diff --git a/xarray/backends/api.py b/xarray/backends/api.py
index 3cd62e8264a..5f88783bb2e 100644
--- a/xarray/backends/api.py
+++ b/xarray/backends/api.py
@@ -10,7 +10,8 @@
 
 from .. import Dataset, backends, conventions
 from ..core import indexing
-from ..core.combine import _auto_combine, _infer_concat_order_from_positions
+from ..core.combine import (
+    _CONCAT_DIM_DEFAULT, _auto_combine, _infer_concat_order_from_positions)
 from ..core.pycompat import basestring, path_type
 from ..core.utils import close_on_error, is_grib_path, is_remote_uri
 from .common import ArrayWriter
@@ -483,9 +484,6 @@ def close(self):
             f.close()
 
 
-_CONCAT_DIM_DEFAULT = '__infer_concat_dim__'
-
-
 def open_mfdataset(paths, chunks=None, concat_dim=_CONCAT_DIM_DEFAULT,
                    compat='no_conflicts', preprocess=None, engine=None,
                    lock=None, data_vars='all', coords='different',
@@ -606,7 +604,7 @@ def open_mfdataset(paths, chunks=None, concat_dim=_CONCAT_DIM_DEFAULT,
     # Coerce 1D input into ND to maintain backwards-compatible API until API
     # for N-D combine decided
     # (see https://github.com/pydata/xarray/pull/2553/#issuecomment-445892746)
-    if concat_dim is None or concat_dim == _CONCAT_DIM_DEFAULT:
+    if concat_dim is None or concat_dim is _CONCAT_DIM_DEFAULT:
         concat_dims = concat_dim
     elif not isinstance(concat_dim, list):
         concat_dims = [concat_dim]
diff --git a/xarray/core/combine.py b/xarray/core/combine.py
index abb2e2c1306..e552d8d900c 100644
--- a/xarray/core/combine.py
+++ b/xarray/core/combine.py
@@ -368,7 +368,7 @@ def _auto_concat(datasets, dim=None, data_vars='all', coords='different'):
         return concat(datasets, dim=dim, data_vars=data_vars, coords=coords)
 
 
-_CONCAT_DIM_DEFAULT = '__infer_concat_dim__'
+_CONCAT_DIM_DEFAULT = utils.ReprObject('<inferred>')
 
 
 def _infer_concat_order_from_positions(datasets, concat_dims):
diff --git a/xarray/tests/test_backends.py b/xarray/tests/test_backends.py
index 02ac06903c9..57e875bb563 100644
--- a/xarray/tests/test_backends.py
+++ b/xarray/tests/test_backends.py
@@ -2367,6 +2367,29 @@ def test_open_single_dataset(self):
             with open_mfdataset([tmp], concat_dim=dim) as actual:
                 assert_identical(expected, actual)
 
+    def test_open_multi_dataset(self):
+        # Test for issue GH #1988 and #2647. This makes sure that the
+        # concat_dim is utilized when specified in open_mfdataset().
+        # The additional wrinkle is to ensure that a length greater
+        # than one is tested as well due to numpy's implicit casting
+        # of 1-length arrays to booleans in tests, which allowed
+        # #2647 to still pass the test_open_single_dataset(),
+        # which is itself still needed as-is because the original
+        # bug caused one-length arrays to not be used correctly
+        # in concatenation.
+        rnddata = np.random.randn(10)
+        original = Dataset({'foo': ('x', rnddata)})
+        dim = DataArray([100, 150], name='baz', dims='baz')
+        expected = Dataset({'foo': (('baz', 'x'),
+                                    np.tile(rnddata[np.newaxis, :], (2, 1)))},
+                           {'baz': [100, 150]})
+        with create_tmp_file() as tmp1, \
+                create_tmp_file() as tmp2:
+            original.to_netcdf(tmp1)
+            original.to_netcdf(tmp2)
+            with open_mfdataset([tmp1, tmp2], concat_dim=dim) as actual:
+                assert_identical(expected, actual)
+
     def test_dask_roundtrip(self):
         with create_tmp_file() as tmp:
             data = create_test_data()