def test_curl_is_equal_to_curl_computed_with_grad_function():
N = 128
L = 2.0
kappa = 0.0
gamma = 1.0
v = np.random.random((2, N, N))
# print(np.shape(v))
st = ScalarTool(N, L)
vt = VectorTool(N, L)
v = vt.div_free_proj(v)
v = vt.dealias(v)
c = st.grad(v[1])[0] - st.grad(v[0])[1]
assert np.allclose(c, vt.curl(v))
def test_l2norm_squared_of_curl_of_vector_is_spatial_integral_of_neg_vector_times_lap_vector(
):
N = 128
L = 2.0
kappa = 0.0
gamma = 1.0
v = np.random.random((2, N, N))
# print(np.shape(v))
st = ScalarTool(N, L)
vt = VectorTool(N, L)
v = vt.div_free_proj(v)
v = vt.dealias(v)
curl = vt.curl(v)
a = st.l2norm(curl)**2.
b = st.sint(np.sum(-vt.lap(v) * v, 0))
assert np.allclose(a, b)