ** 2 / (2 * sigma_z ** 2)
        r = (
            a * (y_locations - turbine_coord.x2 - delta) ** 2
            - 2 * b * (y_locations - turbine_coord.x2 - delta) * (z_locations - HH)
            + c * (z_locations - HH) ** 2
        )
        C = 1 - np.sqrt(1 - (Ct * cosd(yaw) / (8.0 * sigma_y * sigma_z / D ** 2)))

        # compute velocities in the far wake
        velDef1 = GaussianModel.gaussian_function(U_local, C, r, 1, np.sqrt(0.5))
        velDef1[x_locations < x0] = 0

        U = np.sqrt(velDef ** 2 + velDef1 ** 2)

        return U, np.zeros(np.shape(velDef1)), np.zeros(np.shape(velDef1))