Houston: Houston has imposed an overnight curfew beginning on Tuesday night for an indefinite period amid incidents of looting, armed robberies and people impersonating police officers, city officials said.

The curfew will run from 10pm until 5pm, Mayor Sylvester Turner told a news conference on Tuesday evening. The city is also bringing additional police from other regions.

"You cannot drive, nor be in any public place. We have had problems with armed robberies, with people with guns and firearms," said Houston Police Chief Art Acevedo.

The city is opening several additional emergency shelters to alleviate crowding at the convention centre, which has 10,000 people. Some of those will be moved to a nearby concert hall and basketball arena.

It is also opening a shelter on the west side, near where more than 3,000 homes have been flooded. Another center in Humble, Texas, will house people from the city's northern suburbs, Mayor Turner said.

The remnants of deadly Hurricane Harvey menaced Texas and Louisiana alike, while a reservoir west of downtown Houston spilled over for the first time in its history due to record-shattering rainfall.

President Trump arrived in Texas on Tuesday to survey the ongoing devastation, while storm clouds continued a drenching onslaught that has already dropped more than a metre of rain in some areas. Trump's visit, following his pledge of swift action by the federal government to provide relief to states affected by Harvey, comes on the 12th anniversary of Hurricane Katrina making landfall in Louisiana.

Trump came to a state still struggling to determine the extent of its tragedy. The death toll in Texas had reached at least 15 people by Tuesday afternoon, officials said, but they warned it could rise as authorities pursue reports of people apparently lost in the torrential downpours unleashed by Harvey since Friday.

Mayor Turner earlier said on Tuesday that a city police officer died in floodwaters over the weekend while driving to work.

"While I've encouraged other people to stay at home, our first responders they have been working 24 hours, 24-7, on behalf of the people of the city of Houston," the mayor told reporters. "At the same time, they have been putting themselves in harm's way."

"Today, I'm sad and deeply saddened to announce the death of Sergeant Steve Perez," he said, adding the 60-year-old officer died Sunday. 

Separately, Houston Police Chief Art Acevedo said on Tuesday that officers in the city have rescued more than 3500 people so far amid Harvey's flooding. But the storm's impact remained unclear, as the Houston mayor said officials are "still trying to assess" how many people are missing.

Lashing rain continued to pound Houston on Tuesday, falling on people who desperately sought groceries or trudged through water in search of shelter. The streets in the city's centre were littered with abandoned cars, and almost no stores appeared to be open, though people said they needed food and supplies.

Outside a Kroger grocery store in southwest Houston, dozens of people had lined up hours before the store opened. Another crowd had lined up outside Fiesta, a nearby grocery store, where the line grew so long that store officials were limiting how many people they let inside.

"Meat," said Morgan Lewis, 23, who was first in line at Kroger at 7.30am. "I need some meat. I'm tired of eating sandwiches."

The National Weather Service reported that more than 100 cm of rain has already fallen in Houston due to Harvey.

Some parts of Louisiana have also seen more than 30 cm of rain, and flash flood warnings and watches were in effect for much of the Lake Charles region as the rain is expected to continue. New Orleans was under a tornado and flash flood watch until Thursday.

In Texas, one of the two massive stormwater reservoirs to the west of downtown Houston began spilling over on Tuesday - US Army Corps of Engineers efforts Monday to release water as water levels in the reservoirs swelled to record levels.

The Army Corps of Engineers said that water was spilling out from around the dam gates of the Addicks Reservoir, and officials also said they expect the Barker Reservoir — to the south of Addicks — to also begin overflowing some time on Wednesday. Near the Barker dam, helicopters were attempting to rescue families, while some people spent their morning hopping onto jet skis and into boats to help as well.

"We never flood," said a dismayed Gloria Strayhorn, a retired interior designer who was out for a walk with her husband Bill. They were in raincoats and shook their heads at a nearby man-made lake that was overflowing, saying these were only adding to the problem when the dam releases: "They were just refurbished this spring and they spent so much money setting up benches and now look."

Officials in Brazoria County, south of Houston, also warned that a levee there had breached.

Harvey continued grinding toward the northeast, with its centre expected to be just off the upper Texas coast through Tuesday night, the National Hurricane Centre said. After that, the storm is forecast to move inland on the northwestern Gulf Coast on Wednesday.

Forecasters say more than 30 cm of additional rain is still expected to fall through Friday over parts of the Texas coast and Louisiana, and the National Weather Service warned Tuesday of potential flooding in southern Mississippi as well as southeastern Louisiana.

Trump arrived in Corpus Christi, Texas, on Tuesday morning, and intends to visit Austin, the capital, later in the day. His spokeswoman told reporters on Air Force Once that Trump will visit "a different part of the state" on Saturday, while he has also discussed visiting Louisiana the same day.

During a news briefing in Corpus Christi, Trump praised the response from local officials in Texas as well as federal authorities who were grappling with the devastating storm. He also spoke to a group that had gathered to see him.

"This is historic, it's epic what happened, but you know what, it happened in Texas and Texas can handle anything," he told the crowd, which applauded his remarks and cheered more loudly when he waved the Texas state flag.

When Trump arrived, about 50 apparent supporters had gathered near the runway to wave signs bearing his name and welcome him. Suzanne Guggenheim, wearing a red hat bearing Trump's "Make America Great Again" slogan, said she felt he had handled the disaster well.

A small group of young Democrats protested Trump's arrival. Marco Garcia, chairman of the Texas Young Democrats Latinx Caucus, called Trump's visit is disrespectful of the region and of the nation's Latino community.

"Trump should be focusing on getting help to the people who need it, not taking resources by tying up the roads and creating chaos in this region that needs so much help," said Garcia, a 24-year-old business management major at Texas A&M University-Kingsville, who said he has been helping evacuees from Rockport who have no shoes or food.

The Department of Labor on Tuesday announced that it had approved an initial $US10 million grant to help with cleanup efforts in Texas. Trump on Monday declared "emergency conditions" in Louisiana, and not long before that, federal authorities had warned Harvey could force more than 30,000 people from their homes by the time skies are expected to clear later this week.

Life across Texas has abruptly shifted as floodwater turned streets into rivers. Hundreds of schools shut down in the state. Thousands of people have already piled into shelters in Houston and beyond, seeking safety from the storm without a clear idea of when, or if, they could return home.

The George R. Brown Convention Centre in downtown Houston had taken in 9000 people as of Tuesday morning, said Charles Maltbie, a regional disaster officer for the Red Cross who is at the convention. That number is nearly double the centre's anticipated capacity of 5000.

The convention centre is the evacuation site for all air evacuations, Maltbie said, and bus evacuations are being diverted to other shelters around the city. When asked what the centre's top capacity is, Maltbie said: "We will meet the need."

Washington Post, Reuters