Newport Back Bay Fluid Flow Natalie Albor Alexander Holtz Alan Nguyen August 17, 2012 Abstract Water qualities including oxygen, salinity, temperature, and pH are all important qualities of estuaries and coastal systems. They are important to the many animals and aquatic species that can be found there. At the Newport Back Bay, an estuary in Southern California, the mixture of freshwater and saltwater is a delicate environment that many animals have adapted to. We monitored the fluctuations in these qualities throughout the bay using a refractometer on water samples, and also a multi-probe to collect data in the bay over several weeks. We analyzed the effect of fluid flow in the bay and how it disperses these qualities to be able to predict what effects would be seen if there were to be a change in the inflow from either the San Diego Creek (SDC) at the northern end of the estuary, or the Pacific Ocean at the southern end. Fluid flow determines the spread of freshwater and saltwater in the bay, and thus the unique estuarial results caused by this interaction. 1 Introduction the harbor. The water flow then dis- perses and spreads the uplifted sedi- In this study, we analyzed fluid flow of ment throughout the bay, disturbing Upper Newport Bay (UNB) and Lower the settled shellfish, plants, and fish. Newport Bay (LNB) to predict water flow patterns and dispersion of various Within the next decade, the Irvine nutrients such as salinity, pH, temper- Water Company plans on increasing ature, and dissolved oxygen. Being an the San Diego Creek (SDC) water flow estuary, UNB is a mixture of freshwa- into the UNB by ten-fold, dramatically ter and saltwater, making the fluid flow increasing the flow of freshwater into within the bay to be very important to the bay [11]. This new change of wa- the ecosystem. The salt and oxygen ter flow can affect the sensitive bivalves levels are critical to the development and other animals in their relation- and health of the aquatic animals. In ship to the habitat. There have been addition to the many fish and plants many extensive studies into the affects that prosper in the bay, there are also of decreasing the amount of freshwa- many species of bivalves that thrive in ter flow into an estuary, such as in San varying conditions of fresh and salt wa- Francisco, which clearly depicts a neg- ter. In the LNB, dredging is taking ative outcome [1]. Such results include place to allow the passage of ships to a reduction in natural nutrients and 1 shellfish populations with the intro- ability to thrive. ductory of predatory marine animals. In particular, the many species of Although there are not many studies bivalves that reside in UNB and LNB showing the effects of increasing the are essential to the health of the har- freshwater flow, it is predictable that bor. The bivalves, which include vari- there will be a negative outcome. The ous clams and oysters, mainly prey on results could include reduced salinity the millions of phytoplankton that live and die-offs of salinity sensitive plants, in the water, which controls their num- fish, and shellfish. Many of the species bers to a reasonable amount. If the bi- that reside in UNB are endangered in- valves were removed from the harbor cluding the light-footed clapper rail. due to inhabitable water conditions, With the possible change in food sup- the phytoplankton population would ply and nutrients available due to the increase beyond control, thus causing change in freshwater flow, these species eutrophication in the water [10]. This may lose their homes and become ex- will eventually lead to hypoxic condi- tinct. tions, meaning a depletion of oxygen The dredging of LNB is viewed as a in the water, which would cause the necessary action needed to allow move- other aquatic animals to lower in num- ments of ships in the bay, and it is ber. Thus, it is important to ensure believed that any negative effects it that the water in the UNB and LNB is has on the surrounding environment favorable for the bivalves. are negligible. Changes to water qual- Bivalves and other aquatic animals ity due to pollutants mixing with sedi- depend upon favorable water quality ments, and changes in sediment trans- levels of oxygen, pH, salinity, and tem- port are a couple effects known to be perature. Modeling the variations of caused by dredging [6]. The water flow these nutrients is also beneficiary to see carries and disperses the uplifted pol- any fluctuations of the nutrients based lutants and can be transferred to ar- on time, space, and fluid flow. It will eas that were previously healthy. Al- enable us to have a better understand- though LNB is not the location for ing of the environment in general, and most of the endangered species living make predictions of change in water in the bay, it is still a location for quality based on a change of saltwa- fishing and for people to take part in ter/freshwater fluid flow. water activities. The water flow dis- persement of sediments and pollutants spreads throughout the bay, hurting 2 Methods the aquatic animals and the well being of people. 2.1 The Site Modeling the bathymetry and fluid flow throughout UNB and LNB is es- The Newport Bay is located in South- sential in understanding the disperse- ern California between San Diego and ment of freshwater from the SDC and Los Angeles, and is broken up into the pollutants from dredging. This knowl- Upper Newport Bay and Lower New- edge will help predict the impact on port Bay. The UNB is classified as an the estuary and the many species that estuary because it has the freshwater of live there, ensuring their survival and the San Diego Creek flowing into it and 2 the saltwater from the Pacific Ocean (through the LNB). It is about 5.5km in length and spreads about 1000 acres of total protected habitat. Since estu- aries are unique combinations of fresh water and salt water, the UNB is home to many endangered species placing it in the protection of California Bays and Estuaries Policy [7]. Lower Newport Bay [2] 2.2 Modeling Equations A basic understanding of fluid flow was first needed to approach our problem. The St. Venant equations (SVE), or also known as the shallow water equa- tions, provides a more theoretical ap- proach to fluid flow. The SVE are a set of hyperbolic partial differential equa- tions that describe the flow below a pressure surface in a fluid. The SVE is a combination of the continuity equa- tion @A @V @h V + A + b = 0 @t @x @t and the dynamic, or momentum equa- tion @h @V @V g + V + = g(i − j) @x @x @t Upper Newport Bay [4] where A is the cross-sectional area, h is the depth of flow, V is the mean ve- The LNB is the connecting harbor locity, b is the width of the top of the to UNB and the Pacific Ocean. It is a section, x is the position of the section semi-artificial harbor formed by dredg- measured from the upstream end, t is ing during the 1900s. Most of the area time, g is gravity, and ρ is the mass is covered with private homes, docks, density of the fluid. and businesses, including the two main In this form the equations cannot islands Lido Island and Balboa Island. be solved explicitly, having us use the The 39.8 square miles of LNB is con- more convenient characteristic form of stantly in need of dredging for the up- the SVE which is keep of the harbor and the 9000 boats d(v ± 2c) dx that reside there. = g(i−j) for = (v±c); dt dt 3 where c is the celerity, or speed of the a linear, first order, partial differential wave. With this method, numerical so- equation with constant coefficients. It lutions can be found. takes a function and moves it along an axis over time keeping the function in its same form. Note that the equation simply shifts the graph This equation is relevant to our even- tual fluid flow model of the Newport In the figure above, the graph repre- Back Bay because it mimics the tran- sents a flood wave at the upstream end sitional nature of moving water. Much of a channel. The zone of quiet repre- like how the transport equation rep- sents the part of the stream waiting for resents a certain function moving in a disturbance, or effect from a flowing the positive direction of the x-axis (dis- wave. For any point numbered on the tance), so does the Newport Back Bay graph, the velocity and celerity can be water current. We were able to solve determine numerically by the two pre- this derivation using Mathematica and vious points having direct connection created a three-dimensional Model of to it. For instance, the solutions for the transport equation. point 6 can be found using the veloc- ity and celerity from points 3 and 5. The SVE provides a conceptual under- standing for the basic introduction of fluid flow [9]. It allows us to solve nu- merically for specific points, but is dif- ficult to apply for a grander scale. In order to model the fluid flow within the Newport Bay, two partial differential equations were combined. These equations were the transport equation and the diffusion equation (based on Ficks Law of Diffusion). The transport equation Transport Model @u @u Unfortunately, the transport equa- = −k @t @x tion does not account for the spontane- ity of hydrogen molecules in water.